Multiple Imputation and Multiple Regression with SAS and IBM SPSS

Transcription

1 Multiple Imputation and Multiple Regression with SAS and IBM SPSS See IntroQ Questionnaire for a description of the survey used to generate the data used here. *** Mult-Imput_M-Reg.sas ***; options pageno=min nodate formdlim='-'; title 'Multiple Imputation of Missing Data then Multiple Regression.'; run; PROC IMPORT OUT= WORK.IntroQuest DATAFILE= "C:\Users\Vati\Documents\StatData\IntroQ\IntroQ.sav" DBMS=SPSS REPLACE; RUN; Data Priapus; set IntroQuest; SATM_Miss = 0; If SATM =. then SATM_Miss = 1; proc means n nmiss; run; proc corr nosimple; var SATM_Miss; with statoph gender ideal nucoph year; run; The data are imported from an SPSS.sav file. The MEANS Procedure Variable Label N N Miss Gender Gender Ideal Ideal Eye Eye Statoph Statoph Nucoph Nucoph SATM SATM Year Year Pearson Correlation Coefficients Prob > r under H0: Rho=0 Number of Observations SATM_Miss Statoph Statoph Gender Gender MultReg_Mult-Imputation.docx

2 2 Ideal Ideal Nucoph Nucoph Year Year Note that missingness on SATM is associated with statphobia and year Proc MI seed=69301 out=midata; var statoph gender ideal nucoph SATM year; run; Proc MI is used to create five imputations. Data Set Method Multiple Imputation Chain Initial s for MCMC Start Prior Model Information Number of Imputations 5 Number of Burn-in Iterations 200 Number of Iterations 100 WORK.INTROQUEST MCMC Single Chain EM Posterior Mode Starting Value Jeffreys Seed for random number generator Missing Data Patterns Group Statoph Gender Ideal Nucoph SATM Year Freq Percent Group Means Statoph Gender Ideal Nucoph SATM Year 1 X X X X X X X X X X. X X X X. X X X X. X X X X X. X. X X X X X X X X X. X X X. X X

3 The most common pattern (aside from complete data) is missingness only on SATM. We have means for each of the patterns. Those missing data on SATM do not appear to differ much from those with SATM data. Below we have Expectation Maximization estimates of means and covariances. Missingness on SATM is related to statophobia, by the way. 3 EM (Posterior Mode) s _TYPE NAME_ Statoph Gender Ideal Nucoph SATM Year MEAN COV Statoph COV Gender COV Ideal COV Nucoph COV SATM COV Year Variance Information Variable Variance DF Relative Between Within Total Increase in Variance Fraction Missing Information Relative Efficiency Statoph Ideal Nucoph SATM Snip, snip. I have culled the rest of the text output from Proc MI. Proc Reg outest=mrbyimput covout; Model Statoph = gender ideal nucoph SATM year / stb; By _Imputation_; run; quit; Proc MIAnalyze; modeleffects intercept gender ideal nucoph SATM year; run; Here we used Proc Reg to conduct a multiple regression analysis on each of the five imputations Imputation Number= Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total

4 4 Variable Label Root MSE R-Square Dependent Mean Adj R-Sq Coeff Var DF Parameter Parameter s Standard Error t Value Pr > t Standardized Intercept Intercept Gender Gender Ideal Ideal Nucoph Nucoph SATM SATM < Year Year Multiple Imputation of Missing Data then Multiple Regression Imputation Number= Variable Label Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total Root MSE R-Square Dependent Mean Adj R-Sq Coeff Var DF Parameter Parameter s Standard Error t Value Pr > t Standardized Intercept Intercept Gender Gender Ideal Ideal Nucoph Nucoph SATM SATM < Year Year

5 Imputation Number= Variable Label Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total Root MSE R-Square Dependent Mean Adj R-Sq Coeff Var DF Parameter Parameter s Standard Error t Value Pr > t Standardized Intercept Intercept Gender Gender Ideal Ideal Nucoph Nucoph SATM SATM < Year Year Imputation Number= Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total Root MSE R-Square Dependent Mean Adj R-Sq Coeff Var

6 6 Variable Label DF Parameter Parameter s Standard Error t Value Pr > t Standardized Intercept Intercept Gender Gender Ideal Ideal Nucoph Nucoph SATM SATM < Year Year Imputation Number= Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total Root MSE R-Square Dependent Mean Adj R-Sq Coeff Var Variable Label DF Parameter Parameter s Standard Error t Value Pr > t Standardized Intercept Intercept Gender Gender Ideal Ideal Nucoph Nucoph SATM SATM < Year Year Proc MIAnalyze is used to pool the results from the multiple imputations. The variance in the scores is partitioned between that among imputations (A) and that within imputations (W). The Relative Increase in Variance (r) is the increase in variance due to having missing data imputed

