Essays on the Use of PLS Estimation:

Transcription

1 Essays on the Use of PLS Estimation: For Improvement of Non-Financial Performance Indicators Mari Källström Doctoral Dissertation Department of Business Administration Aarhus University

2 To my family - 2 -

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4 Contents Preface Introduction CHAPTER 1: SEM-based customer satisfaction measurement; On multicollinearity and robust PLS estimation Introduction Partial Least Squares Study Design Results Conclusions Appendix A1.1: Simulation results for Model I References CHAPTER 2: Robustness in PLS estimation: Analysing the effects of introducing Non-normality and Multicollinearity in Customer Satisfaction Measurement Data Introduction Estimation Procedure Study Design Results Conclusions References CHAPTER 3: Enhancement of Leadership in Employee Engagement Modelling Introduction European Employee Index Empirical Study Design Results Conclusion and Discussion References Appendix A3.1: Results on Relative effects and Relative importance for specified analysis set-up in A) and B) Appendix A3.2: Results on Profile analysis - Nordic countries CHAPTER 4: Psychological profiling in Employee Engagement Surveys Introduction

5 4.2 Myer Briggs Type Indicator Data Analysis Results Discussion & Conclusion References Appendix 4.1: Prevalence and impact structure following MBTI definition in the Nordic countries Concluding remarks

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7 Preface The journey of this thesis began already with me telling my parents in 3rd grade that; I am going to pursue research after completion of my university studies. Without much knowledge of which area to work in or a complete image of what research is all about at such young age, of course, the travel began to reach this pre-set vision of mine. As the years of education went by, the area of statistics came to my attention. After my master degree I got the opportunity to start a doctoral program at Stockholm School of Economics at the department of Economic Statistics. There I had the privilege of having a great professor, Anders Westlund, teaching me the path of research. The last year of a doctoral program has been spent at Aarhus University, School of Business under the lead of yet another great professor, Kai Kristensen. There are a lot of people to whom I am very grateful and owe so much gratitude towards. First of all I would like to mention my husband for being my solid rock and enabling me time and support at every step of the way together with my three children that has been, and continues to be, an inspiration to me. I would also like to thank my parents for never losing faith in me and for always offering a shoulder to lean on. To my friends and co-workers for showing interest and for all your encouragement and support, I will be forever grateful. The analytical part would not have been a success without the hands of especially Dr Johan Parmler and Bettina Damm. My deepest and warmest thanks for all your time spent on this project, your counsel, and sharp minds. I am forever grateful for your involvement. My utmost professional gratitude is directed to the two professors I have had the honor to get to know and the privilege of having as tutors; Kai Kristensen and Anders Westlund I will always be grateful for all your support, wisdom, guidance and so much more that no words could ever describe. Thank you for showing and guiding me down a path I will never stop walking! - 7 -

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9 Introduction A company s performance has traditionally been rated from a financial perspective using measures such as; EBITDA, EBIT, ROCE, cash flow, etc. However, there has been an increase of supplementing the financial information with performance criteria s from an intangible perspective over the last decades (Ittner & Larcker, 1998a; Ittner & Larcker1998b). The intangible information used for valuation tools are highly focused on; human capital, brand equity and customer asset. In this thesis, the focus is placed on the human capital and customer asset,. One way of rating and assessing the customer asset and human capital is through satisfaction measurements where data is collected through surveys. Two frameworks for this procedure is used here; European Performance Satisfaction Index (EPSI), surveying the customer asset and European Employee Index (EEI), surveying the human capital (ECSI, 1998; Eskildsen et al., 2004). Both of these frameworks pursue both national and international customer and employee satisfaction surveys, respectively, on an annual basis. The methodology within these frameworks relies on Structural Equation Models (SEM). Partial Least Squares (PLS) is applied as the common statistical method (Lohmöller, 1989; Wold, 1985; Fornell & Cha, 1994; Tenenhaus, et al., 2005; Vilares, et al., 2005). SEM together with PLS in satisfaction measurements, as within EPSI and EEI, is based on several authors arguments on PLS showing several advantages in comparison to the covariance based methods (Chin, 1998; Fornell & Bookstein, 1982). Two argued advantages are that PLS is robust against multicollinearity and nonnormality in data (Cassel, et al., 1999; 2000; and 2001). However, even though earlier research has implied PLS being robust, there are still angles to be further viewed within this area. One angle could be to study to a higher extent, the levels of multicollinearity being present in survey data. Yet another angle is the fact that most rarely multicollinearity stands alone as an implication in analysis such as in a context being described here. Non-normality is very much - 9 -

10 (highly) present in data as well. These occurrences of matters in empirical applications are quite common among other things. Therefore there are still gaps in exploring these empirically seen implications. This is why chapter 1 and 2 has a theoretical focus placed on i) multicollinearity and ii) non-normality, in a simplified context of customer satisfaction measurements aligned with the EPSI model. In chapter 1, the area of interest is multicollinearity. The study will introduce multicollinearity in two ways, i) within, i.e. introducing correlations between indicators, also called manifests, on chosen levels and ii) between, i.e. specifying pre-determined levels of correlations between exogenous latent variables being present in the model. Moving into chapter 2, the focus is firstly on introducing non-normality on different levels both in the manifests as well as within the structural residuals. Secondly a study will be conveyed by introducing a combination of non-normality together with multicollinearity in the analytical set-up. By analysing a combination of empirically, common statistical implication should give even more insight as too how robust PLS is. The first two chapter s analytical set-up will be undertaken by the use of Monte-Carlo simulations and the attention will be placed on the structural parameters in evaluating robustness of PLS in the estimation process. Continuing into chapter 3, this part evaluates a further enhancement of leadership in an Employee Engagement context, based on the well-known EEI model. In the EEI model there are seven established drivers for employee satisfaction, where Senior Management (SM) and Immediate Manager (IM) are two factors being specified as exogenous latent variables, i.e. drivers of employee satisfaction. Earlier empirical findings have shown that the leadership dimensions do not seem to have an extended, direct, effect on employee satisfaction. However, since many theories within the area of business excellence has a focus on leadership as drivers it seems rather straight forward to explore this more empirically in a context of employee satisfaction (EFQM, 2011; Shingo Prize, 2011; Baldridge, ). The empirical data being analysed in this study originates from the annual European Employee Index survey, more specifically data collected in 22 countries globally within the years of The main area of interest is the structural parameters between the two leadership dimension and the five defined drivers of employee satisfaction in the EEI model. This will be

11 evaluated following a PLS estimation in a re-arranged EEI model (described under chapter 3). More specifically the effects will be further evaluated by studying the relative effect in between the two leadership dimensions on the five remaining drivers of employee satisfaction within the framework of EEI. Defining structures of data is a common interest in many sciences and within the area of employee satisfaction measurements it is highly interesting to be able to segregate between the employees in the estimation process in order to secure an even better platform for improvement work in every part of the organisation, which is one of the most important step for any organisation conducting an employee survey, i.e. to find concrete and actionable improvement areas to work with in a follow-up process. There are methods from the family of multivariate techniques, with the aim of grouping data, what could be related to the term clustering, within specified data sets; FIMIX-PLS, REBUS-PLS, factor analysis and PLS to mention some. Deeper understanding to these methods could be found in, for instance, Bollen (1989), Jöreskog (1979a), Jöreskog (1970), Hair et al., (1998) Trinchera (2007); Vinzi et al., (2008), Ringle et al. (2007), Tenenhaus, et al. (2005) and Vilares, et al. (2005). Being able to classify employees has a positive effect seen from the perspective of employee satisfaction measurements, meaning we increase an understanding of their differences as well as their similarities. This could be done, for instance by adding in knowledge from demographical or organisational settings in the estimation process in a context being described under chapter 3, i.e. a context of employee engagement by use of PLS in estimating a framework such as EEI. When adding in knowledge from sources, not directly evident in data used for estimation, in such a context would give further added value in understanding the behaviour and preferences among the employees in the analytical results received in a set-up being presented in this dissertation. Earlier research has shown especially demographical differences, which gives some evidence as to why it could be appropriate to discuss results in a context as the one described here (Deaux & Major, 1987; Clark et al., 1996; Eskildsen, et al., 2003). However, the question is if it could be possible to go even deeper in the quest of increasing knowledge regarding behaviour and preferences in an employee engagement context?

