week 8 - binary logistic regression models

Question 1

what is the binary outcome variable

Answer 1

• linear regression can work very well when you have a continuous outcome

Question 2

what are the two possible outcomes

Answer 2

• participants can either be outcome a or outcome, either be happy or unhappy

Question 3

how do we overcome the violation

Answer 3

• When the outcome is binary (two possible outcomes), the assumption of linearity is ALWAYS violated
• We can apply a transform to the data to express the non-linear relationship in a linear way
• Binary logistic regression does this by expressing the linear regression equation in logarithmic terms
• This overcomes the issue of violating this assumption

Question 4

what is binary logistic regression

Answer 4

• Logistic regression is a generalized linear model – flexible generalisation of linear regression
• Predicting an outcome that has only two possible outcomes
• Which of two outcomes is an individual likely to have (e.g. happy/not happy, pass/fail)?
• Predictors can be continuous, categorical, or a combination

Question 5

what is the odds ration

Answer 5

• An odds ratio is one of the most important outcomes of logistic regression
• Odds ratio = Change in odds resulting from a unit change in the predictor
• Measure of association between a predictor and an outcome

Question 6

how do we interpret the odds ratio

Answer 6

• a unit increase in the predictor is associated with a lower odds of the outcome
• unit increase in the predictor is associated with a higher odds of the outcome

Question 7

what does the odds ratio number mean

Answer 7

• Individuals who have a hamster have 4.69x higher odds being happy relative to individuals who do not have a hamster
• You must use the word ‘odds’ when referring to odds ratios

Question 8

what is the independence of errors

Answer 8

• Cases of data should not be related
• For instance, each cases should represent data from a different person
• We can’t really test for this - we should just know this is true based on the methodology

Question 9

what is the failure to coverage

Answer 9

• When you run a binary logistic regression model, R starts by estimating the parameters with a best guess
• It then attempts to estimate the parameters more accurately
• It stops when on each new attempt, the parameters are very similar (it “converges”)
• Sometimes it doesn’t converge:
  Ignore the output – not accurate!!

Question 10

how do we prepare our data

Answer 10

• The binary outcome should be stored as a numeric value with outcomes coded as 0 and 1
• Categorical predictor should be a factor
• Run the binary logistic regression model Code to run the binary logistic regression model

Question 11

how do we evaluate the model

Answer 11

• To assess the fit of our model, we can compare our specified model to a model containing only the intercept (no predictors)
• We do this by looking at a measure called the “deviance”:

Question 12

does the binary logistic regression have R2

Answer 12

• R2 in linear regression = the proportion of variance explained by the model
  In logistic regression, this doesn’t exist

Question 13

what is the intercept

Question 14

how do we evaluate the individual predictors

Answer 14

• To convert back from the log scale, we exponentiate our log odds (“Estimate”).
• This gives us our odds ratio
• We also want a confidence interval arounds the odds ratio
• 95% confidence interval tells us the likely range the true odds ratio in the population is contained in

Question 15

what are predicted probabilities

Answer 15

• But we can obtain probabilities from our model too. For instance:
• If an individual has a hamster, what’s the probability they will be happy?
• If an individual does not have a hamster, what’s the probability they will be happy?