Logistic regression and Interaction Effects in Regression Models

Interaction Effects in Regression Models

• Independent variables are usually entered additively in regression models.
• Interaction effects occur when the relationship between one independent variable and the dependent variable changes depending on the level of another independent variable.
• Interactions are possible between continuous, categorical, and both continuous and categorical variables.
• To implement interactions, fit an additive model, test interactions based on theory or common sense, and evaluate the significance of newly estimated coefficients.
• When including interactions, do not forget to include the independent variables as additive terms to avoid assuming their insignificance.
• Interaction/moderation effects can be analyzed using regression factorial ANOVA and ANCOVA models.
• A product-term approach can be used to create a new variable by multiplying two interacting variables.
• In non-additive models, the change in the slope of the dependent variable on one independent variable is checked when another independent variable increases by one unit.
• Stata command 'gen X1X2=X1*X2' can be used to generate an interaction variable.
• Centring and standardization can be used to make interpretation of coefficients easier.
• Exclusion of non-significant variables is recommended.
• F-tests can be used to determine the overall significance of polytomous (multiple categories) moderator variables.

Introduction to Logistic Regression

• Logistic regression is used when the dependent variable has two values and there is a risk of heteroscedasticity and predicting values outside the 0-1 interval with OLS regression.
• Logistic regression can also be used with a categorical variable (multinomial regression) or a categorical variable that can be logically ordered (ordered logit regression).
• Logistic regression estimates the maximum likelihood and calculates the probability of Y=1 given the values of X.
• Linear regression gives how much the dependent variable changes for an X increase of 1, while logit regression tells you how much the LN of the odds for Y=1 changes for an increase in X of 1 unit.
• The effect of one X variable is dependent on the other variables, and this effect depends on where you are on the logit scale.
• The logit ranges from -infinity to infinity, and with a logit of 0, the probability is 0.5 (50%).
• The odds ratio (OR) adds after a unit change in X, and an OR of 1 means no change, while an OR of 1.24 means a 24% increase in the odds of being 1 for each step up on the independent variable.
• The likelihood ratio test can be used to test for significance in logistic regression and to avoid wrongly rejecting H0.
• Four assumptions need to be met for logistic regression to have an unbiased and sufficient maximum likelihood estimate of logit parameters: correct specification, independent observations, no linear relationship between x-variables, and no discrimination.
• Multicollinearity can occur and should be checked, and a skewed distribution can lead to problems.
• Diagnostics for logistic regression include checking for correct specification, testing the model's predictors, and testing for multicollinearity.
• Multinomial logistic regression is used when the dependent variable has more than two categories with no natural ordering, and important assumptions include independence of irrelevant alternatives and testing the coefficients of all categories with the Suest test.