week 9 - expanding on binary logistic regression

Question 1

how do we interpret the categorical predictors with more than two levels

Answer 1

• Set one level as your reference category that all other levels are compared to (e.g. “Single”
• Everything else is the same

Question 2

how do you evaluate individual predictors

Answer 2

• The process is the same except for:
• Predictor should be a numeric or integer variable (instead of a factor)
• Way to check quasi-complete separation and complete separation
• Interpretation of the Estimates and odds ratios
• An additional assumption: linearity of the logit

Question 3

what’s the difference for continuous predictors

Answer 3

• The process is the same except for:
• Predictor should be a numeric or integer variable (instead of a factor)
• Way to check quasi-complete separation and complete separation
• Interpretation of the Estimates and odds ratios
• An additional assumption: linearity of the logit

Question 4

what are the assumptions

Answer 4

• independence of errors
• linearity of logic
• no multicollinearity

Question 5

what is the ordinal outcome

Answer 5

• Use when the outcome is categorical, there are 3 or more levels, and there is an ordering to the levels
• Mild, moderate or severe disease

Question 6

what is the ordinal logistic regression

Answer 6

• An extension of binary logistic regression used when the outcome is ordinal
• We will focus on the proportional odds model

Question 7

what is the proportional odds model

Answer 7

• When we use a proportional odds model, we make a key assumption about the data:
• The predictor variable has the identical effect at each cumulative split
• As proportional odds models make this assumption, we only get one odds ratio for each continuous predictor/one odds ratio for each comparison of a categorical variable

Question 8

how do you evaluate the intercept-only model

Answer 8

• In binary logistic regression, the intercept-only model was calculated automatically alongside the specified model, allowing us to use output from the model to evaluate the model
• When running a proportional odds model, we only get the residual deviance (deviance for specified model)

Question 9

how do you interpret the predictors

Question 10

what are the predicted probabilities

Answer 10

• Predicted probabilities are a little more complex when we have 3+ levels of the outcomes variable
• Need to know the predicted probability for each individual within each outcome category
• Can use same ‘fitted’ function, but…
  We shouldn’t make this a new variable in our existing dataframe, as it will only display the values for one of the outcome levels (e.g. disagree)

Question 11

what is the proportional odds assumption

Answer 11

*Omnibus = model
*Also value for each comparison (e.g. continuous predictor or comparison for categorical predictors)
* If p > .05 for all, no violation of the proportional odds assumption