Study Guide Module 1 Key Terms general linear model dummy variable multiple regression model ANOVA model ANCOVA model confounding variable squared multiple correlation adjusted squared multiple correlation semipartial correlation standardized slope multivariate general linear model MANOVA model MANCOVA model SUR model path model mediator variable exogenous variable endogenous variable direct effect indirect effect total indirect effect recursive model nonrecursive model conditional direct effect conditional indirect effect GOF test studentized deleted residual multicollinearity variance inflation factor DFBETAS Cook s D missing completely at random missing at random listwise deletion modification index
Concept Questions 1. What does controlling for mean when interpreting a test or confidence interval result for β j in a GLM? 2. What is the consequence of omitting an important confounding variable in a GLM when interpreting a test or confidence interval results for β j? 3. In a GLM y = Xβ + e with n = 8 and q = 2, a) what are the elements in y? b) what are the elements in X? c) what are the elements in β 4. For the MGLM Y = XB + E, a) what is the order of Y if there are 30 participants and 2 response variables? b) what is the order of X is there are 60 participants and 3 predictor variables? c) what is the order of B if there are 2 predictor variables and 4 response variables? 5. Why is it important to report a confidence interval for the squared multiple correlation and not just a sample value? 6. For what type of model would η 2 be an appropriate measure of association? 7. Why are semipartial correlations useful? 8. Draw a path diagram (with y-intercept) for a GLM with q = 2. 9. How does a MGLM differ from a GLM? 10. Draw a path diagram (without y-intercepts) for a MGLM with q = 2 and r = 3. β 01 11. Suppose the parameter matrix of a MGLM is B =[ β 11 β 21 β 02 β 03 β 12 β 22 β 13 ]. β 23 For a multivariate general linear contrast c Bh, give the values of c and h that will define the following contrasts: a) (β 11 β 21 ) (β 12 β 22 ) b) (β 21 + β 22 )/2 β 23 c) (β 11 + β 22 )/2 (β 13 + β 23 )/2
12. What is the main difference between a MGLM and A SUR model? 13. What is the main difference between a SUR model and a path model? 14. Explain the difference between an indirect effect and a direct effect. 15. How could you show that the population values of all included paths are meaningfully large? 16. How could you show that the population values of all excluded paths in a SUR or path model are small or unimportant? 17. What can one conclude if the test for H0: B* = 0 is significant? 18. What are the assumptions for tests and confidence interval for unstandardized slope coefficients in the fixed-x GLM? 19. What are the assumptions for confidence intervals for the squared multiple correlation and unstandardized slope coefficients in the random-x GLM? 20. How are qualitative factors represented in a GLM? 2 2 21. Why is the adj ρ y.x preferred to ρ y.x? 22. If the correlations among all the predictor variables are very small, how would the value of the standardized slope for x j compare to the Pearson correlation between y and x j? 23. What is the main difference between a recursive path model and a nonrecursive path model? 24. If there are a total of 6 variables (predictor variables plus response variables), what is the maximum number of slope and covariance parameters that can be estimated? 25. Why are modification indices useful?
