Exam 1

Question 1

What are the type of research questions multivariate statistics can answer?

Answer 1

1. the degree of relationship among variables
2. significant group differences
3. prediction of group membership
4. structure
5. time course events
6. nested data structures
7. profiles of people.

Question 2

Provide an example of a multivariate technique to determine degree of relationship among variables.

Answer 2

Canonical Correlation Analysis (CCA)

Question 3

Provide an example of a multivariate technique to determine significant group differences

Answer 3

MANOVA

Question 4

Provide an example of a multivariate technique to determine Prediction of group membership.

Answer 4

Discriminant Function Analysis (DFA)

Question 5

Provide an example of a multivariate technique that can be used to answer questions about data structure.

Answer 5

Principal Component Analysis and Exploratory Factor Analysis

Question 6

Provide an example of a multivariate technique that can be used to answer nested data structures.

Answer 6

Hierarchical linear modeling

Question 7

Provide an example of a multivariate technique that can be used to answer questions about the time course of events

Answer 7

Survival/Failure Analysis. Here, we would compare groups or determine variables associated with time.

Question 8

What is an example of a research question that uses CCA?

Answer 8

Do these three variables (odor threshold, odor ID, and taste threshold) relate to each other and these other three variables (anxiety, depression, and HVLT score)?

Question 9

What is an example of a research question that uses MANOVA?

Answer 9

Do those who are E4 positive and E4 negative differ on these demographic variables: age, odor threshold, dementia rating scale?

Question 10

What is an example of a research question that uses DFA?

Answer 10

Do E4 heterozygous carriers, E4 non-carriers, and E4 homozygous carriers differ by scores on the CVLT?

Question 11

What is an example of a research question that uses PCA/EFA?

Answer 11

PCA and EFA answeR: What latent variable underlie our observed variables. I.e. if we wanted to reduce data and put some questions for the CVLT on factors or group them into related questions. Also, BSI could be another example.

Question 12

What is an example of a research question answered by Survival/Failure Analysis?

Answer 12

How long does it take for someone to be diagnosed with Alzheimer’s?

Question 13

What is an example of a question that is answered with hierarchical linear modeling?

Answer 13

A researcher could investigate how the location of the school and classroom affect performance on a test.

Question 14

Provide an example of a multivariate technique that can be used to answer questions about profiles of people?

Answer 14

Latent Class Analysis-creating groups of individuals based on responses to categorical variables

Latent profile analysis- Creating groups of individuals based on responses to continuous variables

Question 15

What is an example of a question that is answered with latent class analysis?

Answer 15

One could see how groups of individuals based on gender, college major, and SES level (poor, middle, upper class) differ on happiness scores.

Question 16

Why would one conduct a canonical correlation analysis (CCA)?

Answer 16

• observes the relationship between 2 sets of variables
• no IVs or DVs
• variables on both sides are combined in an “optimal” way to maximize the relationship between the two sides
• CCA reduces experimentwise type 1 error rates
• ultimate goal is to get a set of variables on one side and see how much they represent the “new thing”
• can relate this new “combined” variable to the other “combined” variable

Question 17

Describe how one would conduct a canonical correlational analysis?

Answer 17

STEP 1: evaluate the correlational matrix. observe your set 1 variables, set 2 variables, and relationship between both sets of variables. From these matrices, linear combinations of variables are formed, reducing the variable sets into canonical variates. CV’s maximize the correlation, using canonical weights.

STEP 2: Observe Wilk’s Lamda to determine if the effect size is statistically significant. We need to determine how many canonical variates we have.

Step 3: Determine how many CV’s there. We need to observe every CV pair to see if it’s significant. The strongest CV is tested first. If it is significant, the first CV pair is used. The second test removes the first CV pair, conducted on residual correlation matches. If this is significant, then the second CV pair adds something unique.

STEP 4: Interpret overall tests looking at Rc, Rc^2, and eta^2. Weights |.30| or above are cosnidered significant.

STEP 5: Interpret loadins or structure matrices (correlations between variables and CV pairs).

STEP 6: Evaluate Canonical Adequacy Coefficient (CAC). This is the proportion of the variance extract by the CV.

STEP 7: Observe the redundancy, the proportion of variance extracted by CV for the other variables.

Question 18

Using your own example, tell me when you would use a MANOVA.

Answer 18

• A MANOVA is used when we want to analyze differences between 2 or more dependent variables between groups that are separated by a categorical variable.
• The DV’s will form a set (another form of the generalized linear model).
• More powerful than a one-way ANOVA because it takes the correlation among DVs (takes into account overlapping variance and partial redundancy) into account and helps protect against Type 1 Error.
• Can run a MANOVA when want to observe demographic variables between groups that are separated on E4 allele status (positive and negative allele)

Question 19

Describe how you would conduct a MANOVA from start to finish.

Answer 19

Step 1: Perform a generalized linear model with categorical variable as IV and continuous variables as DV. The DV’s will be linearly combined into a single synthetic variable and should be correlated, continuous, and have redundancy.

Step 2: Check assumptions of normality and homogeneity of variance and covariance. Both Box’s test of equality of covariance matrices and Levene’s test of equality of error variance. Both tests should be evaluated at an alpha level of 0.001.

Step 3: Examine Omnibus tests using Wilk’s lambda and F statistic to determine significance at alpha of 0.05. Partial eta^2 observed as well to measure practical significance.

Step 4: Perform follow up tests. For univariate tests on individual DVs, conduct an ANOVA on each individual DV. DVs that have significant (Bonferroni) effects will be examined for simple effects between groups. For multivariate tests on new synthetic variables, we can use MANOVA to create new variables for each main effect using standardized canonical weights multiplied by z-scores for each participant. With the new composite DV, a univariate ANOVA can be run and follow-up tests can be examined in the same way as the univariate approach.

