Exam 1 Flashcards
(37 cards)
What are the type of research questions multivariate statistics can answer?
- the degree of relationship among variables
- significant group differences
- prediction of group membership
- structure
- time course events
- nested data structures
- profiles of people.
Provide an example of a multivariate technique to determine degree of relationship among variables.
Canonical Correlation Analysis (CCA)
Provide an example of a multivariate technique to determine significant group differences
MANOVA
Provide an example of a multivariate technique to determine Prediction of group membership.
Discriminant Function Analysis (DFA)
Provide an example of a multivariate technique that can be used to answer questions about data structure.
Principal Component Analysis and Exploratory Factor Analysis
Provide an example of a multivariate technique that can be used to answer nested data structures.
Hierarchical linear modeling
Provide an example of a multivariate technique that can be used to answer questions about the time course of events
Survival/Failure Analysis. Here, we would compare groups or determine variables associated with time.
What is an example of a research question that uses CCA?
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)?
What is an example of a research question that uses MANOVA?
Do those who are E4 positive and E4 negative differ on these demographic variables: age, odor threshold, dementia rating scale?
What is an example of a research question that uses DFA?
Do E4 heterozygous carriers, E4 non-carriers, and E4 homozygous carriers differ by scores on the CVLT?
What is an example of a research question that uses PCA/EFA?
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.
What is an example of a research question answered by Survival/Failure Analysis?
How long does it take for someone to be diagnosed with Alzheimer’s?
What is an example of a question that is answered with hierarchical linear modeling?
A researcher could investigate how the location of the school and classroom affect performance on a test.
Provide an example of a multivariate technique that can be used to answer questions about profiles of people?
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
What is an example of a question that is answered with latent class analysis?
One could see how groups of individuals based on gender, college major, and SES level (poor, middle, upper class) differ on happiness scores.
Why would one conduct a canonical correlation analysis (CCA)?
- 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
Describe how one would conduct a canonical correlational analysis?
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.
Using your own example, tell me when you would use a MANOVA.
- 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)
Describe how you would conduct a MANOVA from start to finish.
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.
Compare/Contrast MANOVA with linear discriminant function analysis.
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.
Describe what a linear discriminant function LDF is.
LDF are weighted combinations of predictors and predictors are combined to predict group membership.
(Just a regression equation from the predictors)
What are the components that comprise an LDF?
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”.
Describe how you go from an LDF to calculation and interpretation of group centroids.
- Predictors are combined to predict group membership. LDF are weighted combinations of predictors.
- Look at Wilk’s Lambda, want this to be significant to demonstrate differences in groups.
- Statistically determine how many LDFs: number of potential LDFs is the smallest between the (1) number of predictors and (2) number of groups -1
- Once the number of LDF is determined, examine the functions at the group centroid.
- 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.
- After group centroids are generated, we evaluate the group centroids of ll the groups as a whole.
- We must also evaluate individual predictors to determine what variable(s) are responsible for these differences.
Describe the process of conducting a discriminant function analysis.
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.
