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1 64 Economie et STATEC Auteur: Cécile DE PUYDT, STATEC Multivariate Analyses on Continuing Vocational Training in Luxembourg Résumé Cet article décrit les résultats de quatre analyses réalisées sur les données de l enquête sur la formation professionnelle continue dans les entreprises au Grand-Duché de Luxembourg. L analyse des correspondances multiples (ACM) est une technique descriptive permettant de mettre en évidence les relations entre les variables et les observations(ici les entreprises). Associée à l analyse des correspondances multiples, la méthode de classification hiérarchique sur composantes principales a été utilisée afin d identifier des groupes d entreprises ayant des comportements similaires en terme de formation professionnelle continue. La taille et le secteur d activité des entreprises ont également été pris en compte afin d illustrer et de documenter les résultats obtenus. La première analyse vise à caractériser les entreprises selon leur offre de formation professionnelle continue (FPC). La seconde analyse différencie les entreprises formatrices selon leur mode d organisation des FPC. Dans la troisième analyse, les entreprises ayant offert des formations professionnelles continues sous forme de cours sont distinguées en fonction des facteurs ayant limité ou non leur offre en formation. La dernière analyse touche les entreprises non formatrices et met en évidence les raisons pour lesquelles ces entreprises n ont pas offert de formation à leurs employés en Ces analyses permettent donc de mettre en évidence différents groupes d entreprises, ainsi que différentes oppositions et associations entre entreprises. Ces résultats révèlent des différences en terme de formation professionnelle continue, mais également des différences dues à la structure du questionnaire utilisé pour récolter les données. Les articles publiés dans la série "Économie et statistiques" n'engagent que leurs auteurs. Ils ne reflètent pas forcément les vues du STATEC et n'engagent en rien sa responsabilité.

2 Economie et Multivariate Analyses on Continuing Vocational Training in Luxembourg 2 Summary This paper reviews four analyses run on the Luxembourgish Continuing Vocational Training Survey data. Multiple correspondence analysis (MCA) allows to highlight associations between variables and the individuals (here, the firms). In association with the method of MCA, hierarchical clustering on principal components was used in order to identify groups of firms having similar behavior in terms of continuing vocational training. The size and the economic activity of the companies were introduced in the analyses to enrich the interpretation of the results. The first analysis tends to differentiate the firms according to their continuing vocational training (CVT) offers. The second one takes into account the training firms and their ways to organize the CVT. In the third analysis, only the businesses which have offered courses of CVT are considered. The factors explaining why their CVT offer was not wider are used to characterize them. Finally, the reasons of the non-provision of continuing vocational training are analyzed to describe the non-training firms. Those results show that distinctions between companies in term of training behaviors exist. But it also shows distinctions which are due to the questionnaire used to collect the data.

3 Multivariate Analyses on Continuing Vocational Training in Luxembourg Economie et 1. Introduction 3 The first Continuing Vocational Training Survey (CVTS) was carried out in 1994 by 12 European countries. The growing policy interest in Continuing Vocational Training in businesses led to a second and third edition of CVTS, carried out in 1999 and 2005, respectively. The goals of CVTS are to study the provision of vocational training in companies in terms of the number of employees who participated in training, the types of training provided, the costs of training, etc. In 2011, Luxembourg undertakes for the fourth time the European Survey on Continuing Vocational Training in businesses (CVTS4). This survey covers the reference period of businesses employing ten or more people were represented in the survey. In terms of economic activities, all the sectors are represented except for the following ones: agriculture, forestry and fishing, public administration, education, human health and social work activities, activities of households and extraterritorial activities. The data were collected via a web-based questionnaire. The present paper/document is based upon data collected by this survey. Information has been extracted from the original data and gives an idea of the offer of continuing vocational training (CVT). Those results are described in Bulletin n 1/2012 La formation professionnelle continue au Grand-Duché de Luxembourg, available on the STATEC website. Note that the data presented in this publication are not weighted in order to be comparable to the results observed in the multiple correspondence analyses. The number could therefore be slightly different from the ones presented in the Bulletin. In 2010, 77% of the respondent firms offer CVT to their employees. We will call them the training businesses. This proportion varies from 67% in the building industry to 92% in the financial businesses and other services. Bigger companies tend to offer more CVT than the smallest ones: 67% of the firms of 10 to 49 employees offered CVT in 2010, 100% of the ones of more than 250 employees offer CVT. A subcategory of training businesses is also considered: the ones that offer only CVT courses. They represent 73% of the respondents of CVTS4. As for the proportion of training firms, the percentage of companies that offer CVT courses vary among the economic activities. It goes from 64% in the building industry and the wholesale, retail and hospitality sector to 88% in the sector of finance and other services. Differences can also be observed according to the size of the firms. Only 55% of the businesses of 10 to 19 employees offer CVT courses, this proportion rise to 100% for the firms of more than 500 employees. In terms of IVT, 25% of the firms had at least one apprentice in But those basic descriptive statistics do not show the relationships existing between all those variables. It does not allow answering questions such as: Are there patterns of answer among the respondents? Are there different groups of firms that tend to give the same answers? If yes, can we describe those groups in terms of economic activities and/or size of the firm? Multiple correspondence analysis (MCA) and hierarchical clustering on principal components (HCPC) are one way of answering those questions. They may give another point of view of the relationships existing between the variables and between the firms. MCA analyses the data under a wider angle than classic descriptive statistics. It gives a more global understanding of the relationships amongst the variables and the businesses. Clustering identifies groups of similar companies that we have better knowledge of the existing training strategies of the firms. The first section of this paper presents the questionnaire of the fourth continuing vocational training survey. The second part reviews four multiple correspondence analysis, giving a preview of what can be expected from such analysis and what are the problems encountered when they were applied on the CVTS data. Conclusions and perspectives will finally be drawn. Explanations of the statistical techniques used in this paper are available in appendix 1. Technical results are reviewed in the second appendix.