12 Myer Briggs Type Indicator (MBTI) is a method supposed to categorize people into different types and profiles depending on people s preferences from a psychological perspective and also how people perceive the world and make their decisions (Carr et al., 2011; Hirsh & Kummerow, 1989). There are other forms for type classification such as JTI and CPI for instance (Budd, 1993; Gough & Bradley, 1996). MBTI relies on typological theory of Jung (Jung, 1923). Chapter 4 will analyse data from 2011 years European Employee Index survey. The ordinary question scheme in the EEI survey was supplemented with four questions, assumed to follow the MBTI approach. The aim of this study is to analyse the possibility of finding any differences in impact structure, i.e. structural parameters, depending on type or profile according to the MBTI, when conducting a PLS analysis in an employee engagement context by applying the EEI framework. This will be evaluated by dividing the survey data according to pre-defined answering scheme of the four specific questions assumed to be related to the MBTI. If possible to combine knowledge from, for instance MBTI, in evaluating analytical results from an Employee Engagement survey, could enhance both the understanding of groups of employees, challenges in different parts of an organisation together with an even more enhanced opportunity for the further improvement work inside an organisation

13 CHAPTER 1: SEM-based customer satisfaction measurement; On multicollinearity and robust PLS estimation Westlund, A.H., Källström, M. & Parmler, J. (2008) SEM Based Customer Satisfaction Measurement; On Multicollinearity and Robust PLS Estimation. Total Quality Management and Business Excellence, 19(7-8),

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15 1.1 Introduction Systems for performance measurement often play a key role for companies when developing strategic plans, and when evaluating the achievement of organisational objectives. Traditionally, the companies have almost exclusively relied on financial performance measures, such as EBIT, EBITDA, ROCE, cash flow, etc. However, the understanding of the significance of non-financial information, as well as the use of non-financial performance measurements, such as human capital, brand equity, the customer asset, and environmental performance, as additional valuation tools to the financial performance measurements, has increased over the recent years (Ittner & Larcker, 1998a, 1998b). Organisations have also seen the value of supplementing the financial measures with frameworks with which they are able to study several nonfinancial performance measures simultaneously. An example of this is the well-known Balanced Scorecard (Kaplan & Norton, 1996; Banker, et al., 2004). A possible way of assessing the value of the customer asset is through customer satisfaction measurements. This is true, in particular, if customer satisfaction measurements are implemented with structural models, where consequences from changes in customer satisfaction are rated. In order to secure comparability and consistency between organisations, national (or even international) measurement standards are needed. So called national customer satisfaction indices here play an important role. The scope of conducting national customer satisfaction surveys has widened, and since the beginning of the 1990 s several countries have developed national indicators measuring customer satisfaction across a wide range of industries, companies and organisations. For example, Sweden was the first nation to establish a national index of customer satisfaction in 1989 (Fornell, 1992); other nations that have developed national indices are, for example, Norway, (Andreassen & Lindestad, 1998), Denmark, (Martensen, et al., 2000), and the US with the American Customer Satisfaction Index (ACSI) (Fornell, et al., 1996). The European Performance Satisfaction Index (EPSI Rating), (ECSI, 1998), conducts annually harmonised customer satisfaction surveys for several industries and in an increasing number of European countries. The EPSI Rating was first initialized by the EC (European

16 Commission) and the Pan-European quality organisations EFQM (European Foundation for Quality Management) and EOQ (European Organisation for Quality) in The main parts, or the core of the national customer satisfaction models, are in most ways standardised. However, some differences in the modelling can be seen (Johnson et al., 2001). Part of the standard is the basic structure which is based on research in areas of consumer behaviour, customer satisfaction and quality aspects (both product and service quality), and theories that are well established (Fornell, 1992, 2007; Fornell et al., 1996). The methodology often relies on a Structural Equation Model (SEM). For example, a structural model is used within the EPSI Rating to measure and evaluate customer satisfaction. Within the framework of EPSI Rating, Partial Least Squares (PLS) is applied as the common statistical method. Alternatives to PLS are covariance-based methods such as LISREL and Neural Network (Hackl & Westlund, 2000). The use of PLS in customer satisfaction measurement has grown over recent years, and many authors argue that PLS shows several advantages in comparison to the covariance-based methods (Chin, 1998; Fornell & Bookstein, 1982). The hypothesis of PLS being robust against statistical quality problems such as data skewness, antecedent multicollinearity and mis-specified structural models, are strong reasons for applying PLS in customer surveys, since the occurrence of such problems in empirical applications is quite common (Cassel et al, 1999, 2000, 2001). Some authors also argue that the multicollinearity problem might not be a big obstacle in SEM estimation, with the estimation being robust against multicollinearity (Malhotra et al., 1999). The purpose of this paper is to analyse to what extent there will be effects on the structural parameter estimates from multicollinearity, when applying a PLS approach for models similar to those used within the EPSI Rating

17 1.2 Partial Least Squares Herman Wold was the first to formalise the main ideas of Partial Least Squares (PLS) in a paper discussing principal component analysis (Wold, 1966). Other references on the PLS algorithm are, for example, Wold (1975, 1982, 1985). PLS is sometimes seen as a soft modeling technique, mainly because the alternative SEM-ML (Jöreskog, 1970), or covariance-based SEM, requires heavier distributional assumptions. The estimates from using a covariance-based method are consistent, but when the assumptions of multivariate normal distribution, large sample size and independence of observations are violated (Bollen, 1989), the covariance-based methods may produce improper solutions, for example, negative variance (Fornell & Bookstein, 1982; Chin, 1998). However, PLS estimates are only consistent at large which means that the bias of estimates from a PLS procedure will tend to zero, only as the number of indicators (per block) and sample size increase simultaneously. To pursue PLS estimation one needs (i) the measurement model, (ii) the structural model, and (iii) the weight relations. The measurement models relate the observable manifest variables, or indicators, to directly unobservable latent variables (unobservable constructs, or factors). The latent variables are denoted ξ (exogenous) and η (endogenous). The structural model describes the relations between a vector of endogenous latent variables and a vector of exogenous latent variables (1.1): η Βη Γξ ζ (1.1) where Β and Γ are impact parameter matrices, and ζ is a vector of error terms, where E { ζ ξ} 0. (1.2)

18 The unobservable latent variables are all described by blocks of observable variables x and y through measurement models. Those models are either reflective, formative or follow the MIMIC (multiple effect indicators for multiple causes) approach. The reflective measurement model is given by (1.3) and (1.4) (the manifest variables are reflections of the latent variables): x λ ξ (1.3) x ε x y λ y ε y (1.4) where E( ξ )= m, Var( ξ )=1 and E( η )= m,var( η )=1. Furthermore, Wold introduces ξ the so called predictor specification condition as in (1.5) and (1.6): E { xξ} λ ξ (1.5) x E { y η} λ η (1.6) y This implies that the residual terms ε x and ε y have a zero mean and are uncorrelated with their respective latent variable, i.e. Corr (,ξ) 0 and Corr (, η) 0 ε x ε y Formative measurement models are given by ξ π x (1.7) ξ δ ξ η π y (1.8) η δ η

19 where the latent variables ξ and η are linear functions of its manifest variables plus a residual term. The predictor specification condition also holds for the formative specification. The weight relations are used to estimate scores or case-values of the latent variables, as weighted averages of the manifest variables: ^ η w y (1.9) η ^ ξ w x (1.10) ξ The weights wξ and w η are estimated in different ways, depending on the type of measurement model used (for example, by Mode A or Mode B). For more details on the PLS algorithm, see, for example, Lohmöller (1989); Wold (1985); Fornell & Cha (1994); Tenenhaus et al. (2005); and Vilares et al. (2005). 1.3 Study Design The purpose of this study is to contribute to our knowledge on the small-sample distributions of the PLS estimator in particular when multicollinearity is present in the data. The most effective way to generate such knowledge is through Monte-Carlo simulations. A shortcoming with that approach is the difficulty to generalise conclusions beyond the study design chosen. Thus, a second purpose is to validate PLS for estimation, in particular, within the EPSI Rating framework, with a study design taking characteristics from EPSI Rating. As a consequence, the model set-up and the parameter specification in the simulation have been specified by examining real survey data from the EPSI Rating

20 The main focus is to study the effects on the PLS estimates of the structural parameters, when introducing multicollinearity in the data. The correlations are introduced in two ways: (i) between exogenous latent variables, and (ii) between indicators. The structural model used by the EPSI Rating for conducting customer satisfaction surveys is given in Figure 1.1. The model consists of seven latent variables. The five on the left Image, Expectation, Product Quality, Service Quality, and Value - are seen as the antecedents of variables on the right-hand side; customer satisfaction and loyalty, the last one being a consequence of customer satisfaction. Each latent variable is measured by multiple manifests. Image Expectation Value Customer Satisfaction Loyalty Perceived Product Quality Perceived Service Quality Figure 1.1. The EPSI Rating structural model The data used for the parameter set-up are taken from the Swedish part of the EPSI Rating, and more specifically from measurements on Retail Banking (B2C) within the 2006 survey. In Sweden, annual surveys are conducted in approximately industries in the Swedish market (in the private sector as well as the public sector). These surveys started in 1989 as the Swedish Customer Satisfaction Barometer and since 1997 are part of the EPSI Rating initiative

21 The structural models in the simulations are simplified versions of the EPSI Rating model (see Figures ). Model I consists of 4 latent variables; two exogenous variables and two endogenous variables with links from each exogenous variable to both of the endogenous variables. Model II has four exogenous variables and two endogenous with corresponding links from each of the exogenous variables. A link between the endogenous variables is also introduced in Model II. The correlations between the exogenous variables are represented by curved lines. Perceived Product Quality Value Perceived Service Quality Customer Satisfaction Figure 1.2. Simulation Model I A sample of approximately observations has randomly been chosen from the database of the 2006 survey for retail banking in order to set the structural parameters in the simulation models. Since the simulation models are simplified versions of the EPSI Rating model, only empirical data for part of the seven latent variables has been used. For Model I, Product Quality and Service Quality are exogenous variables, and corresponds to ξ1 and ξ 2, respectively. For Model II, Image and Expectations are used as exogenous variables ( ξ 3 and ξ 4 ). Value for Money and Customer Satisfaction correspond to the two endogenous variables of the simulation models ( 1 and 2, respectively)

22 Perceived Product Quality Perceived Service Quality Value Image Customer Satisfaction Expectation Figure 1.3. Simulation Model II The measurement models for i, i = 1, 2, 3, 4 follows the formative specification (1.7) where the error terms are uniformly distributed. The measurement model for 1 and 2 is reflective ( ) and, again, the error terms are uniformly distributed. The inner relations for Model I-II are given by (1.1), where: B I 0 Γ I B II Γ IΙ which are specified by using empirical data