Question 20

Compare/Contrast MANOVA with linear discriminant function analysis.

Answer 20

MANOVA: used to evaluate if significant differences exist between groups when there are multiple correlated outcome variables (DVs). can look at main and interaction effects.

DFA: used to describe or predict group membership from a set of predictors where group membership is a categorical variable and the predictors are typically continuous variables. usually only looks at main effects.

DFA and MANOVA: similar, rely on assumption that group membership is associated with group differences on multiple measurable variables.

Question 21

Describe what a linear discriminant function LDF is.

Answer 21

LDF are weighted combinations of predictors and predictors are combined to predict group membership.

(Just a regression equation from the predictors)

Question 22

What are the components that comprise an LDF?

Answer 22

linear component: linear combinations of linearly weighted variables

discriminant = weights chosen to separate groups.

function = constructed from other variables.

Each LDF defines a “new variable”.

Question 23

Describe how you go from an LDF to calculation and interpretation of group centroids.

Answer 23

1. Predictors are combined to predict group membership. LDF are weighted combinations of predictors.
2. Look at Wilk’s Lambda, want this to be significant to demonstrate differences in groups.
3. Statistically determine how many LDFs: number of potential LDFs is the smallest between the (1) number of predictors and (2) number of groups -1
4. Once the number of LDF is determined, examine the functions at the group centroid.
5. Calculate group centroids by creating discrimination scores for each participant and calculate the standardized mean for each group. In other words, find the LDF score for each participant, aggregate that for each group, and see where the differences lie.
6. After group centroids are generated, we evaluate the group centroids of ll the groups as a whole.
7. We must also evaluate individual predictors to determine what variable(s) are responsible for these differences.

Question 24

Describe the process of conducting a discriminant function analysis.

Answer 24

Step 1: Observe the group statistics for the continuous IV variables and see what is happening with the pattern of each group.

Step 2: Test group differences on these IVs (Observe Wilk’s Lambda, F statistic, and significance).

Step 3: Check Box’ test of Equality of Covariance to test homogeneity of covariance assumption with alpha level of .001.

Step 4: Check omnibus or overall test to see how many LDF are significant (using Wilk’s Lambda).

Step 5: Observe functions at group centroids.

Step 6: View standardized canonical discriminant function coefficients to make sure the weights are above absolute threshold of .30.

Step 7: Evaluate classification–how well does function predict group membership. Compare the actual classification versus predicted classification.

Question 25

Describe the basic steps in factor analysis in a broad sense.

Answer 25

Step 1: View the correlation matrix to decide how many factors there are/might be.

Step 2: Extraction process. Factors are derived successfully. Decide which rule will be used to determine how many factors there are. For component extract, we form PCs as linear component variables.

Step 3: Evaluate the relationship between the observed variables and the factors/components. Typically, many look at loadings or structure matrix coefficients. Rotation aids in this process. The two types of rotation are orthogical and oblique. Orthogonal is simple but factors are uncorrelated. Oblique is more difficult but the factors are correlated, suggesting they are realistic.

Question 26

What is Kaiser’s rule (in factor analysis)?

Answer 26

observe the correlation matrix and see which eigenvalues are > 1. Lambda > 1 represent variance in a principle component. We want to account with more variance with our principle components than a variable has to start with.

Question 27

What is the scree test?

Answer 27

Plot each successive lambda for each factor and then examine the elbow. The number of factors is determined by where the factors “level out.”

Question 28

What is the total variance accounted for rule?

Answer 28

We observe the total variance accounted for by each factor. We usually are trying to aim for 50%.

Question 29

What is the parallel analysis rule.

Answer 29

This compares the eigenvalues from the solution to eigenvalues generated from random data. The number of components = the number of eigenvalues that is greater from the eigenvalues based on random data.

can check with a maximum likelihood factor analysis that provides a statistical test of overall model fit.

Question 30

What is the maximum likelihood factor analysis?

Answer 30

dependet on the p value. provides a statistical test of overall model fit.

Question 31

What is the interpretability of factors rule?

Answer 31

we would go back to the structure matrix and try to look at a general factor and group them. We want multiple observed variables to load onto a certain factor. Each PC should have several variables iwth strong loadings / coefficients (>.30) and minimal multi-vocal items (Cross-loadings).

Question 32

Describe the factor rotation procedures.

Answer 32

Step 1: Plot factor loadings in n-dimensional space.
Step 2: Rotate the factors to change the “viewing angle” of the factor space. Here, we’re taking the original axes, picking them up, and rotating them to something that is more useful. The structure is simplified if the axes “spear” variable clusters.
Step 3: Compare the unrotated and rotated structure matrices.

Question 33

What is the goal of factor rotation?

Answer 33

clarify the pattern of the relations between variables and factors. Oblique rotations are meant to “clean up” the structure matrix.

Question 34

What does rotation NOT effect?

Answer 34

• correlations between variables
• communality values
• proportion of variance accounted for by the solution

Question 35

What does rotation effect?

Answer 35

• correlation between each variable and the factors

- variance accounted for by each factor

Question 36

What is the goal of path analysis?

Answer 36

• explain the associations among variables with our a priori models.
• We are trying to explain why variables are correlated using a “temporally sequenced” model.
• would draw and test a mathematical model with underlying equations

Question 37

How is model fit determined with path analysis?

Answer 37

Model fit is determined at two levels: overall model fit and individual parameter model fit. Parameters = path coefficients, analyzed associations. Overall model fit is referred to as goodness of fit. Fit of individual parameters of fit are determined through statistical tests for each parameter, which are referred to as critical ratios.