4 Economie et Multivariate Analyses on Continuing Vocational Training in Luxembourg 4 2. Presentation of the fourth continuing vocational training survey questionnaire The fourth Continuing Vocational Training Survey (CVTS) covers different dimensions of the vocational training. The first part of the questionnaire treats the background information concerning the facilities available in the firms: access to a training center, presence of an individual or department responsible for arranging the training, setting up of a planning plan and/or budget, assessment of training needs, etc. A second section investigates the detailed offer of continuing vocational training (CVT). The characteristics of the internal and external courses offered by the firms are the enquiry of the third part of the questionnaire. The next part of the questionnaire covers the quality of the continuing vocational training offered by the businesses. The firmsthat provided no training are asked in a fifth section about the reason of this non-provision of training. Initial vocational training (IVT) is the aim of the last part of the questionnaire. Thus, the CVTS questionnaire has a complex structure. The firms have to answer different sets of questions depending on what kind of CVT they offer. Three profiles of companies are therefore set by this structure: the non-training firms, the training firms and the firms offering only CVT courses. This structure had to be taken into account when realizing multiple correspondence analyses. If Multiple Correspondence Analyses were run on the data without taking into account this structure, it would be the only visible result. The next figure explains the structure of the survey and helps to understand the different analyses carried out on the data. The firm offering Continuing Vocational Training courses have to answer questions from parts A to D and F. The training firms answer to sections A, B, D and F. Finally, the non-training companies have to fill up sections A, B, E and F of the questionnaire. Note that only parts A, B and F are answered by all the firms. Figure 1 : structure of CVTS4 questionnaire

5 Multivariate Analyses on Continuing Vocational Training in Luxembourg Economie et 3. Multiple Correspondence analysis on the data collected by the fourth Continuing Vocational Training Survey in Luxembourg 5 Keeping the structure of the questionnaire in mind, four analyses were selected to be explained in this paper. Those analyses consist in a hierarchical clustering based on the principal component of a multiple correspondence analysis carried out on the data. An explanation of those two techniques is available in the appendix 1. In order to present those analyses, the data taken into account in the analyses will first be presented. Then, the groups identified by the clustering will be introduced. Afterwards a parallel with the multiple correspondence analyses will be made. The number of dimensions kept for the hierarchical clustering is based on the number of variables taken into account in the multiple correspondence analyses. The dimensions which have eigenvalue superior to the reciprocal of the number of variables are kept for the hierarchical clustering. Only the two first dimensions are commented here. More technical data (eigenvalues, contribution, cosine 2 and correlation ratio) are available and commented in the second appendix. The first analysis takes into account all firms included in the study and focuses on the firm background and their detailed training offer (parts A, B and F of the questionnaire). The second analysis studies the quality of the continuing vocational training (CVT) and the limiting factors of the offer from the firms that have organized CVT in 2010 (section D of the questionnaire). Those factors represent the different causes responsible for the restriction of CVT offer by the firms (e. g. lack of money, lack of suitable CVT on the market ). All the companies offering at least one type of CVT, the training firms, will be selected for this analysis. The study of section C of the questionnaire, which focuses mainly on the skills and competencies targeted by the CVT courses, will be based only on the firms that offer CVT courses in The fourth and last analysis reviews the reasons of the non-provision of CVT by the non-training firms. 4. Analysis of the firm s background and their detailed vocational training offer The first selected analysis concerns all the companies of the study and takes into account variables from sections A (strategies in the matter of CVT, background information of the firm), B (the different kind of CVT offered by the firm) and F (presence of apprentice(s) in the firm) of the questionnaire. An explanation of the methodology of multiple correspondence analysis is available in the appendix 1, the numerical results are available in appendix 2. The questions taken into account in this analysis are all closed-ended questions. For most of them, the respondent will answer either yes or no. The derived variables for those questions are called binary, or dichotomous, variables. They can take only two values. In our case, if the answer is yes, the variable is coded 1. If the answer is no, the variable is coded 0. Those two possible answers are called modalities, or categories, of the variables. Each question is thus associated with one variable, which have two modalities: 1 if the answer is positive, 0 if it is negative. For other questions, the respondents are given the choice between three possible answers. In this case, the variables associated to those questions can take three different values, each one corresponding to the three possible choices. Those sections teach us that 48% of the firms have one or more persons in charge of the organization of CVT. More than 75% of the companies assess their needs of skills and competencies, and nearly 65% of them assess the ones of their employees. But only 35% of the firms develop a written training plan. In terms of provision for CVT, 41% of the participating businesses have an annual training budget. Agreements between social partners exist for 23% of the companies (17% of the firms do not know if such agreement exists). The detailed offer of CVT is also enquired in the Continuing Vocational Training Survey (CVTS) questionnaire. 56% of the firms do offer internal