23 The focus of the study, as mentioned earlier, aims at analysing the effects of introducing multicollinearity in the measurement process. To do this, first a baseline model is used (Case A), where the data is assumed to be perfect from a statistical point a view. It is specified without any multicollinearity, and the manifests for the exogenous latent variables are assumed to be Beta(6,6) distributed. There will be four manifests for each latent variable. They are all measured on a 1 to 10 scale, which is standard within the EPSI framework. The manifest variables for the exogenous latents i (i=1,2,3,4) have all been generated with a Beta(6,6) distribution. The weights x i were all set to be 1/4. The ij were taken from the empirical data and were, in Model I, set to be 0.7, 0.5, 0.5 and 0.3 for i = 1,2 and j = 1,2. In Model II, the corresponding ij are specified as 0.5, 0.1, 0.3, 0.3, 0.25, 0.5, 0.1 and 0.1, for i=1,2; j=1,2,3,4 and 21 =0.5. The y are always set to be 0.75 for i = 1,2, i 8. All error variances are set such that the degrees of explanation ( approximately 0.65, for sample size n = R ) are The sample size is varied on four levels (n= 100, 250, 500 and 1000). The case of n= 250 is most consistent with the situation within the EPSI Rating (approximately 250 observations per company are measured). The other sample sizes are arbitrarily on lower and higher levels. The number of replications in the simulations is set to be Multicollinearity is introduced in two ways. In Case B we will analyse the effects of introducing multicollinearity between blocks, i.e. when pre-setting collinearity between the exogenous factors. The levels of correlation (Corr) will be set on four levels for both Model I and Model II (0.5, 0.7, 0.9, 0.95). In that sense this is an extension of the study by Cassel et al. (1999), where the levels of correlation between the exogenous factors were either 0 or 0.7. The correlations are here introduced by a Cholesky transformation and a correlation matrix R, specified below. The correlation matrix has been specified as follows

24 1 R where is a parameter between 0 and 1. This specification has the effect that the correlation between two neighbouring variables within the same block is. When correlation between the exogenous latents is introduced, the same principle has been used, i.e. the correlation between two neighbouring -variables is. In Case C, collinearity within an exogenous block is introduced (i.e. between the manifests of an exogenous variable). We restricted ourselves to collinearity between the manifests of the first exogenous variable. The different levels of correlations are taken from real-life data. The degree of correlation is calculated by a variance inflation factor, VIF. In both models (Model I and II) VIF=4, 10, 20, 30 and 50. VIF VIF = VIF = VIF = VIF = VIF =

25 The correlations matrices are of size M x M, i.e. quadratic matrices, and then the VIF can be calculated as in (1.11) VIF ( M ( M 2 ) )( 1) M (1.11) The simulations are evaluated by examining the RMSE, bias, and variance of all estimators (over the 1000 replicates). 1.4 Results Tables show the simulation results for the estimation of the inner relation parameters for Model II, and for Cases A (base case), B and C. The tables show the estimated parameters, the estimated RMSE, and the proportion of RMSE originating from the variance of the estimator. The results are given for the smallest (n=100) and largest (n=1000) sample sizes used in the simulation process. Our presentation focuses first on Case A. Table 1 shows that PLS provides very good estimation of the inner structural parameters Β and Γ. The estimated differences between the true and estimated parameter values are, in most cases, very small. This overall picture holds for the smaller sample size n=100, and just minor improvements are observed with increasing sample size. Results for n=250 and n=500 are available from the authors on request

26 Parameter True parameter Case A (n=100/n=1000) VIF 0/Corr / / / / / / / / / / / / / / / / / / / / / / / / / / / 0.67 Estimated parameter Case B (n=100/n=1000) Corr 0.63/ / / / / / / / / / / / / / / / / / / / / / / / / / / 0.55 Case C (n=100/n=1000) VIF 0.70/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / 0.59 Table 1.1: True and estimated parameters in Model II; for Case A, B, and C. The corresponding RMSEs are small (see Table 1.2). Further reduction in RMSE is noticed when the sample size increases. The RMSE component is, for most parameters, dominated by the variance component (see Table 1.3), although the relative variance contribution is reduced with larger sample sizes. That is expected, as PLS is not consistent, but just consistent at-large

27 Parameter Case A (n=100/n=1000) VIF 0/Corr / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / 0.22 RMSE Case B (n=100/n=1000) Corr 0.18/ / / / / / / / / / / / / / / / / / 0.06 Case C (n=100/n=1000) 0.21/ / / / / / / / / 0.07 VIF 0.23/ / / / / / / / / / / / / / / / / / / / / / / / / / / 0.09 Table 1.2: The estimated RMSE of PLS estimates in Model II; for Case A, B, and C

28 Percentage VAR Parameter Case A (n=100/n=1000) VIF 0/Corr / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / 2.7 Case B (n=100/n=1000) 57.8/ / / / / / / 1.2 Corr 25.0/ / / / / / / / / / / / / / / / / / / / / 23.0 Case C (n=100/n=1000) 36.5/ / / / / / / 18.0 VIF 31.6/ / / / / / / / / / / / / / / / / / / / / 11.0 Table 1.3: Percentage Variance in RMSE ( %Varianceγ ) MSE Var x100) in Model II; for Case A, B, and C. ij ( ij 1 ij ij In Case B, correlations between exogenous latents are introduced, the differences between the true and estimated parameters are affected (see Table 1.1), but although the cases of quite extreme multicollinearity are introduced, the effects are rather moderate. This overall picture is supported by the estimated RMSEs in Table 1.2. The bias part of RMSE is, for most cases here, substantially higher compared with Case A. When assuming correlations between manifests (Case C) for one of the exogenous variables ( ξ 1 ), the estimated parameters are, in most cases, almost un-affected (see Table 1.1). For just one structural parameter ( γ 11 ), the effects are more substantial. This picture holds for the smallest sample size used in the simulation study (n=100), and the

29 deviations between correct and estimated parameters are almost the same irrespective of sample size. As a consequence, the RMSEs are mostly rather small (see Table 1.2), with some reductions when increasing the sample size. The bias part of RMSE is, in some cases, higher than in Case A, but as for Case B the picture is rather mixed. The bias part, however, increases substantially when increasing n (although where relative changes have a small magnitude). Overall, the results for Model I appear to be similar to those in Model II (for the results, see Tables A1.1-A1.3 in the Appendix). 1.5 Conclusions The purpose of this study was to contribute to our knowledge on the small-sample distributions of the PLS estimator and evaluate the effects on inner relations of Structural Equation Models when introducing multicollinearity. This was done through Monte Carlo simulation. The multicollinearities introduced in our simulations are substantial, and normally of higher magnitude than is empirically observed in the EPSI Rating. In spite of that, PLS estimation shows a very good robustness, in particular with respect to variance effects. Some increased bias is noticed, but not even the most extreme cases of multicollinearity ( =0.95, and VIF=50) reduce the quality of estimates beyond what could be empirically accepted. As in all Monte-Carlo simulations, the result in this study is limited to the specific models used for data generation. Therefore, several extensions are recommended: (i) examine the effects of introducing multicollinearity between manifests for more than one exogenous latent; (ii) study multicollinearity effects in PLS when the manifests are skewed (which is empirically motivated); (iii) comparing PLS with covariance-based methods, for example LISREL, to evaluate the robustness in comparison with other multivariate methods

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31 Appendix A1: Simulation results for Model I Estimated parameter Parameter True parameter Case A (n=100/n=1000) VIF 0/Corr / / / / / / / / 0.19 Case B (n=100/n=1000) Corr 0.55/ / / / / / / / / / / / / / / / 0.22 Case C (n=100/n=1000) VIF 0.70/ / / / / / / / / / / / / / / / 0.20 Table A1.1: True and estimated parameters in Model I; for Case A, B, and C. RMSE Parameter Case A (n=100/n=1000) Corr VIF VIF 0/Corr / / / / / / / / 0.11 Case B (n=100/n=1000) 0.18/ / / / / / / / / / / / / / / / 0.08 Case C (n=100/n=1000) 0.05/ / / / / / / / / / / / / / / / 0.10 Table A1.2: The estimated RMSE of PLS estimates in Model I; for Case A, B, and C

32 Parameter Case A (n=100/n=1000) Corr VIF VIF 0/Corr / / / / / / / / 5.1 Case B (n=100/n=1000) 31.2/ / / / 3.3 Percentage VAR 41.2/ / / / / / / / / / / / 6.9 Case C (n=100/n=1000) 100.0/ / / / / / / / / / / / / / / / 6.2 Table A1.3: Percentage Variance in RMSE ( %Varianceγ ) MSE Var x100) in Model I; for Case A, B, and C. ij ( ij 1 ij ij

33 1.6 References Andreassen, T.W. & Lindestad, B. (1998) The effects of corporate image in the formation of customer loyalty. Journal of Service Marketing, 1(1), Banker, R. D., Chang, H. & Pizzini, M. J. (2004) The balanced scorecard: judgemental effects of performance measures linked to strategy. The Accounting Review, 79(1), Bollen, K. A. (1989) Structural Equations with Latent Variables, New York: Wiley. Cassel, C., Hackl, P., & Westlund, A.H. (1999) PLS for estimating latent variable quality structures: finite sample robustness properties, Journal of Applied Statistics, 26(4), Cassel, C., Hackl, P., & Westlund, A.H. (2000) On measurement of intangible assets: a study of robustness of partial least squares. Total Quality Management, 11(7), Cassel, C., Eklöf, J, Hackl, P. & Westlund, A.H. (2001) Structural analysis and measurement of customer perceptions, assuming measurement and specification errors. Total Quality Management, 12(7-8), Chin, W.W. (1998) Commentary: issues and opinion on structural equation modelling. MIS Quarterly, 22, pp. vii-xvi. ECSI (1998) European Customer Satisfaction Index Foundation and Structure for harmonized National Pilot Projects. Report prepared by ECSI Technical Committee. ECSI Document no. 005 ed. 1. Fornell, C. (1992) A national customer satisfaction barometer: the Swedish experience. Journal of Marketing, 56(1), Fornell, C. (2007) The Satisfied Customer. New York: Palgrave Macmillan

