Binary Logistic Regression

• Logistic regression is an extension of simple linear regression.
• Where the dependent variable is dichotomous or binary in nature, we cannot use simple linear regression. Logistic regression is the statistical technique used to predict the relationship between predictors (our independent variables) and a predicted variable (the dependent variable) where the dependent variable is binary (e.g., sex , response , score , etc…).
• There must be two or more independent variables, or predictors, for a logistic regression.  The IVs, or predictors, can be continuous (interval/ratio) or categorical (ordinal/nominal).
• All predictor variables are tested in one block to assess their predictive ability while controlling for the effects of other predictors in the model.

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Assumptions for a Logistic regression:

1.  adequate sample size (too few participants for too many predictors is bad!);
2.  absence of multicollinearity (multicollinearity = high intercorrelations among the predictors);
3.  no outliers

• The statistic -2LogL (minus 2 times the log of the likelihood) is a badness-of-fit indicator, that is, large numbers mean poor fit of the model to the data.
• When taken from large samples, the difference between two values of -2LogL is distributed as chi-square.

• Likelihood_Fhas all the parameters of interest.
• Likelihood_Ris nested in the larger model. (nested = all terms occur in the larger model; necessary condition for model comparison tests).
• A nested model cannot have as a single IV, some other categorical or continuous variable not contained in the full model. If it does, then it is no longer nested, and we cannot compare the two values of -2LogL to get a chi-square value.
• The chi-square is used to statistically test whether including a variable reduces badness-of-fit measure.
• If chi-square is significant, the variable is considered to be a significant predictor in the equation.

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