6 Economie et Multivariate Analyses on Continuing Vocational Training in Luxembourg 6 courses to their employees. External courses are available in 66% of the businesses. Another kind of CVT is the Guided on the job training which is offered by 46% of the firms. Job rotation, exchanges or study visits are used by 16% of the firms. 46% of the companies suggested conferences, workshops, trade fairs or lectures. Learning or quality circles exist in 17% of the companies. 21% of the businesses offer selfdirected learning or e-learning to their employees. Finally, 25% of the firms had one or more apprentice in 2010 (initial vocational training IVT). The hierarchical clustering based on the 5 first principal components of the MCA identifies three groups of businesses. Details concerning this method of clustering are available in the appendix. Those three groups are represented on Figure 2. The firms from the first group are located on the left hand part of the two dimensional map (cluster 1). 35% of the businesses belong to this cluster. We will call them the non-training firms. The companies in the cluster near to the origin (cluster 2) are most likely training firms that assess their future skill needs and the ones of their employees, but they do not have specific ways of doing it. 30% of the firms belong to this group. They will be referred to as the firms offering unplanned training. The last group (situated in the right handed part of the map) includes 35% of the whole companies. Those companies will be called the organized training firms. Figure 2: Hierarchical clustering on principal components from the first MCA

7 Multivariate Analyses on Continuing Vocational Training in Luxembourg Economie et As we look at the next display (Figure 3), which represents the firms and the variables on a single plane, a clear distinction appears between two groups of modalities. We find all negative answers (coded 0) on the left side of the first factorial axis, while the positive ones (coded 1) appear on the right side. The firmsrepresented on the left side tend to answer no to the questions taken into consideration in this analysis. On the other side, the firms located on the right are more likely to answer yes to the questions taken into consideration in this multiple correspondence analysis (MCA). We can associate the first axis (the horizontal one) to the continuing vocational training profile of the companies: the firms offering CVT tend to have positive values for the first dimension; they are located on the right-hand side of the display, like the firms of the organized training cluster. In opposition, the non-training firms tend to have negative values for it and therefore tend to be located on the left-hand side of the map. The second dimension can be linked with the offer of Initial Vocational Training (IVT). Firms that tend to offer IVT have positive values on the 2 nd dimension; they are located on the upper part of the map. The companies from the unplanned training group are situated in that part of the map. The respondents that do not offer IVT tend to have negative values on the 2 nd dimension; they are represented on the lower part of the display. Supplementary, or illustrative, elements can be added to the factorial maps. Those elements are added on the map after its construction. They do not intervene in the construction of the principal components. Illustrative variables are added to the map to enrich or to help the interpretation of the data. The projection of the economic activities on the two dimensional map as illustrative variable shows that all the categories are represented near the origin of the display (see Figure 4). 7 Figure 3 : Multiple correspondence map of the two first dimensions of the MCA based on all the firms included in CVTS4 Firm s background Detailed CVT (Continuing Vocational Training) offer A8 Specific person or unit responsible for the planning of CVT (Continuing Vocational Training) B1a Provision of internal CVT courses B1b Provision of external CVT courses A9 Assessment of skill needs of the firm B2a provision of guided on the job training A11a Review of skill and training need of the employees B2b provision of job rotation A13 Written training plan or program of the CVT offer B2c provision of conference A14 - Annual training budget B2d - provision of learning &/or quality circles A15 Agreements betw een social partners B2e provision of self-directed learning F1 provision of Initial Vocational Training (IVT)

