Multiple Regression - Categorical and Continuous Variables, Dummy Variables

Interaction in Statistics

an interaction may arise when considering the relationship among three or more variables, and describes a situation in which the simultaneous influence of two variables on a third is not additive. Most commonly, interactions are considered in the context of regression analyses.

Bias in Predictive Validity

which occurs when a test's use has different implications for two groups. Predictive bias has to do with the relationship between scores on two different tests. For example, college admissions officers might use SAT test scores to predict freshman GPAs. The SAT would be the predictor test and GPAs would be the outcome measure.

How to check Interactions in Multiple Regression

- Center the IV of interest - Multiply the centered IV times the dummy variables to create cross-products - Regress the DV on the IVs. Use the centered IV - Add the cross-products sequentially a. Check the statistical significance of ΔR2 b. If significant, graph and conduct follow-up c. If not significant, interpret findings without the addition of the cross-product - This process can be simplified if only a single dummy (or effect) variable

Specific Types of Interactions between Categorical & Continuous Variables?

1. Bias in predictive validity 2. Aptitude—treatment interactions 3. Testing for pretest by treatment interactions in experimental research

Definition of Categorical Variables?

Categorical variables take on values that are names or labels, it can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property.

Example of Dummy Variables?

Example: Female (0=M; 1=F) or Southern (0=Non-Southern; 1=Southern), Race, Religion

Examples of Continuous Variables?

Height, weight, temp, time, distance.

Definition of Continuous Variables?

Is a variable that has an infinite number of possible values. In other words, any value is possible for the variable. Measure not counted.

Slope Bias

Occurs when there is differential validity- i.e. when the validity coefficients for a predictor (e.g. cognitive ability test) differ for different groups. The values that are similar to the common regression equation, but that their slope values differ from the common slope. This would indicate that the connection between predictor scores and outcome scores differs between the two groups.

Examples of Categorical Variables?

The color of a ball (e.g., red, green, blue) or the breed of a dog (e.g., collie, shepherd, terrier) - gender, hair color, this or that.

What are Dummy Variables?

They are simply dichotomous variables that are entered into regression. They have 0 - 1 coding where 0 = absence of something and 1 = presence of something.

Intercept Bias

When the test is over or under predicting for a group. This will look like the slopes of the lines being the same, but one line will be high and one line will be low. This means that the test is like automatically giving one group more points. YOU WILL SEE TWO DIFFERENT INTERCEPTS. If a test suffers only from intercept bias (i.e., the group-level intercepts are not equivalent to the common intercept, but the slopes and values are unbiased), then the size of the group discrepancy would be constant across all aptitude scores. Example male and female, each variable has an extreme slope line from the common line.

What are the steps for Testing for ATI?

a. Is the overall regression statistically significant? b. Is the interaction term significant? - Treatments are differentially effective depending on trait - Graph & Follow-up the interaction c. Are the intercepts different? - Suggests one treatment more effective