34 Fornell, C. & Bookstein, F.L. (1982) Two structural equation models: LISREL and PLS applied to consumer exit-voice theory. Journal of Marketing Research, 19(4), Fornell, C. & Cha, J. (1994) Partial least squares. In: R.P.Bagozzi (Ed.) Advanced Methods in Marketing Research (pp.52-78). Cambridge, MA: B. Blackwell. Fornell, C., Johnson, M. D., Anderson, E. W., Cha, J., & Everitt Bryant, B., (1996) The American customer satisfaction index. Nature, purpose, and findings. Journal of Marketing, 60(4), Hackl, P. & Westlund, A.H. (2000) On structural equation modeling for customer satisfaction measurement. Total Quality Management, 11(4-6), Ittner, C.D. & Larcker, D.F. (1998a) Innovations in performance measurements: Trends and research implications. Journal of Management Accounting Research, 10, Ittner, C.D. & Larcker, D.F. (1998b) Are nonfinancial measures leading indicators of financial performance? An analysis of customer satisfaction, Journal of Management Accounting Research, 36, Studies on Enhancing the Financial Reporting Model, Johnson, M. D., Gustafsson, A., Andreassen, T. W., Lervik, L.& Cha, J. (2001) The evolution and future of national customer satisfaction index models. Journal of Economic Psychology, 22(2), Jöreskog, K.G. (1970) A general method for analysis of covariance structures. Biometrika, 57(2), Kaplan, R. S. & Norton, D. (1996) The Balanced Scorecard. Boston: Harvard University Press. Lohmöller, J-B (1989) Latent Variable Path Modeling with Partial Least Squares. Heidelberg: Physica

35 Malhotra, N.K., Peterson, M. & Kleiser, S.B. (1999) Marketing research: a state-of-theart review and directions for the twenty-first century. Academy of Marketing Science, 27(2), Martensen, A., Gronholdt, L. & Kristensen, K. (2000) The drivers of customer satisfaction and loyalty: cross-industry findings from Denmark. Total Quality Mangement, 11(4-6), Tenenhaus, M., Vinzi, V. E., Chatelin, Y-M. & Lauro, C. (2005) PLS path modeling. Computational Statistics and Data Analysis, 48(1), Vilares, M.J., Almeida, M.H. & Coelho, P.S. (2005) Comparison of likelihood and PLS estimators for structural equation modelling. A simulation with customer satisfaction data. Technical Report. New University of Lisbon. Wold, H. (1966) Estimation of principal components and related models by iterative least squares. In: P.R. Krishnaiah (Ed.), Multivariate Analysis (pp ). New York: Academic Press. Wold, H. (1975) Soft modeling by latent variables: the non-linear iterative partial least squares approach, in J. Gani (Ed.) Perspectives in Probability and Statistics, Papers in Honour of M. S. Bartlett. London: Academic Press. Wold, H. (1982) Soft modeling: The basic design and some extensions. In K.G Jöreskog & H. Wold (Eds.), Systems under indirect observation: Causality, structure, prediction (Vol. 2, pp. 1-54). Amsterdam: North Holland. Wold, H. (1985) Partial Least Squares. In: S. Kotz & N. Johnson (Eds), Encyclopedia of Statistical Sciences (Vol. 6, pp ). New York: Wiley

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37 CHAPTER 2: Robustness in PLS estimation: Analysing the effects of introducing Non-normality and Multicollinearity in Customer Satisfaction Measurement Data Mari Källström Stockholm School of Economics, Aarhus University

38 2.1 Introduction Performance measurements and information are high priority areas within organisations. The most common performance measures have a focus on financial performance indicators such as ROI (Return on Investment) and ROS (Return on Sales). However the use of non-financial performance information, or intangible assets, such as the human capital and the customer asset, has grown and also the value of non-financial performance measurements has widened. (Ittner & Larcker, 1998a; 1998b). Organisations of today often evaluate their growth and prospects in terms of a combination of financial (tangible) and non-financial (intangible) information. In 1992, the Balanced Scorecard was introduced to provide organisations with a framework for selecting multiple performance measures, not only focusing on the tangible information but also supplementing with intangible information (Banker et al., 2004; Kaplan & Norton, 1996). Customer measures are intended to measure the organisational performance from the customer s perspective. When evaluating the customer asset, a common strategy is to use customer satisfaction measurements. Sweden was the first country to develop and establish a national index of customer satisfaction in 1989 (Fornell, 1992) and since the beginning of the 90 s several nations has developed national indicators measuring consumer satisfaction across a wide range of industries, companies and organisations (Andreassen & Lindestad, 1998; Martensen et al., 2000; Fornell et al., 1996). European Performance Satisfaction Index (EPSI Rating) is a nonprofit organisation that has widened the scope of conducting consumer satisfaction measurements by placing it more on a European level with harmonized customer satisfaction surveys over several industries and in an increasing number of European countries (ECSI, 1998). This makes it possible to have a common currency when the interest also lies at performing benchmark between companies, industries, countries as well as over time. A common methodology within customer satisfaction measurements is to use Structural Equation Models (SEM). These models are presumed to give information on cause and effect relations between the antecedents and consequences of customer

39 satisfaction imposed in the models. The processes described with a structural model are also assumed to generate measures of association among the variables depicted in the model (Williams et al., 2003). The well-established theories which underlies the basic structure of structural models used in the area of customer satisfaction as well as years of research within areas such as consumer behaviour and customer satisfaction give strength to the methodology used (Fornell, 1992; Fornell et al., 1996; and Fornell, 2007) SEM is also the methodology used within EPSI Rating when measuring and evaluating customer satisfaction. Within the framework of EPSI Rating the common statistical method used is Partial Least Squares (PLS), which is a variancebased multivariate method. Many authors argue that PLS shows several advantages in comparison with covariance-based methods such as LISREL, EQS and AMOS. These advantages have contributed to the increasing application of PLS over the recent years (Chin, 1998; Fornell & Bookstein, 1982). Another alternative to PLS is Neural Network based SEM, which shows some similarities to PLS but also some distinctions, for instance Neural Network based techniques in SEM has the possibility to perform simultaneous measures in the approximation process (Hackl & Westlund, 2000; Hsu et al., 2006). The hypothesis of PLS being robust against statistical quality aspects such as multicollinearity, miss-specified structural models and non-normality (i.e. skewness in the data), which are also empirical issues common in customer satisfaction studies, shows strong evidence in favour of using PLS (Cassel et al., 1999; 2000; and 2001, Westlund et al., 2008). However, the research within the area of studying statistical aspects of PLS, such as the statistical quality aspects mentioned above, more theoretically, still faces some gaps. The aim of this study is to analyse to what extent there would be effects on the structural parameter estimates when firstly introducing non-normality in the data and secondly when in combination with non-normality also introduce multicollinearity in the data, when applying a PLS approach for a model similar to the structural model used within the framework of EPSI Rating

40 2.2 Estimation Procedure The estimation of Structural Equation Models faces some difficulties such as; i) the latent variables are not observed, ii) the manifest variables that correspond to responses on a questionnaire from a customer satisfaction survey may (highly) likely not follow a normal distribution and skewness to the right on the scale is more common, iii) the occurrence of multicollinearity on some levels are often present. The two families of methods commonly used to estimate these types of structural models are covariancebased methods and variance-based methods, i.e. PLS. PLS is seen as a soft modelling technique. The reason is that PLS can be seen as a distribution free method, since there is no need of any assumptions regarding the distribution of the manifest variable, or about the independence of observations. This in comparison with SEM-ML, covariance based SEM, also known as Hard modelling," which has stronger distributional assumptions and several hundreds of cases are necessary (Jöreskog, 1970). The estimates from using a covariance-based method are consistent, but when the assumptions of multivariate normal distribution, large sample size and independence of observations are violated, the covariance-based methods may produce improper solutions, for example negative variance (Fornell & Bookstein, 1982; Chin 1998). However, PLS estimates are only consistent at large which means that the bias of estimates from a PLS procedure will tend to zero only as the number of latent variables (per block) and sample size increase simultaneously. Covariance-based methods will not be a part of this study, so the estimation process will not be discussed here. The author refers to the numerous literatures discussing the different techniques further; see for example Jöreskog (1970); Boomsma et al. (2001) and Hsu et al. (2006). The first to formalize the idea of Partial Least Squares was Herman Wold in a paper discussing principal component analysis (Wold, 1966). To pursue PLS estimation you need i) the measurement model, ii) the structural model, and iii) the weight relations. The measurement model (or outer model) relates the manifest variables, or indicators (observable constructs), to pre-specified

41 latent variables (unobservable constructs). The latent variables are defined as ξ and η, depending on if the latent variable is exogenous ( ξ ) or endogenous ( η). The structural model (or inner model) describes the relations between some endogenous latent variables with other latent exogenous variables. This is denoted as in (2.1): η Βη Γξ ζ (2.1) where Β and Γ are impact parameter matrices, and ζ is a vector of error terms, where E { ζ ξ} 0. (2.2) Since the latent variables are unobservable they are all individually described by a block of observable variables x and y. The ways of relating the indicators to their respective latent variable are threefold; the reflective one, the formative way and the MIMIC (multiple effect indicators for multiple causes) approach. The reflective measurement model is given by (2.3) and (2.4) (the manifest variables are reflections of the latent variables): x λ ξ (2.3) x ε x y λ y ε y (2.4) where E( ξ )= m, Var( ξ )=1 and E( η )= m,var( η )=1. Furthermore, a hypothesis to be ξ fulfilled, introduced by Wold, is the so called predictor specification condition as in (2.5) and (2.6):

