Complex Analytic Designs

Outcomes (DVs) Predictors (IVs)1 ContinuousMany Continuous1 CategoricalMany Categorical None(histogram)Factor Analysis: PCA, FA, CFA (MDS, CLAN) (frequencies)loglinear models 1 Category - 2 levels many levels t test Anova general Manova  2 tests for independence, loglinear & logit modelsloglinear models Many Categorical factorial Anova factorial Manova, repeated measures Manova, doubly multivariate designs (only for 2-level DV’s:) logit models, logistic regressionloglinear models 1 Continuousregressioncanonical correlationDiscriminant Function Analysis, logistic regression factorial ANOVA in reverse interpretation Many Continuous multiple regression canonical correlation, covariance structure analysis Discriminant Function Analysis, logistic regression factorial MANOVA in reverse interpretation

ANOVA  “Factorial” = 2 or more factors that have at least 2 levels each  Example of a 2x2 design: Factor 1 Level 1 Level2 FactorLevel A mean A1mean A2 2Level B mean B1mean B2 2Level B mean B1mean B2

Example TreatmentGender malesfemalesRow mean Experimental51510 Control555 Column Mean (grand mean) Main effect of Treatment Main effect of Gender Note: Cell means are a combined effect of row effects, column effects, the grand mean and the interaction.

Interactions Male teacher Female teacher Male Female score Male Female Male teacher Female teacher score Male Female Male teacher Female teacher score Male Female Male teacher Female teacher DesignMain Effect Interaction Anone yes Bboth no Cboth yes Done yes AB C D

More complex factorial designs  2 factors, many levels: 3x2, 3x3, 6x8….  >2 factors: 2x2x2, 3x4x2  Nested designs: levels within levels  Repeated measures: multiple values per subject  Mixed (Between-within) designs: some factors are groups of different subjects and some are repeated measures on the same subjects

Mediators and Moderators A moderator is variable that affects the direction and/or strength of the relation between the IV and DV (i.e. sex, gender, level of reward) A mediator is a variable that accounts for the relation between the IV and DV.

Mediation Independent Variable Dependent Variable a Mediator bc Criteria for mediator: Before mediator inclusion: path a is significant After mediator inclusion: paths b and c are both significant but a is not

Models and modeling  Hypothesize the data structure by specifying the model  “Fit” the data to the model  Test the fit of the data  Easiest example: simple regression is a linear model (i.e. is a straight line a good approximation of the data)

Regression on more than one IV  Predictor is a combination, typically linear (aka additive) of several IV.  Y = a + bX 1 + bX 2 + bX 3 + …. + ε  Same principles apply, but also some new ones emerge…

Y X1X1 Weak correlation Y X1X1 Strong correlation Y X3X3 X2X2 X1X1 Linear combination Y X2X2 X1X1 X3X3 Linear combination with multicolinearity

Hierarchical Regression  You can add or subtract terms to make a new model and test differences Model 1: Y = a + bX 1 + εR 2 Model 2: Y = a + bX 1 + bX 2 + εR 2 change R 2 is the proportion (%) of variance in Y that is explained by the model. R 2 change is the proportion (%) of variance in Y that is explained by the model over and above the previous model.

Adult Depression Stressful events Teen Depression Example: 1: adult depression  teen depression 2: adult depression  teen depression + stressful events Change in R2 : proportion of variance in adult depression explained by stressful events after controlling for previous levels of depression

What has not been covered  Use of categorical variables in regression (i.e. dummy coding)  Loglinear analysis (linear contrasts of frequency data) and Discriminant Function Analysis (DFA).  Person-centered approaches and cluster analysis  Factor Analysis, Principle Components Analysis (PCA)  Structural Equation Modeling (SEM), Hierarchical Linear Modeling (HLM), and other more difficult or esoteric analyses.