Results

The first line of the Model Summary table tells us about the model when only the constant is included (i.e., all predictor variables are omitted). The Deviance of this baseline model is 271.957, which represents the fit of the model when including only the constant. At this point, the model predicts that every participant is a singer, because this results in more correct classifications than if the model predicted that everyone was a guitarist. You can see this because the intercept is negative and 'Singer' is coded as 0.

The second line of the Model Summary table describes the model fit after these predictors have been added to the model. The overall fit of the new models is assessed using the Deviance. Remember that large values of the Deviance statistic indicate poorly fitting statistical models. The value of the Deviance for a new model should, therefore, be smaller than the value for the previous model if the fit is improving (the same goes for the BIC and AIC). When only the constant was included, Deviance = 271.96, but with the two predictors added it has reduced to 46.78 (i.e.,  = 225.18), which tells us that the model is better at predicting which instrument participants’ played when both predictors are included.

The table labelled Coefficients tells us the estimates for the coefficients for the predictors included in the model. These coefficients represents the change in the logit (log odds) of the outcome variable associated with a one-unit change in the predictor variable. The Wald statistics suggest that both extroversion, Wald(1) = 22.90, p < .001, and agreeableness, Wald(1) = 15.30, p < .001, significantly predict the instrument played. The corresponding odds ratio (labelled Odds Ratio) tells us the change in odds associated with a unit change in the predictor. The odds ratio for extroversion is 0.238, which is less than 1 meaning that as the predictor (extroversion) increases, the odds of the outcome decrease, that is, the odds of being a guitarist (compared to a singer) decrease. In other words, more extroverted participants are more likely to be singers. The odds ratio for agreeableness is 1.429, which is greater than 1 meaning that as agreeableness increases, the odds of the outcome increase, that is, the odds of being a guitarist (compared to a singer) increase. In other words, more agreeable people are more likely to be guitarists. Note that the odds ratio for the constant is insanely large, which brings us neatly onto the next task …