42 E { xξ} λ ξ (2.5) x E { y η} λ η (2.6) y This implies that the residual terms ε x and ε y have a zero mean and are uncorrelated with their respective latent variable, i.e. Corr (,ξ) 0 and Corr (, η) 0 ε x ε y Often a more appropriate way for the exogenous variables will be to use a formative specification of the relations. If the exogenous latent variable/-s is supposedly generated by its own manifest variables then it is called a formative model for ξ. Formative measurement models are given by; ξ π x (2.7) ξ δ ξ η π y (2.8) η δ η where the latent variables ξ and η are linear functions of its manifest variables plus a residual term. The predictor specification condition also holds for the formative specification. The general definition of the weight relations is that they are used to estimate scores or case-values of the latent variables, as weighted averages of the manifest variables: ^ η w y (2.9) η ^ ξ w x (2.10) ξ

43 Estimation of the weights wξ and w η are twofold, Mode A and Mode B, depending on if the measurement model follows a reflective or formative approach. For more details on the PLS algorithm, see for example, Lohmöller (1989); Fornell & Cha (1994); Tenenhaus, et al. (2005); and Vilares, et al. (2005). 2.3 Study Design The purpose of this study is to continue the contribution of the knowledge on smallsample distributions of the PLS estimator in particular when non-normality and multicollinearity are present in data. This will be done through Monte Carlo simulations, due to the complexity of SEM models and PLS, which makes it hard to assess the robustness in an analytical form. The second purpose is to compare the results in this analysis with Westlund et al. (2008), where a study on multicollinearity present in data was undertaken and the impact and robustness on PLS estimation was evaluated. Both the model set-up and the parameter specifications in the simulation process have been specified according to Westlund et al. (2008). The focus of this study is to analyse the effects non-normality have on PLS estimates of the inner model (structural) parameters. The non-normality will be introduced as a combination of i) non-normality within the manifest data and ii) nonnormality within the structural residuals. These aspects will be studied simultaneously in order to examine to what extent the structural parameters will be affected when also combining the two non-normality perspectives. However, the two criteria s mentioned above will also be analysed separately in order to study what the impact will be if only one of the non-normality issues is present. Another focus will be to introduce multicollinearity from two perspectives: i) between multicollinearity, i.e. between exogenous latent variables and ii) within multicollinearity, i.e. within exogenous variable (between manifests). With this set-up it will be possible to study the combined effects on the structural parameters when having both non-normality and multicollinearity present when performing a PLS estimation

44 The structural model used in customer satisfaction surveys by EPSI Rating consists of seven latent variables, where the first five are seen as driving factors (Image, Expectation, perceived Product Quality, perceived Service Quality and Value) and the other two, Customer Satisfaction and Loyalty, are seen as the resulting (performance) factors in the model. Each latent variable is measured by multiple manifests (Westlund et al. 2008; ECSI, 1998). The same parameter set-up is used in this study as in Westlund et al. (2008). One of the simplified versions of the EPSI Rating model also analysed in Westlund et al. (2008) will be undertaken in this article. The structural model consists of 4 latent variables; two exogenous and two endogenous with links from each exogenous variable to both of the endogenous variables. The correlation between the two exogenous variables is represented by a curved line (see Figure 2.1). Perceived Product Quality Value Perceived Service Quality Customer Satisfaction Figure 2.1 Simulation Model The two exogenous variables ( ξ 1 and ξ 2 ) corresponds to Product Quality and Service Quality. Value ( 1 ) and Customer Satisfaction ( 2 ) corresponds to the two endogenous variables. The measurement models for i, i =1,2, follows the formative specification (2.7) where the error terms are uniformly distributed. The measurement model for 1 and 2 is reflective (3-6) and again, the error terms are uniformly distributed. The inner relation for the simulation model is given by (2.1), where:

45 B 0 Γ which are specified as in Westlund et al. (2008). The focus of the study, as mentioned earlier, aims at analysing the effects of introducing non-normality in the measurement process and also combining the two statistical aspects of skewness and multicollinearity and study the effects on PLS estimation such a set-up has on the inner parameters of a structural model. The base case, or baseline model in this study, will be where the simulation is specified without any impact of multicollinearity, the manifest variables of the exogenous variables are generated from the symmetric beta(6,6) distribution and the structural residuals are assumed to be normally distributed. x i, ij and As mentioned earlier the set-up of the parameters in the structural model; y will be specified as in Westlund et al. (2008) which means that i xi be set to be ¼, ij will be set to be 0.7, 0.5, 0.5 and 0.3 for i = 1,2 and j = 1,2 and set to be 0.75 throughout the simulation process. All error variances are set such that the degrees of explanation ( yi will 2 R ) are approximately 0.65, for sample size n = 500. The number of manifests is set to be four in every part of the simulation process. They are all measured on a 1-10 scale, which is the standard procedure within the EPSI Rating framework. The sample size will vary on two levels; n=100 and n=500. The number of replications is set to be The first focus will be to study the effects of introducing non-normality as a combination of two perspectives, namely i) non-normality within the manifests of the exogenous variables and ii) non-normality within the structural residuals. There will be 16 combinations of non-normality to study on two levels of sample size, which implies a total of 32 cases of non-normality to analyse. is

46 Count Structural Residuals Count The non-normality will be introduced by generating both the manifests and the structural residuals from skewed beta distributions (see Table 2.1). For both the manifests and the structural residuals an EPSI specific case (*) has been developed by analysing empirical data from the financial sector from the Swedish part of EPSI Rating. Empirical data has been analysed over two years (2005 and 2006) in a trial-anderror environment to be able to match a beta distribution on both the manifests and the structural residuals. The purpose of the chosen beta distributions is to be able to analyse i) a symmetrical case (beta(6,6)) ii) moderate non-normality (beta(6,4), beta(6,2)) and iii) a severe case of non-normality (beta(8.1)). Manifest Distribution Design beta (6,6) beta (6,4) beta (6,2)* beta (8,1) N(0, 0.22) "Basecase" beta (6,4) beta(7, 3.5)* beta (8,1) * EPSI Specific distributions, from the financial sector Table 2.1: Beta distribution for the manifest variables and the structural residuals The four beta distributions used in this article are depicted in Figure , to show the skewness of the chosen beta distributions graphically beta(6,6) beta(6,4) Figure 2.2. Beta(6,6) distribution Figure 2.3. Beta(6,4) distribution

47 Count Count beta(6,2) beta(8,1) Figure 2.4. Beta(6,2) distribution Figure 2.5. Beta(8,1) distribution The second focus will be to also introduce multicollinearity in combination with non-normality as specified above. In Westlund et al. (2008) multicollinearity was analysed in two ways; i) between blocks by setting the levels of correlation (Corr) on four levels and ii) within the first exogenous block by studying the Variance Inflation Factor (VIF) on five levels. This approach will be replicated here, however the levels of Corr in this study will only be set on two levels (0.5 and 0.95) and the levels of VIF will also be set on two levels (VIF= 10 and 30). The purpose of this is to be able to study the effects when multicollinearity is introduced on i) a moderate level and ii) on a more severe level. The introduction of the within block multicollinearity will be done firstly on the first exogenous latent variable (denoted 1 Ksi under Results) and an extension with this study in comparison to Westlund et al. (2008) is that the within block multicollinearity will be introduced and studied on both exogenous variables simultaneously (denoted 2 Ksi under Results). The correlations are introduced by a Cholesky transformation, as in Westlund et al. (2008) and the correlation matrix has been specified as follows

48 1 R where is a parameter between 0 and 1. This specification has the effect that the correlation between two neighbouring variables within the same block is. However, it also specifies the correlation to decrease when increasing the number of manifests. This might induce a more positive effect on estimation and will be evaluated in the simulation process. When correlation between the exogenous latents is introduced, the same principle has been used, i.e. the correlation between two neighbouring -variables is. VIF VIF = VIF = The correlations matrices are of size M x M, i.e. quadratic matrices, and then the VIF can be calculated as in (2.11). This application follows the same structure as in Westlund et al. (2008) VIF ( M ( M 2 ) )( 1) M (2.11)

49 The simulations are evaluated by examining the Root Mean Square Error (RMSE), bias, and variance of all estimators (over the 5000 replicates). 2.4 Results As described earlier the theoretical model used in this study consists of four latent variables, two exogenous and two endogenous. The presentation of the results from the simulation study undertaken is threefold. Tables show the simulation results when non-normality is present; both when skewness is present between the manifest variables as well as within the structural residual. Tables show the simulation results when a combination of nonnormality, as described above and multicollinearity is introduced between the exogenous latent variables, when pre-setting the levels of correlation on two levels, denoted Corr, in the tables. The last part of the result presentation consists of Tables 2.8a-2.10b. Here the results from the simulation process are presented, where a combination of nonnormality and multicollinearity between the manifest variables are present in the data, when pre-setting the level of within multicollinearity on two levels using VIF. Tables show the estimated parameters, the estimated RMSE, and the proportion of RMSE originating from the variance of the estimator in each case. The results are presented for the two levels of sample sizes being analysed; n=100 and n=500. PLS is a biased multivariate method, i.e. it is not consistent, but consistent at large. The consensus of this is that the bias in the estimation process will decrease as i) the model increases in terms of increasing the number of manifests per latent variable and ii) the sample size increases. In this study the focus has been on increasing the

50 sample size and not to increase the number of manifests at any stage of the simulation process. When examining the basecase in Table 2.2, the parameter estimates are good, even on the smaller sample size. This is mainly due to the large number of replicates used in this simulation. Improvements in estimation can be seen when increasing the sample size, which is also expected. Despite the lack of non-normality the estimates are negatively biased. This is related to the fact that PLS is only consistent at large and is yet another confirmation to the theoretical aspect of PLS. These findings are in line with the results found in Westlund et al. (2008)

