Sociology 601 Class 28: December 8, 2009 Homework 10 Review –polynomials –interaction effects Logistic regressions –log odds as outcome –compared to linear model predicting p –odds ratios vs. log odds coefficients –inferential statistics: Wald test –maximum likelihood models and likelihood ratios –loglinear models for categorical variables: e.g. 5x5 mobility table –logit models for ordinal variables –event history models 1

Sociology 601 Class 28: December 8, 2009 Homework 10 (Thursday) Review: interaction effects F-tests –review: for full equation –for partial model Multicollinearity –example: state murder rates –not an issue for polynomials, multiplicative interactions Next class: review – us topics you want reviewed! 2

Review: Regression with Interaction effects 3 Two approaches: separate regressions by groups (e.g., two regressions one for men and one for women) multiplicative interaction term in one regression same estimates for effects in either way multiplicative interaction term provides a significance test of difference multiplicative interaction term less easily interpreted Multiplicative interaction models types: categorical (e.g., gender, race) or interval (e.g., age) first, main concern: is interaction coefficient statistically significant? “component” coefficients are just estimates when the other component = zero plotting helps

Inferences: F-tests Comparing models 4 Comparing Regression Models, Agresti & Finlay, p 409: Where: R c 2 = R-square for complete model, R r 2 = R-square for reduced model, k = number of explanatory variables in complete model, g = number of explanatory variables in reduced model, and N = number of cases.

Example: F-tests Comparing models 5 Complete model: men’s earnings on age, age square, age cubed, education, and currently married dummy. Reduced model: men’s earnings on education and currently married dummy. F-test comparing model is whether age variables, as a group, have a significant relationship with earnings after controls for education and marital status

Example: F-tests Comparing models 6 Complete model: men’s earnings. regress conrinc age agesq agecu educ married if sex==1 Source | SS df MS Number of obs = F( 5, 719) = Model | e e+10 Prob > F = Residual | e R-squared = Adj R-squared = Total | e Root MSE = conrinc | Coef. Std. Err. t P>|t| [95% Conf. Interval] age | agesq | agecu | educ | married | _cons | Note: none of the three age coefficients are, by themselves, statistically significant. R c 2 =.2387; k = 5.

Example: F-tests Comparing models 7 Reduced model: men’s earnings. regress conrinc educ married if sex==1 Source | SS df MS Number of obs = F( 2, 722) = Model | e e+10 Prob > F = Residual | e R-squared = Adj R-squared = Total | e Root MSE = conrinc | Coef. Std. Err. t P>|t| [95% Conf. Interval] educ | married | _cons | R r 2 =.1818; g = 2.

Inferences: F-tests Comparing models 8 F = ( – ) / (5 – 2)df 1 =5-2; df 1 =725-6 ( ) / (725 – 6) = / /719 = 26.87, df=(3,719), p <.001 (Agresti & Finlay, table D, page 673)

Multicollinearity (A&F 14.3) 9 “ Redundant” variables large standard errors loss of statistical significance variable 1 is significant in Model 1 variable 2 is significant in Model 2 neither 1 nor 2 is significant in Model 3 including both variables. sometimes: strange sign of coefficient sometimes: magnitude jumps unrealistically problem is not enough cases high on 1 and low on 2 and vice-versa. Every case that is high on 1 is also high on 2. So, you can’t separate the two effects in this sample.

Multicollinearity: Solutions 10 Choose one (and footnote the other) Get a bigger or better sample If both variables are alternate measures of the same concept, make a scale.

Multicollinearity: Not a problem always 11 Only if you are trying to separate the effects of variable 1 and variable 2 what is the effect of variable 1 holding variable 2 constant? Not an issue if: polynomials multiplicative interaction effects

Next: Review for Final 12 Please us any topics you want reviewed!