8 Economie et Multivariate Analyses on Continuing Vocational Training in Luxembourg 8 Figure 4 : Projection of the economic activities 7 categories of economic activities are taken into consideration: label Economic activity Corresponding NACE NACE 1 Metal fabrication industry and machine manufacturing C24 to C30 & C33 NACE 2 Other manufacturing industry C10 to C23, C31 & C32 NACE 3 Construction F NACE 4 Wholesale, retail and hospitality G45 to G47 & I NACE 5 Transportation and communication organisations H & J NACE 6 Financial sector and other services K64 to K66, L, M, N, R & S NACE 7 Ressources & energies B05 to B09, D & E This observation reflects a similar behavior through those sectors. The only exception is the financial sector, which tends to have higher values for the first dimension. In other words: the firms from the financial sector tend to offer more CVT than the ones from the other sectors. As we look at the original data, we could see that 92% of the companies in the financial sector offer continuing vocational training to their employees (only 77% if all the sectors are taken into account). No particular sector seems to be linked to one of the three clusters. Nonetheless, it seems that companies from the financial sector are more likely to be found in the group of the organized training firms. The size of the firm can also be included as illustrative variable (Figure 5). It is linked to the first dimension of the MCA. The smaller categories of size are found on the left-hand side of the map, while the largest categories are found on its right-hand side. The map confirms the relationship between the offer of CVT and the number of employees: bigger firms are more likely to offer continuing vocational training to their employees than smaller ones. Nontraining firms will therefore tend to have smaller size than the organized training firms.

9 Multivariate Analyses on Continuing Vocational Training in Luxembourg Economie et Figure 5 : Projection of the size's categories of the firms 9 Summary This first multiple correspondence analysis (MCA) allows to take a look at the data with a different perspective. It confirms the expected relationships between the variables and that difference exists between training and nontraining firms. It shows that three different groups of firms can be identified. First, there are the non-training firms. They are located on the lower left side of the two dimensional map. Those firms tend not to offer any continuing vocational training (CVT) to their employees. They are not linked to any particular economic sector, but the businesses tend to have small sizes (less than 50 employees). Their location on the map shows a tendency of no assessment of the need of skills and competencies for the firm or at individual level. The companies in this cluster seems to ignore the existence (or non-existence) of an agreement between social partners which could cove provisions for CVT. Then, there are the firms offering unplanned training which are located near the origin of the two dimensional map. Those companies tend to offer trainings, but they have no precise way of doing it. Those firms tend to have at least one apprentice and seem not to have any agreement between social partners for the provisions for CVT. Finally, the third cluster is tagged organized training firms. The firms from this group tend to offer training to their employees and to have a specific way to organize them. They are more likely to assess the future skill needs of the firm as part of overall planning process. Those businesses also have the tendency of assessing the individual needs with the use of structured interviews. They generally write a training plan or program for CVT and include provisions for CVT in their annual training budget. They tend to have national, sectorial or other agreement between the social partners, which usually covers the provision of CVT. Self-directed learning and e-learning are more likely to be offered by the firms from this group. The ways the questions are framed have consequences on this kind of analysis. We observed an opposition between the positive and the negative modalities of the variables. This phenomenon is a consequence of the wording of the questions. Even without asking the questions we can predict that the training firms will tend to answer yes to them, but the non-training firms will tend to deny them. It is not really an issue for the MCA itself, but one could ask if the businesses, while answering the questionnaire, really paid attention to the questionnaire or if the tendency to acquiesce has a role in the distribution of the answers. Maybe changing the wording of those questions will have an influence on the results. It will also be interesting to add questions focusing on potential explanation for

10 Economie et Multivariate Analyses on Continuing Vocational Training in Luxembourg 10 the non-provision of CVT and the limitation of CVT offer. Those questions exist in the questionnaire, but they are not asked to both training and non-training firms. Thus, we cannot analyze them together. An idea could be to reframe those questions so that training and non-training firms answers exactly the same questions. 5. How do the firms assess the trainings and what limits the provision for CVT? The next analysis includes only the training companies. It takes into account the questions about the assessment of the quality of the continuing vocational training (CVT) and the factors limiting the provision of CVT. We already know that those firms tend to have more employees than the non-training one and that all economic activities are represented. The questions taken into account in this second analysis are also closed-ended questions. The respondent has to select either one or many choices from a list. A variable is created for each of those choices, so that there are as many variable as there are choices. The derived variables are binary variables: if the respondent has selected a given choice, the variable is coded 1 ; if not, the variable is coded 0. The firms could choose several items to describe how they assess the quality of the CVT. 37 % of them based themselves on the certification of the external providers. 26% train their internal trainers. The CVT and the certification based on national or sectorial recognized standards stand as a quality assessment for nearly 37% of the training firms. 25% consider other facts to assess the quality of the CVT. Finally, 20% of the companies do not consider any aspect of the CVT to ensure their quality. The section of the questionnaire concerning the training companies also enquires the limiting factors for the provision of CVTs. The firms could select different aspects in a list of 9 items. In the end, 30% of them had offered as much CVT as needed by the firm. 20% of the companies recruited employees based on their skills and competencies so that no training was needed. The difficulty of assessing training needs was critical for 6% of the businesses. No suitable CVT courses were available for 13% of them. The costs of the CVT were too high for nearly 27% of the firms. 5% of the companies prefer to focus on the provision for IVT, 7% had made major efforts in the past years. For 32% of the companies, no time was available to provide CVT to the employees. Finally, nearly 15% of the firms called for other reasons. Another kind of question was used to study the assessment of the outcomes of the CVT. The respondent had the choice between three answers, but he had to select only one option. The coding for this kind of variable is slightly different. The variable has three modalities, each one corresponding to the three possible answers. The outcomes of the CVT are assessed for all activities by 23% of the firms, for some of the activities by 36% of them. 41% of the companies consider the participation enough to ensure the outcomes of the CVT or did not answer the question. It should be noted that among the different variables, a recurrent phenomenon occurs: the frequencies for the different modalities are unbalanced. We say that modalities are unbalanced when the proportions of answers for each modalities differs widely. For example, 5% of the firms have limited provision of CVT because they prefer to focus on IVT. This means, that on the other hand, 95% of the firms do not. In such cases, the modalities are described as unbalanced. The consequence of unbalanced categories is that the two modalities of one binary variable, displayed on the factorial map of the multiple correspondence analysis (MCA), will not be equidistant in regards with the origin of the graph. In this kind of display, the modalities located near the origin are the ones chosen by most of the respondents. The ones located on the outskirts are the ones chosen by a reduced number of respondents. In such cases, the modality with the small frequency will have more weight in the MCA for the construction of the principal components than the more frequent modality. But the real issue is that the results are therefore unstable, as the dimensions are influenced only by a few firms. The conclusions have therefore to be taken as cautiously as possible and cannot be generalized.

