SMR and HMR Learning Objectives Flashcards
(17 cards)
Explain the research questions that can be addressed using standard multiple regression
The research questions that can be addressed are if the predictors jointly account for significant variance in the criterion, and does each predictor uniquely account for significant variance in the criterion.
Define validities and collinearities and explain why we want high validities and low collinearities
Validities are correlations between each predictor and the criterion. Collinearities are intercorrelations among predictors. We want high validities and low collinearities because when that is the case, the higher R^2 is.
Explain multicollinearity and the principle of parsimony
Multicollinearity is where several/multiple IV/predictors in a model are correlated. The principle of parsimony is the idea that among competing models that explain Y equally well, the simplest model is preferred. To achieve parsimony only the important predictors should be included, redundant predictors should be removed, and predictors which overlap with one another statistically and theoretically should be combined.
Describe how the overall model and individual coefficients are assessed in multiple regression
In multiple regression, the overall model is assessed by using the F-test and R^2. Individual coefficients are evaluated using t0tests and their corresponding p-values.
Explain the difference between unstandardised coefficients and standardised coefficients
The unstandardised multiple regression equation represents the best fitting linear composite of all predictors in the model, each weighted by a coefficient representing their unique relationship with Y (b), plus a constant/intercept (a). The standardised version has no constant.
Identify the test used to assess the significance of the overall variance explained
The test used to assess the significance of the overall variance is a F test, where the coefficient of multiple determination (R^2) (the variance explained by overall regression model) is divided by the regression degrees of freedom, which is then divided by the residual variance divided by the residual degrees of freedom. It can also be calculated by using sums of squares, and dividing MSregression by MSresidual.
Identify the test used to assess the significance of individual predictors in their prediction of the criterion
t-test
For significant individual predictors, know how to interpret the direction of a relationship using the individual coefficients
A positive t-test means that there is a positive relationship, a negative result means that there is a negative relationship between the predictor and criterion.
In the linear model for a multiple regression analysis with two predictors, explain what b1, b2, and a represent
B1 and B2 are the coefficients for X1 and X2 respectively.
In any type of multiple regression, explain what each of the following tell us:
- A significant F test for the overall model
A significant t test for each individual predictor
A significant F test for the overall model tells us that the predictors are collectively explaining a significant amount of variance in the criterion. A significant t-test for each individual predictor tells us that that the predictor individually explains a significant amount of unique variance in the criterion.
Explain the key difference between standard multiple regression and hierarchical multiple regression
The key difference between a SMR and a HMR is that during a HMR the predictors are entered into the model sequentially in a pre-specified order based on logic and/or theory. Each predictor is evaluated in terms of what it adds to prediction at its point of entry.
Explain the research questions that can be addressed using hierarchical multiple regression
Using HMR, research questions that want to determine unique and incremental contributions of predictor variables to an outcome variable, while controlling for other variables.
Explain the rationales for the order in which predictors may be entered in hierarchical multiple regression
There are three rationales for order of entry. One is partialling out the effect of control variable/s - add control variable/s at step 1, then adding focal predictors at step 2. Another is building on knowledge - adding known predictors of Y at step 1, then adding novel predictors of Y at step 2. Another is interaction-testing - adding predictors at step 1, and then adding interaction term at step 2.
In hierarchical multiple regression, explain what each of the following tell us:
- A significant F test for the overall model at each step
- A significant Fchange test for the overall model at each step
- A significant t test for each individual predictor at each step
A significant F test for the overall model at step one tells us that the overall model explains a significant amount of variance in Y. A significant F test for the overall model at step two tells us that the overall model explains a significant amount of variance in Y. A significant Fchange test for the overall model at step one tells us that the change in R2 is significant. A significant Fchange test for the overall model at step two tells us that the change in R2 is significant. A significant t test at each step reflects the contributions of each predictor in explaining Y.
Explain what R2 change indicates in hierarchical multiple regression, in relation to R2
In HMR R2change indicates the change in R2 at each step.
In HMR with two steps, explain the difference (if any) between R2 and R2 change:
- At Step 1 of the analysis (i.e. Model 1)
- At Step 2 of the analysis (i.e. Model 2)
At step one of the analysis, R^2 is equivalent to R^2change because it is the starting point. At step 2 of the analysis, R2 change indicates a change in R2 at each step - there is an increase in amount of variance in Y accounted for by overall model with predictors entered at that step. At each step R2 is the cumulative total of each R2change along the way.
Explain the link between results at Step 2 of a hierarchical multiple regression (e.g. with predictor A entered at Step 1, and predictors B and C entered at Step 2), and the results of a standard multiple regression (e.g. with predictors A, B, and C in the model)
The coefficients and t-tests for each individual predictor in step 2 of a HMR are equivalent to those results of a SMR.