51 Parameter True Parameter Value Sample size n Inner Structural Model Parameter Estimates (mean value over 5000 replicates) Manifest Distributions beta(6,6) beta(6,4) beta(6,2) beta(8,1) * * * * N(0,0.22) * * * * beta(6,4) ** ** ** ** 0.41 beta(7, 3.5) ** ** ** ** beta(8,1) Table 2.2: True and estimated parameters; when non-normality is present in the data and structural residuals. 1 1 Set up of inner structural model distribution as in Westlund et al. (2008). *Basecase **EPSI specific case

52 When the manifests are assumed to follow a moderate beta distribution, no larger effects can be seen on the parameter estimates compared to basecase. As can be seen in Table 2.3 RMSE shows no distinct effects in any direction and no severe increase in bias are indicated. This is confirmed by the quite steady levels of variance from Table 2.4. These findings support the hypothesis of PLS being robust against non-normality in, at least moderate, manifest distributions. In the case of introducing severe non-normality in the manifests, larger effects on the parameter estimates are indicated. The large increase in RMSE is almost exclusively due to large increase in bias. However, when increasing the sample size the parameter estimates improve and could also be seen as an indication of PLS being quite robust even when having severe non-normality within the manifest distribution, a case which is seldom (or never) seen empirically. The results seem positive with regards to the robustness of PLS; however a discussion regarding the choice of set-up could also be interesting to review

53 Parameter Sample size n Inner Structural Model RMSE (mean value over 5000 replicates) Manifest Distributions beta(6,6) beta(6,4) beta(6,2) beta(8,1) * * * * N(0,0.22) * * * * beta(6,4) ** ** ** ** 0.10 beta(7, 3.5) ** ** ** ** beta(8,1) Table 2.3: The estimated RMSE of PLS estimates; when non-normality is present in the data and structural residuals. In the case of introducing non-normality in the structural residuals, an interesting finding is that the estimates improve. An implication that might have an effect is a lack

54 of controlling for E{ ζ ξ} 0 in the simulation process. However, the level of parameter estimates are quite steady when increasing the non-normality in the structural residuals. This together with the findings of lowered RMSE and an increase in variance, which indicates decreased bias effects, still gives some evidence of robustness. But the shortcoming mentioned indicates that further research should be undertaken, since no further evaluation of this has been undertaken here

55 Parameter Sample size n Inner Structural Model Percentage VAR (mean value over 5000 replicates) Manifest Distributions beta(6,6) beta(6,4) beta(6,2) beta(8,1) * * * * N(0,0.22) * * * * beta(6,4) ** ** ** ** 14.4 beta(7, 3.5) ** ** ** ** beta(8,1) Table 2.4: Percentage Variance in RMSE ( %Varianceγ MSE Var x100 ); when nonnormality is present in the data and structural residuals. ij 1 ij ij Both the theoretical model used as well as the parameter set-up originates from the EPSI framework. Even the distribution of manifests and structural residuals has been

56 tested in comparison with empirical data from EPSI, where an EPSI specific case has been identified. This case is interesting to discuss since this has an empirical link to the simulations undertaken. Compared to basecase, the EPSI specific case yields better estimates (see Table 2.2). RMSE decreases (Table 2.3), which is mainly due to the increased variance effects as can be confirmed in Table 2.4. This implies further that the bias effects are in some way decreased. These results support the hypothesis of PLS being robust against non-normality in cases which, at least, are empirical evident. Parameter True Parameter Value Sample size n Inner Structural Model Parameter Estimates (mean value over 5000 replicates) Manifest Distributions - Corr 0.5 Parameter Estimates (mean value over 5000 replicates) Manifest Distributions - Corr 0.95 beta(6,6) beta(6,4) beta(6,2) beta(8,1) beta(6,6) beta(6,4) beta(6,2) beta(8,1) N(0,0.22) beta(6,4) ** ** ** ** ** ** ** ** 0.53 beta(7, 3.5) ** ** ** ** ** ** ** ** beta(8,1) Table 2.5: True and estimated parameters; A combination of when i) non-normality is present in the data and structural residuals and ii) multicollinearity is introduced between the exogenous latent variables

57 In the case of introducing moderate beta distributions on the manifests, only slight improvements are noticeable, regardless of structural residual distribution or sample size. However, in the more extreme case of non-normality (beta(8,1)), the effects are more severe. From Table 2.6 and Table 2.7 it is evident that the corresponding RMSE:s, in comparison with basecase, decrease when introducing between block multicollinearity, however the variance proportion is much higher especially when n is low (see Table 2.7). Parameter Sample size n Inner Structural Model RMSE (mean value over 5000 replicates) Manifest Distributions - Corr 0.5 RMSE (mean value over 5000 replicates) Manifest Distributions - Corr 0.95 beta(6,6) beta(6,4) beta(6,2) beta(8,1) beta(6,6) beta(6,4) beta(6,2) beta(8,1) N(0,0.22) beta(6,4) ** ** ** ** ** ** ** ** 0.05 beta(7, 3.5) ** ** ** ** ** ** ** ** beta(8,1) Table 2.6: The estimated RMSE of PLS estimates; A combination of when i) non-normality is present in the data and structural residuals and ii) multicollinearity is introduced between the exogenous latent variables

58 Increasing the level of multicollinearity to 0.95 increases the bias effect substantially for example in 12 and 22, so that the variance proportion is nearly negligible. The opposite pattern is shown for example in 11 and 21, where the variance proportion in RMSE seems to increase in most cases. Parameter Sample size n Inner Structural Model Percentage VAR (mean value over 5000 replicates) Manifest Distributions - Corr 0.5 Percentage VAR (mean value over 5000 replicates) Manifest Distributions - Corr 0.95 beta(6,6) beta(6,4) beta(6,2) beta(8,1) beta(6,6) beta(6,4) beta(6,2) beta(8,1) N(0,0.22) beta(6,4) ** ** ** ** ** ** ** ** 50.8 beta(7, 3.5) ** ** ** ** ** ** ** ** beta(8,1) Table 2.7: Percentage Variance in RMSE ( %Varianceγ MSE Var x100); A combination of when i) non-normality is present in the data and structural residuals and ii) multicollinearity is introduced between the exogenous latent variables. ij 1 ij ij When introducing more severe beta distribution (beta(8,1)) the effects are more severe. The estimates decrease, however improvements are seen both with regards of increasing n and also when increasing the level of multicollinearity. The corresponding RMSE:s in Table 2.6 and the proportion of variance explained in RMSE in Table 2.7 show no clear

59 overall pattern, however in most cases the increase in the RMSE:s seems to a higher extent be originating from bias effects. In the case of introducing multicollinearity within the exogenous variables (between manifests), the results reveal that when setting the level of VIF on 10 and focusing only on the first exogenous variable (1 Ksi) the estimates improve compared with basecase, however this is only seen for 11 and 21 (Table 2.8a.). Parameter True Parameter Value Sample size n Inner Structural Model Parameter Estimates (mean value over 5000 replicates) Manifest Distributions - VIF 10 (1 Ksi) Parameter Estimates (mean value over 5000 replicates) Manifest Distributions - VIF 10 (2 Ksi) beta(6,6) beta(6,4) beta(6,2) beta(8,1) beta(6,6) beta(6,4) beta(6,2) beta(8,1) N(0,0.22) beta(6,4) ** ** ** ** ** ** ** ** 0.60 beta(7, 3.5) ** ** ** ** ** ** ** ** beta(8,1) Table 2.8a: True and estimated parameters; A combination of when i) non-normality is present in the data and structural residuals and ii) multicollinearity is introduced within the manifest variables when VIF=10, only on the first exogenous variable (1 Ksi) and in both exogenous variables (2 Ksi)

60 An interesting observation is that the estimates for especially γ12 and γ 22 seem to be improving when introducing multicollinearity within both of the exogenous variables. The above described pattern is also seen in the case of introducing multicollinearity on both exogenous variables (see Table 2.8a). This picture also holds when VIF=30 (Table 2.8b). However, a difference seem to be an increase in variance proportions in the corresponding RMSE:s, see Table 2.9b and Table 2.10b. The variance proportions are even more substantial when multicollinearity is introduced on both exogenous variables. Parameter True Parameter Value Sample size n Inner Structural Model Parameter Estimates (mean value over 5000 replicates) Manifest Distributions - VIF 30 (1 Ksi) Parameter Estimates (mean value over 5000 replicates) Manifest Distributions - VIF 30 (2 Ksi) beta(6,6) beta(6,4) beta(6,2) beta(8,1) beta(6,6) beta(6,4) beta(6,2) beta(8,1) N(0,0.22) beta(6,4) ** ** ** ** ** ** ** ** 0.62 beta(7, 3.5) ** ** ** ** ** ** ** ** beta(8,1) Table 2.8b: True and estimated parameters; A combination of when i) non-normality is present in the data and structural residuals and ii) multicollinearity is introduced within the manifest variables when VIF=30, only on the first exogenous variable (1 Ksi) and in both exogenous variables (2 Ksi)