7 (relative to the condition where no data are missing), 1 m r W 1 A, where m is the number of imputations. A related statistic, Fraction of Missing Information, is an index of how much more precise the parameter estimate would have been if there had been no missing data. Power will, of course, be greater when the fraction of missing information and relative increase in variance are small. The greater the number of imputations, the less the error and the greater the power, ceteris paribus. Relative efficiency tells you how much power you have for the number of imputations you have employed relative to what you would have if you used an uncountably large number of imputations. The MIANALYZE Procedure Variance Information Parameter Variance DF Relative Between Within Total Increase in Variance Fraction Missing Information Relative Efficiency intercept gender ideal nucoph SATM year Parameter 95% Confidence Limits DF Minimum Maximum t Pr > t intercept gender ideal nucoph SATM <.0001 year

8 Multiple Imputation with IBM SPSS 8 Analyze, Multiple Imputation, Impute Missing Data Values *Impute Missing Data Values. DATASET DECLARE IntroQ_Imputed. MULTIPLE IMPUTATION Statoph Gender Ideal Nucoph SATM Year /IMPUTE METHOD=AUTO NIMPUTATIONS=5 MAXPCTMISSING=NONE /MISSINGSUMMARIES NONE /IMPUTATIONSUMMARIES MODELS /OUTFILE IMPUTATIONS=IntroQ_Imputed. Multiple Imputation [DataSet] C:\Users\Vati\Documents\StatData\IntroQ\IntroQ.sav

9 9 Imputation Specifications Imputation Method Automatic Number of Imputations 5 Model for Scale Variables Linear Regression Interactions Included in (none) Models Maximum Percentage of 100.0% Missing Values Maximum Number of Parameters in Imputation 100 Model Imputed Values Imputation Results Imputation Method Fully Conditional Specification Fully Conditional Specification Method Iterations 10 Imputed Statoph,Ideal,Nucoph,SATM Not Imputed(Too Many Dependent Variables Missing Values) Not Imputed(No Missing Values) Gender,Year Imputation Sequence Gender,Year,Nucoph,Ideal,Stato ph,satm Nucoph Ideal Statoph SATM Type Linear Regression Linear Regression Linear Regression Linear Regression Imputation Models Model Missing Values Imputed Effects Values Gender,Year,I deal,statoph,s ATM 2 10 Gender,Year,N ucoph,statoph, 5 25 SATM Gender,Year,N ucoph,ideal,s 9 45 ATM Gender,Year,N ucoph,ideal,st atoph

10 10 At this point SPSS has created a new data set with the original data (imputation 0) and the imputed data (in this case, imputations 1 through 5). The cells with imputed scores fall are highlighted. At this point, all you need do is run the desired analysis. If that analysis is supported, it will automatically analyze the original data and each imputed set of data and give you convenient summaries of the results. DATASET ACTIVATE IntroQ_MultipleImputation. REGRESSION /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT Statoph /METHOD=ENTER Gender Ideal Nucoph SATM Year.

11 11 Model Summary Imputation_ Model R R Square Adjusted R Square Std. Error of the Original data a b b b b b a. Predictors: (Constant), Year, Nucoph, Ideal, SATM, Gender b. Predictors: (Constant), Year, Gender, Nucoph, SATM, Ideal ANOVA a Imputation_ Model Sum of Squares df Mean Square F Sig. Regression b Original data 1 Residual Total Regression c 1 1 Residual Total Regression c 2 1 Residual Total Regression c 3 1 Residual Total Regression c 4 1 Residual Total Regression c 5 1 Residual Total a. Dependent Variable: Statoph b. Predictors: (Constant), Year, Nucoph, Ideal, SATM, Gender c. Predictors: (Constant), Year, Gender, Nucoph, SATM, Ideal

12 12 Coefficients a Imputation_ Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta (Constant) Gender Original data 1 Ideal Nucoph SATM Year (Constant) Gender Ideal Nucoph SATM Year (Constant) Gender Ideal Nucoph SATM Year (Constant) Gender Ideal Nucoph SATM Year (Constant) Gender Ideal Nucoph SATM Year

13 13 Coefficients a Imputation_ Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) Gender Ideal Nucoph SATM Year (Constant) Gender Pooled 1 Ideal Nucoph SATM Year Coefficients a Imputation_ Model Fraction Missing Info. Relative Increase Variance Relative Efficiency (Constant) Gender Pooled 1 Ideal Nucoph SATM Year a. Dependent Variable: Statoph Karl L. Wuensch, October, 2017 Return to Wuensch s Stats Lessons Page Treatment of Missing Data recommended reading, David Howell.