11 Multivariate Analyses on Continuing Vocational Training in Luxembourg Economie et Figure 6 : Hierarchical clustering on the principal components of the second MCA 11 Three tendencies emerged from the hierarchical clustering (Figure 6). The first group is located on the upper left corner of the map. 30% of the firms belong to this cluster. The firms located in this area correspond to a group that we can call No assessment and other limits, as they tend not to assess the quality of the CVT or to assess it only by checking that the participants attended the trainings. They also are more likely to choose other factors to explain the restriction of their CVT offer. The next cluster (cluster 3 in figure 6) located on the lower part of the map will be labeled as Assessment and no limit. It is composed by 26% of the companies included in the analysis. Those companies tend to offer as much training as needed by the firms or the employees. Finally, the third group represented as cluster 2 on the factorial map can be tagged with Assessment and limits. Those firms tend to call for different reasons explaining why they could not provide all the trainings needed by the firms or the employees. They also tend to use different ways of assessing the quality of the continuing vocational training offered. A particular pattern appears in this second MCA (see Figure 7) due to the unbalanced categories observed in the data. The positive modalities of the variables taken into account (the ones which equals 1) are located on the outskirts of the map, while the negative modalities are located near the origin. Thus, we can say that the firms have a tendency to answer no to the questions taken into consideration. The axes are mostly defined by few companies which did not answer like the majority: as the descriptive statistics showed, their proportions vary between 5% and 37%. In practical terms, this means that we have to be careful while interpreting those results, particularly concerning the limiting factors of CVT, which show the more unbalanced frequencies. An opposition appears between three kinds of answers regarding the limiting factors of the CVT offer. First, some firms do not limit the provision of CVT (D3a = 1). They tend to belong to the No limit cluster. They consider that their offer of CVT is not limited by any factors. Their offer is consistent with their needs. Then, there are the firms that call for other reasons, which are more likely to be in the No assessment and other limits group. Those companies seem to have restricted their CVT offers, but they did not find any suitable reason for this limitation in the list of suggestions. The last type of answers concerns firms, which have selected one or more reasons from the list of choices. They tend to found in the Assessment and limit cluster.

12 Economie et Multivariate Analyses on Continuing Vocational Training in Luxembourg 12 Figure 7 : Factorial map of the two first dimension of the MCA carried out on the training firms D1 Aspects considered to ensure the quality of CVT [1 = Yes; 0=No] D1a certification of external providers D1b continuous training of internal trainers D1c CVT and certification is based on national/sectorial recognized standards or framew orks D1d Others D1e Does not consider any particular aspect to ensure the quality of CVT D2a Assessment or documentation of the outcome of CVT D2a_0 - no, confirmation of participation is sufficient/no answ er D2a_1 - yes, for all activities D2a_2 - yes, for some activities D3 factors limiting the provision of CVT activities [1 = Yes; 0=No] D3a No limiting factors D3b Preferred to recruit individuals w ith the required skills and competencies D3c Difficulties in assessing training needs D3d Lack of suitable CVT courses D3e High costs of CVT D3f Higher focus on IVT provision D3g Major efforts in CVT realized in recent years D3h No available time for participation in CVT D3i - Other reasons Regarding the aspects taken into consideration for assessing the CVT, three patterns of answers emerge from this analysis. First, the companies taking into consideration no particular aspects to assess the quality of the CVT (D1e) are located in the upper-left corner of the two-dimensional map. They correspond to the No assessment and other limits group of firms. The second pattern of answer concerns he firms which do take into account the certification of the external trainer (D1a), the training of the internal trainer (D1b) and the standard certification of the CVT (D1c). Those modalities are aggregated in the lower-right part of the display. Finally, the last modality, which corresponds to other factors (D1d) to assess the CVT offer, is found near the origin of the map. This last pattern can be seen as an intermediate behavior of the firms. A link exists between the size of the firms and the two first dimensions of the MCA (see Figure 8). The smallest companies appear on the upper-left part of the display. The No assessment and other limits group tends therefore to have a higher proportion of smaller firms than the other groups. On the other hand, the bigger firms tend to be located in the lowerright part of the map. The smaller firms tend to take no particular aspects of CVT into consideration to assess their quality. To assess