61 The deviations between true and estimated parameters are almost the same irrespective of sample size. The effect of improved parameter estimates is evident when introducing moderate beta distributions on the structural residuals, but not when introducing moderate beta distributions in the manifests. However, the parameters decrease in the severe case of beta distribution on either the structural residuals or the manifests, but not as low (a level) as might have been expected. A consequence of having small deviations between the true and estimated parameters is that the RMSE:s are mostly rather small (see Table 2.9a). The bias part, however, increases in most cases substantially when increasing the sample size. This is yet another confirmation to the findings in Westlund et al. (2008). Parameter Sample size n Inner Structural Model RMSE (mean value over 5000 replicates) Manifest Distributions - VIF 10 (1 Ksi) RMSE (mean value over 5000 replicates) Manifest Distributions - VIF 10 (2 Ksi) beta(6,6) beta(6,4) beta(6,2) beta(8,1) beta(6,6) beta(6,4) beta(6,2) beta(8,1) N(0,0.22) beta(6,4) ** ** ** ** ** ** ** ** 0.10 beta(7, 3.5) ** ** ** ** ** ** ** ** beta(8,1) Table 2.9a: The estimated RMSE of PLS estimates; A combination of when i) non-normality is present in the data and structural residuals and ii) multicollinearity is introduced within the manifest variables when VIF=10, only on the first exogenous variable (1 Ksi) and in both exogenous variables (2 Ksi)

62 The estimates improve when setting VIF=10 and increasing the non-normality in both the structural parameter as well as increasing non-normality in the manifests. Even the severe case, beta(8,1), the estimates are on an acceptable level, but what is showing is that in most cases the bias effect increases to a higher extent. The same pattern is shown regardless of VIF=10 for case 1 ksi as well as in 2 ksi, with a distinction of lowered RMSE when 2 ksi case is evaluated. This is mainly due to an increase in variance. Parameter Sample size n Inner Structural Model RMSE (mean value over 5000 replicates) Manifest Distributions - VIF 30 (1 Ksi) RMSE (mean value over 5000 replicates) Manifest Distributions - VIF 30 (2 Ksi) beta(6,6) beta(6,4) beta(6,2) beta(8,1) beta(6,6) beta(6,4) beta(6,2) beta(8,1) N(0,0.22) beta(6,4) ** ** ** ** ** ** ** ** 0.12 beta(7, 3.5) ** ** ** ** ** ** ** ** beta(8,1) Table 2.9b: The estimated RMSE of PLS estimates; A combination of when i) non-normality is present in the data and structural residuals and ii) multicollinearity is introduced within the manifest variables when VIF=30, only on the first exogenous variable (1 Ksi) and in both exogenous variables (2 Ksi). Increasing the correlation within the exogenous variable for 1 Ksi does not show any strong effects on the parameter estimates, which still lies on an acceptable level. This

63 could be seen as a strong confirmation of PLS being very robust when focusing on the parameter estimate. However, could the set-up have a strong implication to the results given in this study? Parameter Sample size n Inner Structural Model Percentage VAR (mean value over 5000 replicates) Manifest Distributions - VIF 10 (1 Ksi) Percentage VAR (mean value over 5000 replicates) Manifest Distributions - VIF 10 (2 Ksi) beta(6,6) beta(6,4) beta(6,2) beta(8,1) beta(6,6) beta(6,4) beta(6,2) beta(8,1) N(0,0.22) beta(6,4) ** ** ** ** ** ** ** ** 5.8 beta(7, 3.5) ** ** ** ** ** ** ** ** beta(8,1) Table 2.10a: Percentage Variance in RMSE ( %Varianceγ MSE Var x100); A combination of when i) non-normality is present in the data and structural residuals and ii) multicollinearity is introduced within the manifest variables when VIF=10, only on the first exogenous variable (1 Ksi) and in both exogenous variables (2 Ksi). ij 1 ij ij

64 Parameter Sample size n Inner Structural Model Percentage VAR (mean value over 5000 replicates) Manifest Distributions - VIF 30 (1 Ksi) Percentage VAR (mean value over 5000 replicates) Manifest Distributions - VIF 30 (2 Ksi) beta(6,6) beta(6,4) beta(6,2) beta(8,1) beta(6,6) beta(6,4) beta(6,2) beta(8,1) N(0,0.22) beta(6,4) ** ** ** ** ** ** ** ** 4.0 beta(7, 3.5) ** ** ** ** ** ** ** ** beta(8,1) Table 2.10b: Percentage Variance in RMSE ( %Varianceγ MSE Var x100); A combination of when i) non-normality is present in the data and structural residuals and ii) multicollinearity is introduced within the manifest variables when VIF=30, only on the first exogenous variable (1 Ksi) and in both exogenous variables (2 Ksi). ij 1 ij ij 2.6 Conclusions The purpose of this study was to continue the contribution of the knowledge on smallsample distributions of the PLS estimator in particular when non-normality and multicollinearity is present in the data. This was done through Monte-Carlo simulations. Both the non-normality criteria s used as well as the level of multicollinearity being incorporated, both within block and between blocks, on a moderate as well as severe levels

65 In the case of introducing non-normality, the results imply that PLS is quite robust against non-normality issues, both when skewness is present in the manifests variables and also in a combination of also introducing skewness in the structural residuals. However, in the more severe case of non-normality (beta(8,1)) the impact on the estimates is more severe. It is also evident that the bias effect increases substantially when introducing a more severe case of non-normality. When introducing non-normality in a combination with introducing multicollinearity between the exogenous variables the estimates improve in some cases, but two parameters seem to be more affected when especially increasing the level of multicollinearity. The variance effect increases in most cases, however the bias effect is more substantial both when increasing the level of multicollinearity and when nonnormality is introduced on a more severe level. Comparing the results above with the case of combining the aspect of nonnormality with the introduction of multicollinearity within exogenous variable/-s, minor improvements in the estimates appear. This is also evident when severe non-normality is introduced. The bias effect becomes more evident when increasing the level of within multicollinearity but also when having multicollinearity on both exogenous variables. Looking at the results given in this simulation study the results show that PLS is very robust on the moderate levels of both non-normality and multicollinearity. Interesting is also that when severe cases are introduced, PLS still generates estimates beyond what would be empirically acceptable. At first glance we could give a star to PLS for its robustness, however a question arises are the numbers valid? As with all Monte-Carlo simulations the results and conclusions is only valid for the specific model generated. To be able to generalize even more the set-up should be evaluated to be even more similar to empirical situations. There are quite a number of research papers focusing on PLS and its suitability for satisfaction surveys with regards to both theory and set-up (Kristensen & Eskildsen, 2010; Nielsen et al., 2009). What would the effect be on the parameter estimates if a larger model were to be evaluated? It is very common to look at simplified models (looking at the tradition), but since this is not the case empirically the researcher emphasize this a bit

66 more. Would the same pattern, in relation to non-normality and multicollinearity being introduced, be shown when introducing more complexity with regards to modelling setup (i.e. a full EPSI model in this case)? Another shortcoming might be the correlation set-up used in this research. The set-up, in this study, implies the correlations to diminish when including more and more factors, which is highly not likely to be the case in reality. Above implies yet another research approach to be able to draw even more general conclusions, that is to use a correlation set-up between the factors more similar to reality, for instance the suggested set-up presented in Nielsen et al., (2009), where the suggestion is to have at least the same correlation between the factors, since this is more often seen in empirical data. To be able to discuss the positive effect of conducting satisfaction surveys using PLS as the statistical method instead of other methods on the market, more comparisons should be undertaken to also be able to compare the robustness, towards the quality aspects discussed here, between the diversity of multivariate methods. Some extensions should therefore be in focus; i) examine the effects when a larger model is introduced, ii) study the correlation effect with situations more evident empirically and iii) extend the scope of the results with a comparison with more covariance based methods

67 2.7 References Andreassen, T.W. & Lindestad, B. (1998) The effects of corporate image in the formation of customer loyalty. Journal of Service Marketing, 1(1), Banker, R. D., Chang, H. & Pizzini, M. J. (2004) The balanced scorecard: judgemental effects of performance measures linked to strategy. The Accounting Review, 79(1), Boomsma, A. & Hoogland, J.J. (2001) The Robustness of LISREL Modeling Revisited, in R. Cudeck, S. Dau Toit, D. Sörbom, D. (Ed.), Structural Equation Modeling: Present and Future, a Festschrift in Honor of Karl Jöreskog (pp ). SSI Scientific Software International, Lincolnwood, IL. Cassel, C., Hackl, P., & Westlund, A.H. (1999) PLS for estimating latent variable quality structures: finite sample robustness properties, Journal of Applied Statistics, 26(4), Cassel, C., Hackl, P., & Westlund, A.H. (2000) On measurement of intangible assets: a study of robustness of partial least squares. Total Quality Management, 11(7), Cassel, C., Eklöf, J, Hackl, P. & Westlund, A.H. (2001) Structural analysis and measurement of customer perceptions, assuming measurement and specification errors. Total Quality Management, 12(7-8), Chin, W.W. (1998) Commentary: issues and opinion on structural equation modelling. MIS Quarterly, 22, pp. vii-xvi. ECSI (1998) European Customer Satisfaction Index Foundation and Structure for harmonized National Pilot Projects. Report prepared by ECSI Technical Committee. ECSI Document no. 005 ed. 1. Fornell, C. (1992) A national customer satisfaction barometer: the Swedish experience. Journal of Marketing, 56(1),

