## (b) Heirarchical entry of independent variables

Select Analyze > Regression > Linear

Select the dependent variable and put it in the top box

When you run HEIRARCHICAL models, you need to divide your independent variables into groups.

Select the FIRST SET of independent variables and put these in the ‘Independent(s)’ box

Press the ‘Next’ button. The independent variables box will clear.

Select the SECOND SET of independent variables and put these in the ‘Independent(s)’ box

Press the ‘Next’ button. The independent variables box will clear.

Select the THIRD SET of independent variables and put these in the ‘Independent(s)’ box

Press OK. The regression will run and the output screen will appear

How do you interpret a hierarchical linear regression?

The simplest way to think about it is that each of Model 1, Model 2, and Model 3 are completely separate FORCED ENTRY models.

The coefficients for each variable in the three models are interpreted as ‘controlling for all the other variables in the model’. The difference with the later models (like Model 3) is that there are more controls (and more variables with coefficients).

So how would we interpret this set of models?

Look in the ‘Sig.’ column for the p-values

If the p-value < 0.05 then the independent variable has a significant impact on the dependent variable

For the significant variables, we then read the B values (coefficients), which are the effect of a one unit increase of the independent variable on the dependent variable.

In this case the dependent variable is a scale from ‘Never’ to ‘Extremely Often’.

- Let’s look at the transition of one variable - age - over the three models.
In models 1 and 2, age is statistically significant (Sig. column p, 0.05).

In model 3, age just drops out of statistical significance (p = 0.051). Why? Because we added the variable ‘I feel guilty when I have sex’. This variable turns out to be highly statistically significant: the guiltier a person is, the less they masturbate (or the less they report masturbating).

The fact that age loses significance when we add ‘guilt’ suggests that the variables are related, and the simplest interpretation is this:

‘The older a person is, the more they masturbate, but the reason that they masturbate more is that they feel less guilt. Once we control for guilt, there is no effect of age on masturbation. Older people are probably less guilty, and older people masturbate more, but they do so because they are less guilty, not because of their age per se.’

## (c) Stepwise regression

**WARNING: YOU SHOULD PROBABLY NOT BE RUNNING A STEPWISE REGRESSION WHY? BECAUSE THEY ARE A-THEORETICAL, AND SO PRONE TO MASSIVE CONCEPTUAL FLAWS.**

Let me show you through an example:

Select Analyze > Regression > Linear

Select the dependent variable and put it in the top box

When you run STEPWISE models, you tend to put a lot of variables into the model. You don’t generally have multiple blocks.

Select the independent variables and put these in the ‘Independent(s)’ box

Under the independent variables, there is the label ‘Method’. Select ‘Backward’ from the dropdown menu.

Click on ‘Options’.

This will reveal the options for ‘Stepping’. Because we are doing ‘Backwards selection’, you can just look at the ‘Removal’ box. Variables with Significance (p-value) greater than 0.10 will be removed from the model, one at a time. If you want you can adjust this up or down. Press ‘Continue’. Then press OK and run the model

- How do you interpret stepwise linear regression?

First you need to wade through the huge mass of output.

The way a stepwise backwards selection regression works is that SPSS estimates a complete model with all the variables, and then if any variables have a significance of greater than 0.10, then it removes the one with the highest p-value (i.e. the least significant variable is removed). It then re-estimates the model, and repeats this process until only variables with p-values < 0.10 are left.

So generally we interpret a STEPWISE model by just interpreting the LAST model as a FORCED ENTRY model.

Here are the last two models for our example. Notice the 21 and 22 next to the word (Constant). These are the model numbers, and this means that the method has dropped out 21 variables before getting to the final model.

So how would we interpret this set of models?

Look in the ‘Sig.’ column for the p-values

If the p-value < 0.05 then the independent variable has a significant impact on the dependent variable

Almost all the variables are significant at p < 0.05 level. But does this mean that we should SAY that these variables are significant CAUSE of masturbation?

Well take a look at the variables ‘v16 Have you masturbated’. This is positive and of large magnitude, but is it really a causal variable? Does it make sense to ‘If you have masturbated you are like to masturbate more.’ Maybe, but you would need to make a strong argument.

**THIS IS THE PROBLEM WITH STEPWISE MODELS: THEY DON’T DO THE THINKING FOR YOU, AND IF YOU GIVE IT SILLY MODELS, IT WILL STILL RUN THEM.**