13 Multivariate Analyses on Continuing Vocational Training in Luxembourg Economie et the outcomes of CVT, smallest firms tend to consider only the confirmation of participation. The biggest firms tend to have a different behavior in terms of assessment. They are more likely to assess their CVT by checking the training of the internal trainers, the certification of the external trainers and/or the CVT itself. Biggest firms also document the outcomes of all their CVT. But no link can be highlighted between the size of the firms and the factors limiting the provision for CVT. All the economic activities are represented close to the origin of the map (see Figure 9), which means that no clear difference between them can be suggested. However, the energies and resources firms are more likely to say that their offer of CVT is not limited by any factors, than the firms from other sectors. They are more likely to belong to the Assessment and no limit group. Summary Three groups have been identified by the hierarchical clustering. But as the modalities of the variables taken into account are unbalanced, the results have to be interpreted cautiously. First, the No assessment and other limits cluster corresponds to firms which have a tendency not to take any particular aspects into consideration to ensure the quality of the CVT. Those companies tend to assess the outcome of the CVT only by the confirmation of the participation of the trainee or did not say how they assess the outcome of CVT activities. They also tend to call for other factors than those listed in the questionnaire to explain their restriction of CVT offer. Smaller firms are more likely to be in this group. Then, the Assessment and no limit group of companies tends not to have any factors limiting their CVT offer. They tend to assess the outcome of the CVT and/or to document it. Large firms seem to be more numerous in this cluster. Finally, the firms from the Assessment and limits cluster seems to limit their offer in CVT because of several factors: higher focus on IVT, lack of time, high costs, difficulty of assessing the need in CVT, no suitable CVT, efforts made in the past years. They also tend to ensure the quality of CVTs by promoting recognized CVT and by training the internal trainers. In regards to the outcome of the CVT, they do assess and/or document some of the CVT activities. Bigger firms are found more often in this cluster. Different issues have been highlighted by this analysis. They concern the wording and the structure of different questions. The structure of the question regarding the assessment of the quality of the CVT allows three different kinds of answers. First, some firms could answer that they do not assess at all the quality of CVT, while the others systematically assess the quality. Beside those two types of answers, a third one can be identified: the firms which assess the quality of CVT by other criteria than those suggested in the questionnaire. As a firm answers other factors, it will not select any other possibility. Companies that say that they do not assess the quality of the CVT, will also select only one answer among the list of choices. This structure stands out in the MCA. As a result, the only thing that we can say is that some of the firms do assess the quality of CVT by one or more technique given by the list; some of the companies do assess the quality by other means; and some do not assess at all the quality of CVT. As 25% of the firms say that they use other aspects than those listed in the questionnaire, it will be interesting to update the choices so that we can understand better the way the CVT are assessed by the companies. In term of factors restricting the offer of CVT, differences and associations have been identified. The clustering highlighted three groups that differ in terms of those restricting factors. First, the firms that do not have any restricting factors. Then the ones that choose one or more factors amongst the different choices. And finally, the companies that called for other factors. Here again, the structure of the question stands out in the analysis. An update of the different choices proposed in the questionnaire could help to highlight differences based more on the behavior of the firms that on the structure of the question. This analysis shows that the structure of the questions does not allow to determine how the companies assess the quality of their CVT, or to identify the limiting factors of their CVT offers. The only thing that can be extracted from the data is whether or not they assess the quality of the CVT/they limit their CVT offer. And if they do: if the suggested choices fit what they want to answer, or if they select other reasons / other factors. 13

14 Economie et Multivariate Analyses on Continuing Vocational Training in Luxembourg 14 Figure 8 : Projection of the size's categories of the firms Figure 9 : Projection of the economic activities

