Categorical Variables in Regression

Question 1

Degrees of freedom

Answer 1

For correlations & simple linear regression- df=n-2

For multiple regression, report df that ANOVA gives

Question 2

Predictor Variables

Answer 2

Typically regressions use internal-level data

Regressions are robust so can use ordinal or categorical predictors

Question 3

Categorical variables

Answer 3

Can include categorical predictors in regression analysis 
Binary categorical (2 categories) easier than multicategorical (>2 non-ordinal categories) 
Still cannot use categorical outcome variables in normal linear regression (requires logistic regression)

Question 4

Dummy variables

Answer 4

The way we include binary variables as predictors in a regression is to use dummy variables
Rather than using nominal categories in our binary categorical data we need to code one variable as 0 & the other as 1
Then we can look at the effect on our outcome variables of this predictor changing from 0 to 1
This lets us generate beta score for categorical data

Question 5

Why code dummy variables

Answer 5

Regressions can only handle numerical variables

Question 6

Dummy coding for multicategorical variables

Answer 6

Need to create a dummy variable for all but one of your category levels
This only works by keeping one category as the reference category which all other categories in your variable are compared to (usually neurotypicals)

Question 7

How logistic regression lets us predict a binary outcome

Answer 7

Logistic regression only for binary outcome
Trying to fit straight line of best fit won’t do much good for a binary outcome
Rather than looking at simple linear effects, can approximate the change with a sigmoid function (S-shape)
Means that logistic regression is based on different set of statistical assumptions

Question 8

No more assumption of linearity

Answer 8

In logistic regression, aren’t looking at linear effects of X’s on Y
Means that our assumptions in regression & parametric estimate break down
Changing our assumptions means that logistic regression can’t use the same parametric tests

Question 9

Regression model

Answer 9

Effects we’re looking at are non-linear so can’t use ANOVA, can use other maths to give values interpreted in similar way
SPSS gives 2 estimates of what equivalent R^2 would be in linear regression.
Can report & interpret these just like standard R^2

Question 10

Fit statistics

Answer 10

Can use fit statistics- -2 log likelihood (-2LL)
Not a significant/non-significant outcome
The higher the -2LL score, the better the model fits the data
Always relative, what counts as low or high score depends on sample size

Question 11

Odds ratios

Answer 11

For each predictor in logistic regression, report B(italic) value
Also report odds ratio- odds of change in y value for single point increasing corresponding x value
Odds are another war if expressing probability
If the OR for a predictor is <1, predictor makes outcome variable less likely (like -ve B(italics) value)
If OR for predictor is >1 that predictor makes the outcome more likely
Then we fear whether ORs differ from 1 yang 95% confidence intervals

Question 12

Multicategorical outcome variables

Answer 12

Can group multicategorical into binarys before doing a regression