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52 Cards in this Set
- Front
- Back
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What happens to R2 and its F test when we enter a categorical variable using different codes? (Do they change or not?) |
They do not change. They are consistent across models with different codes, including the p-value, and absolute value of t-test of B1. |
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What happens to the regression coefficients when we enter a categorical variable using different codes? (Do they change or not?) |
Linear transformations; they DO change. The B0 and its t-test and p-values as well as B1 are NOT consistent. |
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When the regression model has one dichotomous predictor entered with a dummy code, what does B0 tell? |
B0 is the predicted score for the reference group. The predicted score for a group is its mean. |
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When the regression model has one dichotomous predictor entered with a dummy code, what does B1 tell? |
The change in predicted score for a one unit increase in the predictor. It is the difference between the groups’ means on the DV. |
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How do results for a regression with one dichotomous predictor compare with results for the same data using an independent samples t-test in terms of p-value? |
OLS regression produces the same results as an independent samples t-test.
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How many dummy codes are required to enter a categorical predictor in a regression (as a function of the number of categories in the categorical predictor)?
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For a variable having “g” categories, g-1 dummy codes are needed.
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When the regression model has one categorical predictor with 3+ categories entered with dummy codes, what does B0 tell?
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B0 is the predicted value of Y when all predictors equal 0; it is the DV mean for the reference group
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When the regression model has one categorical predictor with 3+ categories entered with dummy codes, what does B1 tell? |
B1 is the change in predicted Y for a one-unit change in D1, partialling the effect of D2. It is the difference between the DV means for B1 and B0.
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When the regression model has one categorical predictor with 3+ categories entered with dummy codes, what does B2 tell? |
B2 is the difference between the DV means for B2 and B0. Similar to B1.
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How do results for a regression with one categorical predictor compare with results for the same data using a one-way ANOVA in terms of p-value for the overall F test?
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Like other coding schemes, dummy codes and effect codes are linear transformations of each other, so they yield the same overall model results (R sq. and F test)
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How does adding other predictors to the regression change the means that the coefficients describe differences between?
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B1 becomes the difference between that variable mean and the overall mean. Same with all the B_. B0 is the unweighted overall mean.
(They are now adjusted means, adjusted for the other predictor or predictors.) |
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If one dummy code out of a set of dummy codes is nonsignificant, should it be removed from the model alone?
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No, dropping one code would change the meaning of the remaining code
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What test is used to test the significance of a categorical predictor entered using a set of dummy codes or effects codes?
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F test of R sq. |
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If other predictors are included in the model, should they be entered before or after the dummy or effects codes for the categorical predictor?
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Before with hierarchical regression
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Should dummy codes or effects codes be standardized?
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No. with dummy or effects coding, we have already scaled predictors to have an interpretable metric; standardization ruins this. Also don’t center.
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In a model without an interaction, does the effect of one IV on the DV depend on the level of another IV
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NO. |
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In a model without an interaction, does the effect of one IV on the DV depend on the level of another IV? |
Yes, models with interactions are not main effects models, so the effect of the predictor on DV is multiplicative and the effects of diff predictors on DV are dependent on one another. |
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What is an interaction? |
The effect of one predictor on the DV is not constant across levels of another predictor. The effect of one predictor depends on the level of another predictor |
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How do we make an interaction term between continuous variables?
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Interactions are entered in regression by multiplying predictors together
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What is a simple slope?
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Change in y for one unit increase in X
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Simple intercept
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B0; simple regression line crosses 0.
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In a regression with two continuous predictors and their interaction, what does B3 (the coefficient for the interaction) tell?
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B3 tells how much the simple slope changes for one unit increase in X2 or X1. Report simple slopes for predicting the DV from proximal predictor and B3 as the change in those simple slopes at diff levels of the context predictor. One predictor (X1 or X2) is treated as proximal cause and the other as a context (report the one that is clearest)
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In a regression with two continuous predictors and their interaction, what do B1 and B2 tell?
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B1 is slope of simple regression of SSL when n is 0. In quadratic model, it tells slope when the same predictor is 0. B2 is also simple slope in a simple regression. In a quadratic model, there is only one simple slope; in an interaction model, there are two.
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In a regression with two continuous predictors and their interaction, what does B0 tell?
