# Logistic Regression with interactions and contrasts

#### Yankel

##### New Member
Hello All,

I need some advice for choosing the correct model. I have 3 binary variables: Risk (0 = the person doesn't take financial risks, 1 = the person takes financial risks), gender (0 = female, 1 = male), and type of person (type 0 vs. type 1). The types are well defined, but for me, it's a binary variable for comparison. The questions of interest are: 1. Do type 0 males take more risks than females (of any type)? 2. Does type 0 males takes more risks than type 1 males? 3. Same like question 2, just for females.

Which model should I use? I thought maybe logistic regression, with interaction and perhaps contrasts, but I am not sure. Could you please advice me on which model is most appropriate? I will be using SPSS, so if contrasts are required, I would appreciate a tip on how to do it there.

#### noetsi

##### Fortran must die
Binary variables are usually referred to as dummy variables when they are predictors. Its not clear to me if they are what you are predicting [Y] or the predicting variables.

You need to clarify what variable is being predicted and which is predicting it. Contrast are useful, but not required (more often they are used in ANOVA, but they can be used in some forms of regression - not sure about logistic regression). You have to have a reason to specify interaction. Do you have one?

#### GretaGarbo

##### Human
If risk is the dependent variable and gender and type of person are the explanatory factors, then I suggest that you merge the two factors into one factor so that you get a "gen_type" factor with four levels: (female+type 0), (female+type 1), (male+type 0) and (male+type 1). Then you can do significance testing between pairs of each one of them.

The effects of this one-factor-with-four-levels can also be estimated with a two-factor model with one overall mean (an intercept), a main effects for gender, a main effect for person type and an interaction effect between the two factors. (Note that this is also four estimated parameters and it will give the same numerical result as the one-factor model.)

I suggest a one factor model because it is easier for the original poster.

(By the way, you don't need any specific reason to specify an interaction effect. And it is implicit in a one factor model.)

#### noetsi

##### Fortran must die
You should, but of course don't have to, have some theoretical reason to specify a variable for ANOVA or regression including an interaction. Or so I was taught

#### Yankel

##### New Member
Thank you both for replying. Indeed risk is the dependent variable, while type and gender are dummies.

I though that you always check if the interaction is significant. The reason I though of contrasts was because I am asked about specific comparisons, e.g. Do type 0 males take more risks than females?

#### hlsmith

##### Omega Contributor
Yes, use logistic regression.

GG's approach will work and an equivalent to the interaction would be if 1,1 - 1,0 - 0,1 + 0,0 > 0 (1,1 = yes to both groups,...,0,0 = no to both groups). The other thing you should do is determine the probability of risk for each unique grouping and plot all four of these values on a graph. Next, what you will look for is that 1,1 is greater than the individual effects of gender or type summed together.