15 Multivariate Analyses on Continuing Vocational Training in Luxembourg Economie et 6. Skills targeted by the CVT courses in Luxembourg 15 The third selected analysis concerns only the firms, which have offered continuing vocational training (CVT) courses during Among the topics covered by the section of the questionnaire asked only to this profile, was the skills targeted by the CVT courses. Twelve categories were suggested to the firms, which could select the appropriate items. 47% of the companies offered CT courses which focus on general information technologies, 24% on professional information technologies. CVT courses on management were offered by 35% of the companies, courses on team working by 37%. Courses targeting customer handling skills were planned by 42% of the businesses. The CVT courses offered by 31% of the firms were related to problem solving skills. Office administration skills were covered by courses offered by 25% of the companies. Foreign languages were part of the skills targeted by 34% of the firms. Technical, practical or jobspecific skills were the focus of the courses offered by 78% of the companies. Oral and communication were targeted by the courses of 20% of the companies, while numeracy and/or literacy skills were the focus of the courses offered by only 6% of the firms. Finally, 5% of the firms targeted other skills and competencies with their CVT courses. We could expect different things from the clustering of this analysis. For example, we could hope to see differences trough the economic sectors, as the skills needed are not the same in the financial services and the manufacture activities for instance. We also could hope to see oppositions and associations between different skills which does not seem to concerns similar profiles. But the results are a bit different. Two groups can be identified, as shown by the map derived from the hierarchical clustering (Figure 10). First, we find on the right side of the display the firms which targeted skills that they have found in the different choices available. We will call them the At least one of the suggested skills groups. The firms which answered no to all the choices but yes to the other category belong to the second group, tagged Other/None of these, represented on the left side of the map. Figure 10 : Hierarchical clustering on the principal components of the third MCA

16 Economie et Multivariate Analyses on Continuing Vocational Training in Luxembourg 16 Figure 11 : Factorial map of the two first dimension of the MCA carried out on the firms offering CVT courses Almost all negative modalities (coded 0 ) are located on the left side of Figure 11. The only exception concerns the positive modality of the variable Other/None of these (C5l_1), represented on the upper left side of the factorial map of the multiple correspondence analysis (MCA). This means that the firms located on the left side of the display tend to choose the Other/None of these modality. The companies located on the right side are more likely to identified specific skills among the suggested skills. But it is difficult to identify skills that tend to be chosen simultaneously; or on the contrary, skills that tend to be chosen from different kind of firms. Only two main oppositions can be identified. Firms which selected Other/None of these tend to have negative coordinates on the first axis, while the others tend to have positives coordinates. Concerning the second dimension, companies which targeted technical, practical or job-specific skills tend to have positive coordinates, while the others are more likely to have negative coordinates on this second axis. Figure 12 shows that the firms displayed on the left side of the factorial map tend to be smaller than the ones located on the right side of the displays. Thus, the bigger firms seem to choose skills from the list of choices, but the smaller ones tend to offer training targeting other skills than those suggested in the questionnaire. In terms of economic activities, the different sectors are all displayed near the origin of the factorial map (Figure 13). The financial and other services sectors tend to be located more on the right part than the other sectors, but no clear difference can be identified. The suggested answers are one of the reasons, if not the main reason, of the pattern observed in this analysis. The firms could select more than one skill through the possibilities. Thus, each skills, each possibility, corresponds to one variable in the data set. Among the choices available for the companies was Other skills/none of these. A pattern is therefore created: the businesses which answers Other skills/none of these select only that possibility. As a result, those firms have not only one variable in common, but all twelve variables taking into account in this analysis. This pattern of answer will strongly influence the construction of the axis. The projections of those companies on the factorial map are located at the same place. The other firms (the one tagged At least one of the suggested skills ) can select more than one skill. The patterns their answer are thus more diversified: some of them will select only one skill, but other will select up to 11 skills. Thus, all those different patterns of answers will have less weight on the construction of the factorial axes.

17 Multivariate Analyses on Continuing Vocational Training in Luxembourg Economie et Figure 12 : Projection of the size's categories of the firms 17 Figure 13 : Projection of the economic activities