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B0 is predicted value of the DV when all predictors are 0;slide 48
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What is the purpose of centering in aregression model with an interaction? |
Reducenonessential multicollinearity; makes more meaningful; find simple slopes andsimple intercepts to interpret interaction |
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What effect does centering have on R2and its F test? |
No effect. They stay the same. (p valuestays the same too) |
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What effect does centering at different valuesof one predictor have on B3 (the coefficient for the interaction)? |
It has no effect because B3 is the highest order term. |
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When one predictor is centered at differentvalues (typically the mean and +1 or –1 standard deviation) while the other iskept centered at its mean, which predictor’s coefficient changes and whichpredictor’s coefficient remains the same? Why? |
The predictor’s coefficient that changes is the predictor thatis kept centered at its mean. This is because each coefficient describes the simple slope whenthe other predictor is zero. |
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When the interaction is significant, we canrearrange the model in two different ways, depending on which predictor wetreat as focal and which as background. How many of these two differentrearrangements should we report? |
Just one. |
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What does the regression surface look like whenthere is an interaction term in the model versus when there is not? (When is itflat and when is it warped?) |
The plane is flat when there is no interaction and it is warpedwhen there is an interaction |
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What lower-order terms need to be included in amodel for an interaction term to be interpretable? |
All corresponding lower-order terms. |
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How many interaction terms are needed to enterthe interaction between a categorical and a continuous predictor? |
g-1 |
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How many interaction terms are needed to enterthe interaction between a categorical and a continuous predictor? |
Each dummy code is multiplied by the continuous predictor |
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What test is used to test an interaction that ismade up of more than one term? |
F test of R sq change |
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When we interpret results for a regression witha categorical by continuous interaction, which predictor (categorical orcontinuous) do we typically make the context predictor and which the proximalpredictor? |
Context predictor = categoricalpredictor Proximal predictor = continuous predictor |
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When a regression model includes a dichotomouspredictor entered with a dummy code, a continuous predictor, and theirinteraction, what does B3 (the coefficient for the interaction)tell? What does the coefficient for the dummy code tell? What does thecoefficient for the continuous predictor tell? What does the intercept tell? |
B3 tells the difference in simpleslopes, comparing the group coded 1 with group coded 0. Continuous - Simple slope forreference group Intercept – simple intercept (ormean) for reference group |
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Should dummy codes be centered? Should thecontinuous predictor be centered? |
Dummy codes should not becentered (they are already at easily read numbers) Yes, to make them more interesting. |
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When a regression model includes a categoricalpredictor entered with dummy codes, a continuous predictor, and theirinteraction, what do the coefficients for the interaction tell? What do thecoefficients for the dummy codes tell? What does the coefficient for thecontinuous predictor tell? What does the intercept tell? |
They describe the simple slopes and intercept Coefficients describe the reference group (0) B0 is the intercept of the group coded 0. B1 is the simple slope for the group coded 0. B2 is the difference in intercepts, comparing the group coded 1with the group coded 0. B3 is the difference in simple slopes comparing group coded 1with group coded 0. |
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If one of a set of dummy code by continuousvariable interactions is nonsignificant, should it be removed from the modelalone? |
No. |
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How do we get a test of a simple slope for theassociation between the continuous predictor and the outcome variable at aparticular level of the categorical variable? |
We setthat particular level as the reference group when dummy coding |
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When would we use logistic regression ratherthan OLS regression? |
When dependent variable is dichotomous. Logistic regression doesn’t the OLS assumptions ofhomoscedasticity or normality of residuals by predicting a transformed versionof the outcome variable, log odds. |
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What can the logistic regression model bewritten in terms of? |
In terms of probability, odds, and log odds. See study guide for pictures of the formulas. |
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What problems arise when the linear probabilitymodel is used on data with a dichotomous dependent variable? |
Nonnormalityof residuals, when probabilities are out of range |
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What should results of logistic regression beinterpreted in terms of? |
Logistic regression results are interpreted in terms of oddsrather than probabilities Useodds, specifically odds-ratios, heteroscedasticity |
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How are coefficients estimated in logisticregression? |
Maximumlikelihood and estimated by log odd B0 is the log odds of scoring in the 1 group for X=0 B1 is the change inthe log odds of scoring in the 1 group for a one unit increase in X. |
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What is mediation? |
- Effect of one variableon a second variable passes through a third variable - Third variable carriesor transmits the effect from the first to the second. Third variable is themediator - Wheneffect transmits through another variable. - Tells how the predictor changes the outcome; tells us by what mechanismthe predictor changes the outcome |
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What three regressions are run to test amediation model? |
- X to Y (x predictor) - M to Y (M is outcome predicted by X) - (simultaneous) X and M predicting Y |
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What do the mediated effect (ab) and the directeffect (c′) add up to? |
c (which is thepathway from X to Y) The total effect |
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What is moderation? |
Changes the effect ofX on Y. Tells us under what circumstances X affects Y. Requires one regressionwith an interaction. Regression with aninteraction term |
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What regression coefficients have to besignificant for mediation to be present according to the Baron & Kennyapproach? |
The X to Y regression(c) The X to M regression(a) The M to Y regression,controlling for X (b) Thetotal effect; X has to sig predict M and Y. b has to sig predict Y controllingfor effects of X. |
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What test is used to determine whethermediation is full or partial? |
Effect size Whetherc’ is sig. |
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What regression coefficients have to be significantfor mediation to be present according to the joint significance approach? |
The X to M regression(a) The M to Y regression,controlling for X (b) |