Module 2 Key Terms alternate form reliability test-retest reliability inter-rater reliability internal consistency reliability Spearman-Brown formula measurement error factor loading strictly parallel measurement model parallel measurement model tau-equivalent measurement model congeneric measurement model communality standardized factor loading confirmatory factor analysis model exploratory factor analysis scree plot structure matrix pattern matrix orthogonal rotation varimax method oblique rotation promax method direct oblimin method goodness of fit function ML estimation ULS estimation principal axis extraction Cronbach s alpha coefficient McDonald s omega coefficient chi-squared goodness of fit test chi-squared model comparison test Satorra-Bentler scaled chi-square robust standard errors bootstrap standard errors
Concept Questions 1. What is the effect of measurement error in y and x on ρ yx? 2. What is the effect of measurement error in x on β 1 in a simple linear regression model? 3. What is the effect of measurement error in y on the confidence intervals for β 1? 4. Explain the difference between the strictly parallel and parallel measurement models. 5. Explain the difference between the parallel and tau-equivalent measurement models. 6. Explain the difference between the tau-equivalent and congeneric measurement models. 7. Why are standardized factor loadings useful? 8. What is the maximum number of parameters that can be uniquely estimated in a factor analysis model with r = 5 observed variables? 9. Draw a path diagram of a factor analysis model with correlated factors, uncorrelated unique factors, factor 1 predicting y 1 and y 2, and factor 2 predicting y 3 and y 4. 10. What is the main difference between a confirmatory and exploratory factor analysis? 11. What is the difference between an orthogonal and oblique rotation? 12. Why is it important to report a confidence interval for the population value of Cronbach s alpha instead of just reporting the sample value? 13. How can a screen plot be used to approximate the number of factors? 14. If the reliability of a single measurement of some attribute is.5, what is the reliability of the average of 3 equally reliable measurements of that attribute? 15. Suppose the Cronbach alpha reliability for a 6-item scale is.8 and assume the 6 items are equally reliable. What is the reliability of a single item? 16. Why are structure and pattern matrices the same with orthogonal rotation?
17. When would ULS estimates be preferred to ML estimates? 18. How can model modification indices be used in a CFA? 19. Why is a confidence interval for λ 1 λ 2 more informative that a test of H0: λ 1 = λ 2? 20. When would you consider using robust standard errors? 21. When would McDonald s reliability coefficient be preferred to Cronbach s reliability coefficient? 22. How could you show that the population error variances for three measures of some attributed are similar? 23. How could you show that the population factor loadings for three measures of some attributed are similar? 24. How could you show that the omitted population factor loadings in a CFA are small or unimportant? 25. How could you show that the included population factor loadings in a CFA are meaningfully large?
Module 3 Key Terms latent variable path model common method variance latent growth curve model level-1 model level-2 model baseline centering time-invariant covariate time-varying covariate multiple-group model measurement invariance NFI CFI TLI RMSEA equivalent models Concept Questions 1. What is the benefit of using a latent predictor variable? 2. What is the benefit of using a latent response variable? 3. What is the effect of measurement error on indirect effects? 4. Why is baseline centering often used in latent growth curve models? 5. Why might the CFI or TLI be preferred to the NFI? 6. Explain how fit indices are misused. 7. Explain how goodness of fit tests are misused. 8. Draw a path diagram of a MGLM with two latent predictor variables, two latent responses variables, with all latent variables having two indicators. Include all the parameters in the graphs.
9. Draw a path diagram of a path model where two latent predictor variables predict one latent response variable which predicts an observed response variable. The two latent predictor variables each have three indicators and the latent response variable has two indicators. Include all the parameters in the graphs. 10. Draw a path diagram of latent growth curve model with 3 time periods where ξ 1 predicts the latent intercept, ξ 2 predicts the latent slope, x 1 and x 2 are tau-equivalent indicators of ξ 1, and x 3 and x 4 are tau-equivalent indicators of ξ 2. Include all the parameters in the graphs. 11. What is the effect of kurtosis on the GOF test statistic and standard errors? 12. How could you show that the included paths in a latent variable path model are meaningfully large. 13. How could you show that the omitted paths in a latent variable path model are small or unimportant? 14. When would you consider using a bootstrap confidence intervals? 15. How can Group x Variable interaction effects be estimated in a multiple group model? 16. Why is a confidence interval for an average of unconstrained parameters preferred to a confidence interval for an equality-constrained parameter in a multiple-group design? 17. What is the minimum sample size requirement when using ULS estimation in a latent variable model with platykurtic or mildly leptokurtic data? 18. What is the minimum sample size requirement when using ML estimation in a latent variable model with platykurtic or mildly leptokurtic data? 19. What is the minimum sample size requirement when using a robust (mean adjusted or mean and variance adjusted) chi-squared GOF test with platykurtic or mildly leptokurtic data? 20. When would you use a latent variable growth curve model in lavaan rather than a mixed-effects model in SPSS or SAS?