18 Economie et Multivariate Analyses on Continuing Vocational Training in Luxembourg 18 Summary This analysis is therefore a perfect example of multiple correspondence analysis (MCA) that is difficult to interpret because of the structure of the questionnaire. Analyzing this kind of question using MCA will enlighten its structure. But no relationships between the different variable can be identified. We cannot link any topic of CVT courses together, nor determinate profiles of companies that tend to offer CVT courses targeting a specific skills. The only fact that this MCA shows is that there is an opposition between the firms that could identified skills in the list suggested in the questionnaire tagged At least one of the suggested skills - and other than could not - the Other skills/none of these group. It could be interesting to change the wording of this question to see the consequences that it could have on the answers. A first possibility could be the remove the Other skills/none of these category and to replace it with categories that are not yet included in the list of choices. Another way of changing the question is to standardize the different choices, so that they all describe comparable skills. The actual choices are indeed un-harmonized. For example, as foreign languages describe skills quiet easy to understand and unambiguous, technical, practical or job-specific skills is a category more general that could include all kind of skills. 7. Why do some firms not provide any CVT in Luxembourg? The last analysis that will be presented concerns the non-training firms. A section of the questionnaire covers the reasons for this nonprovision of the continuing vocational training (CVT). The original data give us already some information. First of all, those firms have less than 250 employees. All the economic activities included in the sample are represented in the non-training group. The businesses could choose between nine reasons that explain the non-provision of CVT. Nearly 75% of them did not offer CVT in 2010 because the existing competencies and skills were appropriate to the current need of the company. 34% prefer to hire people who already have the skills and competencies needed by the firm. 5% of the non-training companies had difficulties in assessing their need of CVT. 3% of them could not find suitable CVT to their need. 14% of the firms find that the costs of CVT were too high, while 20% of them said that there was no available time for participating in CVT. 6% of the companies explain the lack of CVT provision by the fact that higher focus is made on IVT provision, 2% by the fact that major efforts were made in the last years. Finally, 18 % the businesses called for Other reasons. The hierarchical clustering on principal component enables to identify three groups represented in Figure 14. For the first group: CVT may be a solution, but the needs are not defined, major efforts were already done in the past years, etc. 25% of the non-training companies belong to this cluster.the firms from this cluster will be tagged Undefined CVT needs. The firms from the second groupcorrespond to 18% of the non-training firms. They have chosen other strategies than CVT: the companies have found solutions elsewhere (higher focus on IVT, recruitment of persons already having the skills needed ); CVT seems to be inappropriate for them (too expensive, not enough time, lack of suitable CVT on the market ). This cluster will be labeled with Practical reasons. Finally, the remaining 57% of the non-training firms are the ones (in green on the map) who did not offer any training because the skills and competencies available suit already their needs. Their label will be Skills already appropriate. Nearly all the negative modalities are located near the origin of the factorial map of the multiple correspondence analysis (Figure 15). The only exception concerns the modality which expresses the lack of CVT need of the firms (E1a_1). This means that most of the firms do not offer CVT in 2010 because the existing skills and competencies were judged appropriate to their current needs. Those companies tend to have positive coordinates on the second dimension. Besides this general observation, two tendencies can be identified: the companies who are likely to select reasons D (lack of suitable CVT in the market), E (high costs of CVT), F (higher focus on IVT provision than on CVT) and/or H (no available time for participation in CVT). The second tendency regroups the firms who tend to choose I (other reasons), G (major efforts in CVT realized in previous years) and/or C (difficulties in assessing training needs). Those firms are more likely to have negative coordinates on the first axis..

19 Multivariate Analyses on Continuing Vocational Training in Luxembourg Economie et Figure 14 : Hierarchical clustering on the principal components of the fourth MCA 19 Figure 15 : Factorial map of the two first dimension of the MCA carried out on the non training firms Reasons for the non provision of CVT E1a The existing skills were already E1g Major efforts in CVT realized in recent appropriate years E1b Preferred to recruit individuals with the E1h No available time for participation in required skills and competencies IVT E1c Difficulties in assessing training needs E1i Other reasons E1d Lack of suitable CVT courses E1e High costs of CVT E1f Higher focus in IVT

20 Economie et Multivariate Analyses on Continuing Vocational Training in Luxembourg 20 Figure 16 shows that the smaller non training firms (less than 50 employees) tend to answer like the majority of the non- training firms: they did not offer CVT in major part because the skills and competencies were already appropriate to their needs. The non-training companies with more than 50 employees tend to have a different behavior and tend to call for Other reasons to explain their lack of CVT offer. They explain this lack of provision by a major effort realized in previous years, difficulties of assessing the need in CVT and other reasons. They correspond to the Undefined CVT needs cluster. Figure 16 : Projection of the size's categories of the firms Figure 17 : Projection of the economic activities

21 Multivariate Analyses on Continuing Vocational Training in Luxembourg Economie et In terms of economic activities (see Figure 17), the firms from the sector resources and energy (electricity, gas, steam and air conditioning supply, mining and quarrying) tend to have a slightly different behavior and to select more practical reasons for the lack of CVT (high cost, lack of time, no appropriate CVT and higher focus on IVT), which correspond to the Practical reasons group. The firms from the financial sector also deviate from the average and tend to call for Other reasons, like the companies of more than 50 employees. Those companies tend to belong to the Undefined CVT needs cluster. The businesses from the other sectors tend to already have skills and competencies appropriate to the needs of the firm, which explain the lack of provision for CVT. Summary Different profiles of firms have been determined amongst the non-training companies. Three patterns of answers concerning why they do not have provided any CVT have been determined. The first reason concerns some of the nontraining firms which deliberately decide not to offer CVT because the skills and competencies available already suit their needs. They have been tagged Skills already appropriate. A second group concerns the Practical reasons firms. Those companies seem to have found other solution to meet their needs: higher focus on IVT, recruitment of persons already having the skills needed, etc. Some of them did not found CVT that fits their needs (too expensive, not enough time, lack of suitable CVT on the market ). 21 The third pattern tagged Undefined CVT needs - corresponds to companies which seem to have difficulties to see continuing vocational training as an appropriate solution for their needs. Those different profiles seem therefore to need different approaches to improve their CVT offer. It could be interesting to use those results in order to help the firms in regards to what they really need. For some of them, CVT more adjusted to their needs can be developed.