Psychology 716 - Multivariate Statistics

1 Psychology 716 - Multivariate Statistics Review Sheet for Test 3 (Final Exam)

New material: Discriminant Function Analysis, Canonical correlation, Factor Analysis, Path Analysis, and Structural Equation Modeling

In addition, major points from across the semester (see below)

Be able to determine which form analysis is appropriate for a given research question

For significance tests, know the null hypotheses that are being evaluated. You don’t need to know statistical notation, but know, for example, that the sig test (Wald test) for a slope in a logistic regression reflects our willingness to reject the null hypothesis that the slope in the population is zero (what would the null hypothesis be, in terms of the odds ratio?).

Readings o DFA 7A, 7B o Exploratory Factor Analysis 12A, 12B o Canonical correlation 193-195 o Confirmatory Factor Analysis 13A, 13B (just to get a sense of results) o Path Analysis & SEM 14A

Discriminant Function Analysis o Purpose o Read and interpret key SPSS output (eg coefficients in a structure matrix, canonical discriminant function coefficients) o Read and interpret a description of results (eg, from a journal article)

Exploratory Factor Analysis o Purpose o What is the trade off in terms of parsimony and “completeness” o Key questions in EFA o Key decision points in conducting an EFA, and the relevant information o Types of extraction o What is the basic difference between PCA and Factor analysis, in terms of what is causing what (see the CFA chapter for more about this) o Scree plot o What exactly is plotted? o Interpreting the plot o Rotation o What is rotation used for? o Kinds of rotation – . what are the two basic forms of rotation and how do they differ? . Specific rotational strategies (varimax, promax, oblimin) - o Factor loadings o What do they represent? o What are they used for? o Roughly, what size factor loading suggests that a variable loads on a factor? o Structure vs pattern coefficients o What is a “clean” structure (ie, simple structure)? o Why is factor analysis often a back-and-forth process? o Interpret SPSS output 2 o Interpret results presented in an article o Be able to “eyeball” a correlation matrix and speculate about the factor structure (number of factors, which variables load on which factors, correlations among factors

Canonical Correlation o Purpose o Read and interpret key output o Canonical correlations – what are they? o Significance tests of canonical correlations o Structure coefficients – in relation to latent variables/factors o Draw a model, based on output o Interpret results with regard to a given hypothesis o Read and interpret a description of results (eg, from a journal article)

Confirmatory Factor Analysis o Purpose o What is hypothesized in a CFA analysis? What needs to be articulated in specifying a model? o What parameters are generally estimated? o CFA does at least 3 basic things: 1) Evaluate the overall quality of the Model: o What is “fit”? Where does an “implied corr/covariance” matrix come from? What are residuals? What does the size of a residual represent? How are residuals related to modification indices and fit (in general)? o Fit indices (three different kinds) o Interpret – chi square, NFI, RMSEA. – which values reflect good fit? Problem with X2? 2) Provide parameter estimates o what parameters are generally estimated? o Interpreting parameter estimates 3) Provide modification indices o What are these? how are they used? o Explain what a CFA model implies a. (eg, what does it imply about the association between LVs and MVs) b. What do the elements represent (circules, arrows, etc) o Draw a model, based on a verbal description of the model o Meaning of common and unique factors o What is the trade off in terms of parsimony and “completeness” o Steps/process of a CFA o Reading & interpreting results presented in an article

Path Analysis and Structural Equation Modeling o Purpose o Similarity to CFA (model testing, model fit, parameter estimation, etc) o Different modes of conducting path analysis (logic, differences, current use?) o Series of regression o Model testing (what do we get from this mode that we don’t get from regression mode?) o Differences/overlap among CFA, PA, and SEM o Measurement models versus structural models o Endogenous vs exogenous variables o Single-stage vs multi-stage “causal” models o Process (again, similar to CFA) o Interpreting reported results o Alternative models o “Causality” – be familiar with issues of making causal inferences from supposedly “causal” modeling 3

In addition, major points from across the semester (see below) For the various procedures we’ve discussed – o Purpose (eg design, type of data/variables/questions, etc) o Interpreting results from a report o Interpreting SPSS output o Process (eg steps in a MANOVA or mediational analysis) o NO EQUATIONS