Complex Analytic DesignsComplex Analytic Designs

Outcomes (DVs)

Predictors (IVs) 1 Continuous Many Continuous 1 Categorical Many Categorical

None (histogram) Factor Analysis: PCA, FA, CFA (MDS, CLAN)

(frequencies) loglinear models

1 Category - 2 levelsmany levels

t testAnova

general Manova

2 tests for independence,loglinear & logit models loglinear models

 Many Categorical

factorial Anova

factorial Manova,repeated measures Manova,doubly multivariate designs

(only for 2-level DV’s:) logit models, logistic regression loglinear models

1 Continuous regression canonical correlation Discriminant 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

ANOVAANOVA

““Factorial” = 2 or more factors that have at Factorial” = 2 or more factors that have at least 2 levels eachleast 2 levels each

Example of a 2x2 design:Example of a 2x2 design:

Factor 1Factor 1

Level 1 Level 1 Level2Level2

FactorFactor Level ALevel A mean A1mean A1 mean A2mean A2

22 Level BLevel B mean B1mean B1 mean B2mean B2

ExampleExample

TreatmentTreatment GenderGender

malesmales femalesfemales Row meanRow mean

ExperimentalExperimental 55 1515 1010

ControlControl 55 55 55

Column MeanColumn Mean 55 1010 7.5 7.5 (grand mean)(grand mean)

Main effect of Treatment

Main effect of GenderNote: Cell means are a combined effect of row effects, column effects, the Note: Cell means are a combined effect of row effects, column effects, the grand mean and the interaction.grand mean and the interaction.

InteractionsInteractions

Male teacher

Female teacher

Male Female

scor

esc

ore

Male Female

Male teacher

Female teacher

scor

e

Male Female

Male teacher

Female teacher

scor

e

Male Female

Male teacher

Female teacher

Design Main Effect Interaction

A none yes

B both no

C both yes

D one yes

A B

C D

More complex factorial designsMore complex factorial designs

2 factors, many levels: 3x2, 3x3, 6x8….2 factors, many levels: 3x2, 3x3, 6x8…. >2 factors: 2x2x2, 3x4x2>2 factors: 2x2x2, 3x4x2 Nested designs: levels within levelsNested designs: levels within levels Repeated measures: multiple values per Repeated measures: multiple values per

subjectsubject Mixed (Between-within) designs: some Mixed (Between-within) designs: some

factors are groups of different subjects and factors are groups of different subjects and some are repeated measures on the same some are repeated measures on the same subjectssubjects

Mediators and ModeratorsMediators and Moderators

A A moderatormoderator is variable that affects the is variable that affects the direction and/or strength of the relation direction and/or strength of the relation between the IV and DV (i.e. sex, gender, between the IV and DV (i.e. sex, gender, level of reward)level of reward)

A A mediatormediator is a variable that accounts for is a variable that accounts for the relation between the IV and DV. the relation between the IV and DV.

MediationMediation

Independent

Variable

Dependent

Variablea

Mediator

b c

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 modelingModels and modeling

Hypothesize the data structure by Hypothesize the data structure by specifying the modelspecifying the model

““Fit” the data to the modelFit” the data to the model Test the fit of the dataTest the fit of the data Easiest example: simple regression is a Easiest example: simple regression is a

linear model (i.e. is a straight line a good linear model (i.e. is a straight line a good approximation of the data)approximation of the data)

Regression on more than one IVRegression on more than one IV

Predictor is a combination, typically linear Predictor is a combination, typically linear (aka additive) of several IV.(aka additive) of several IV.

Y = a + bXY = a + bX11 + bX + bX22 + bX + bX33 + …. + + …. + εε

Same principles apply, but also some new Same principles apply, but also some new ones emerge…ones emerge…

YX1

Weak correlation

YX1

Strong correlation

YX3

X2X1

Linear combination

Y

X2X1 X3

Linear combination with multicolinearity

Hierarchical RegressionHierarchical Regression

You can add or subtract terms to make a new You can add or subtract terms to make a new model and test differencesmodel and test differences

Model 1: Y = a + bXModel 1: Y = a + bX1 1 + + εε RR22

Model 2: Y = a + bXModel 2: Y = a + bX1 1 + bX+ bX22 + + εε RR22changechange

RR22 is the proportion (%) of variance in Y that is is the proportion (%) of variance in Y that is explained by the model.explained by the model.

RR22 change is the proportion (%) of variance in Y that change is the proportion (%) of variance in Y that is explained by the model over and above the is explained by the model over and above the previous model.previous model.

Adult Depression

Stressful events

Teen Depression

Example: Example: 1: adult depression 1: adult depression teen depression teen depression2: adult depression 2: adult depression teen depression + stressful events teen depression + stressful events

Change in R2 : proportion of variance in adult depression Change in R2 : proportion of variance in adult depression explained by stressful events after controlling for previous explained by stressful events after controlling for previous levels of depressionlevels of depression

What has not been coveredWhat has not been covered

Use of categorical variables in regression (i.e. Use of categorical variables in regression (i.e. dummy coding)dummy coding)

Loglinear analysis (linear contrasts of frequency Loglinear analysis (linear contrasts of frequency data) and Discriminant Function Analysis (DFA).data) and Discriminant Function Analysis (DFA).

Person-centered approaches and cluster Person-centered approaches and cluster analysisanalysis

Factor Analysis, Principle Components Analysis Factor Analysis, Principle Components Analysis (PCA) (PCA)

Structural Equation Modeling (SEM), Structural Equation Modeling (SEM), Hierarchical Linear Modeling (HLM), and other Hierarchical Linear Modeling (HLM), and other more difficult or esoteric analyses.more difficult or esoteric analyses.