68 Fornell, C. (2007) The Satisfied Customer. New York: Palgrave Macmillan. Fornell, C. & Bookstein, F.L. (1982) Two structural equation models: LISREL and PLS applied to consumer exit-voice theory. Journal of Marketing Research, 19(4), Fornell, C. & Cha, J. (1994) Partial least squares. In: R.P.Bagozzi (Ed.) Advanced Methods in Marketing Research (pp.52-78). Cambridge, MA: B. Blackwell. Fornell, C., Johnson, M. D., Anderson, E. W., Cha, J., & Everitt Bryant, B., (1996) The American customer satisfaction index. Nature, purpose, and findings. Journal of Marketing, 60(4), Hackl, P. & Westlund, A.H. (2000) On structural equation modeling for customer satisfaction measurement. Total Quality Management, 11(4-6), Hsu, S-H., Chen, W-H., & Hsieh, M-J. (2006) Robustness Testing of PLS, LSIREL, EQS and ANN-based SEM for measuring Customer Satisfaction. Total Quality Management, 17(3), Ittner, C.D. & Larcker, D.F. (1998a) Innovations in performance measurements: Trends and research implications. Journal of Management Accounting Research, 10, Ittner, C.D. & Larcker, D.F. (1998b) Are nonfinancial measures leading indicators of financial performance? An analysis of customer satisfaction, Journal of Management Accounting Research, 36, Studies on Enhancing the Financial Reporting Model, Jöreskog, K.G. (1970) A general method for analysis of covariance structures. Biometrika, 57(2), Kaplan, R. S. & Norton, D. (1996) The Balanced Scorecard. Boston: Harvard University Press

69 Kristensen, K. & Eskildsen, J. (2010) Design of PLS-Based Satisfaction Studies. In: V. Esposito Vinzi et al. (Ed.) Handbook of Partial Least Squares (pp ). Berlin Heidelberg: Springer Verlag. Lohmöller, J-B (1989) Latent Variable Path Modeling with Partial Least Squares. Heidelberg: Physica. Martensen, A., Gronholdt, L. & Kristensen, K. (2000) The drivers of customer satisfaction and loyalty: cross-industry findings from Denmark. Total Quality Mangement, 11(4-6), Nielsen, R. Kristensen, K. & Eskildsen, J.K. (2010) Robustness of PLS path modeling under conditions common in satisfaction studies, paper presented on the 6th International Conference on Partial Least Squares and Related Methods, Kina, Beijing Tenenhaus, M., Vinzi, V. E., Chatelin, Y-M. & Lauro, C. (2005) PLS path modeling. Computational Statistics and Data Analysis, 48(1), Vilares, M.J., Almeida, M.H. & Coelho, P.S. (2005) Comparison of likelihood and PLS estimators for structural equation modelling. A simulation with customer satisfaction data. Technical Report. New University of Lisbon. Westlund, A.H., Källström, M. & Parmler, J. (2008) SEM Based Customer Satisfaction Measurement; On Multicollinearity and Robust PLS Estimation. Total Quality Management and Business Excellence, 19(7-8), Williams, L.J., Edwards, J.R. & Vandenberg, R.J. (2003) Recent Advances in Causal Modeling Methods for Organisational and Management Research. Journal of Management, 29(6), Wold, H. (1966) Estimation of principal components and related models by iterative least squares. In: P.R. Krishnaiah (Ed.), Multivariate Analysis (pp ). New York: Academic Press

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71 CHAPTER 3: Enhancement of Leadership in Employee Engagement Modelling Mari Källström Aarhus University

72 3.1 Introduction Searching the Internet for a definition of a leader gives millions of hits, not surprisingly since leadership is a wide-spread concept depending on the context for which it is used. Taking an organisational perspective one definition could be a person who rules, guides or inspires others. The cultural phenomena surrounding leadership, was not seen as any big issue before the middle of 1990 (Dorfman, 1996), but the image of this has changed. Reviewing research and theory on international leadership imply that reflections on cultural influences in leadership processes are highly evident (House et al., 1999; House, 2004; Yukl, 2002). In an organisation the leaders could be seen as the steering wheel and employees as the engine together with the management. Some might argue that management and leadership are one and the same; however a distinct difference between these is you manage things and lead people. Depending on the size of a company, (most) organisations may have different layers of leadership. Looking more closely at two kinds of leadership highly evident in most organisations i) Top management, i.e. senior management, having a strategic overview and ii) Immediate manager/-s having a more operational focus for everyday life in an organisation. The impact from different levels of leadership on employees is very interesting to measure and analyse, but it is a context hard to measure directly and needs to be incorporated in concept. One perspective where it could be interesting to analyse the effect of management is with regards to employee satisfaction and loyalty. A reason for this could be that research has shown that employee satisfaction does have an impact on the financial results (Kristensen & Westlund, 2004). Learning more about impact from management towards employee satisfaction from different layers within an organisation will strengthen the focus even more in organisational development from this perspective. When evaluating the human capital, a common strategy is to pursue Employee Satisfaction surveys. A company focusing on leadership from two perspectives when surveying and analysing employee satisfaction is Ennova. The two

73 angles are; i) Senior Management (i.e. top management) and ii) Immediate Manager. A major focus area when conducting these surveys is to be able to find areas to be set as priority in the improvement work towards increasing employee satisfaction in a cost efficient way. A methodology well suited for this purpose is the use of Structural Equation Models, which is also the case within Ennova (Williams et al., 2003). A structural model has been defined as European Employee Index Model (EEI model), which is shown in Figure 3.1. (Eskildsen & Dahlgaard, 2000; Eskildsen et al., 2004). Within the framework of Ennova, Partial Least Squares (PLS) is applied as the common statistical method. The usage of PLS in employee satisfaction measurements, as within Ennova, is based on research and many authors have argued that PLS is showing several advantages in comparison to the covariance-based methods (Chin, 1998; Fornell & Bookstein, 1982). For more details of PLS from a theoretical perspective as well as algorithms see, for example, Lohmöller (1989); Wold (1985); Fornell & Cha (1994); Tenenhaus, et al., (2005) and Vilares, et al., (2005). The aim within Ennova is to analyse the direct impact from seven different antecedents for employee satisfaction and loyalty; Reputation, Senior Management (SM), Immediate manager (IM), Daily work, Cooperation, Development and Remuneration. Action areas Result areas Reputation Perception Behaviour Senior Management Satisfaction Retention Immediate Superior Satisfaction & Motivation Loyalty Co-operation Daily Work Motivation Commitment Remuneration Development Figure 3.1. European Employee Index Model

74 Ennova conducts an annual representative survey, European Employee Index (EEI), in a number of countries over the world, with a stronger focus on the Nordic countries specifically. This study will use empirical data from EEI and by re-modelling the EEI model be able to analyse the in-direct impact from these two leadership dimensions. Through this it should be possible to evaluate how the leadership dimensions role in an Employee Engagement model could, or maybe should, be settled. The empirical analysis will cover 4 years of data in 15 European countries, 3 Asian countries, 3 countries in South America and USA in total 22 countries worldwide. 3.2 European Employee Index In 2000 Markedskonsult A/S (changed name to Ennova in 2006) introduces the Danish employee Index. The scope widened to constitute the Nordic countries in 2001, which was evaluated in a joint project between Markedkonsult A/S and CFI group in 2004 (Eskildsen et al., 2004) and the project changed name to Nordic Employee Index. The aim in that project was to develop and test a generic model of measuring employee satisfaction and loyalty as well as their antecedents. The model developed, has been based on wide academic research within this field (Baker, 1995; Eby et al., 1999, de Jonge et al., 2001; Eskildsen & Dahlsgaard, 2000) and one of the main purposes was to develop a model for measuring employee satisfaction regardless of organisational settings. In 2002 this Nordic project was incorporated on a European arena and by that also a new label of the survey was at hand, namely European Employee Index. The scope of the survey increased over the years to include over 20 countries from The largest focus is still on Europe, but includes also USA, Japan, China, India and Brazil among others, so by now it is more recognised as a global initiative

75 In the EEI model there are seven different drivers, i.e. exogenous variables where the aim is to analyse the relative impact each exogenous variable has on employee satisfaction and loyalty. As mentioned earlier the exogenous variables are; Reputation questions covering the perception among employees on the general knowledge about their organisation. Senior Manager (i.e. Senior management) questions within this area to cover the top management s abilities. Immediate manager questions within this area to receive employees perception on perceived abilities and qualifications on the manager to which they report to. Daily work area of questions to capture the perception on employees daily activities and working conditions. Cooperation block of questions with regards to perception of quality of working with people in the organisation. Development the perception from employees on their individual increase of competency and Remuneration general questions to capture employees perception on compensation within their organisation in relation to other work places. 3.3 Empirical Study Design Analyses done earlier on the effects (direct effects) from the seven different drivers in the EEI model have shown that generally the management perspectives do not have any high direct effect on employee satisfaction. Should the leadership dimension not be prioritised then? The discussion on this should be that working with leadership development might not be a priority in order to raise satisfaction and loyalty directly but leadership on different levels has influences on satisfaction among employees through other dimensions, i.e. by having an effect on factors that can be shown to have a direct effect. The purpose of this study is to analyse the in-direct effect that SM and IM have on employee satisfaction, i.e. analyse the effect from the two specified leadership dimensions on the remaining five factors being considered as antecedents in the EEI model. Figure 3.2, presents the re-arranged EEI model to fulfil this purpose

76 Figure 3.2. Rearranged EEI model Re-arranging the structural equation model and pursue the PLS analysis in a three-stepmodel will show how large effect senior and immediate management have and by that the influence management has when analysing on a broader range. Figure 3.2 constitutes a model with some similarities to the perception on effect scheme in the EFQM excellence model (EFQM, 2011), where the concept is based on that performance is driven through policy and strategy with the focus on customers, people (employees) as well as society as base for business excellence, but with leadership as the driver. This coincides with many organisational theories with regards to business excellence, focusing on leadership from this perspective. (Shingo Prize, (2011), Baldridge, ( )). Even the well-defined framework of the Balanced Scorecard, with which organisations are able to study several performance measures, simultaneously has the idea of leadership as the driver for business excellence (Kaplan & Norton, 1996). This gives the theoretical perspective of accepting leadership s role from a business excellence perspective, but the idea of re-arranging a well-defined model for Employee Engagement has not, according to the author, been conducted to any higher extent