## 9.1 Fitting the cusp catastrophe in `SPSS`

In the file Cusp Attitude.sav, you can find data from a (simulated) experiment. Assume the experiment tried to measure the effects of explicit predisposition and affective conditioning on attitudes towards Complexity Science measured in a sample of psychology students using a specially designed Implicit Attitude Test (IAT).

- Look at a Histogram of the difference score (post-pre) \(dZY\). This should look quite normal (pun intended).

`Perform a regular linear regression analysis predicting $dZY$ (Change in Attitude) from $\alpha$ (Predisposition).`

- Are you happy with the \(R^2\)?

- Look for Catastrophe Flags: Bimodality. Examine what the data look like if we split them across the conditions.

- Use \(\beta\) (Conditioning) as a Split File Variable (
`Data >> Split File`

). And again, make a histogram of \(dZY\). - Try to describe what you see in terms of the experiment.
- Turn Split File off. Make a Scatterplot of \(dZY\) (x-axis) and \(\alpha\) (y-axis). Here you see the bimodality flag in a more dramatic fashion.
- Can you see another flag?

- Perhaps we should look at a cusp Catastrophe model:

- Go to
`Analyse >> Regression >> Nonlinear`

(also see Basic Time Series Analysis). First we need to tell SPSS which parameters we want to use, press`Parameters.`

- Now you can fill in the following:
`Intercept`

(Starting value \(0.01\))`B1`

through`B4`

(Starting value \(0.01\))- Press
`Continue`

and use \(dZY\) as the dependent.

Now we build the model in

`Model Expression`

, it should say this:`Intercept + B1 * Beta * ZY1 + B2 * Alpha + B3 * ZY1 ** 2 + B4 * ZY1 ** 3`

- Run! And have a look at \(R^2\).

- Now you can fill in the following:

- The model can also be fitted with linear regression in SPSS, but we need to make some extra (nonlinear) variables using
`COMPUTE`

:

```
BetaZY1 = Beta*ZY1 *(Bifurcation, splitting parameter).
ZY1_2 = ZY1 ** 2 *(ZY1 Squared).
ZY1_3 = ZY1 ** 3 *(ZY1 Cubed).
```

- Create a linear regression model with \(dZY\) as dependent and \(Alpha\), \(BetaZY1\) and \(ZY1_2\) en \(ZY1_3\) as predictors.
- Run! The parameter estimates should be the same.

- Finally try to can make a 3D-scatterplot with a smoother surface to have look at the response surface.

- HINT: this is a lot easier in
`R`

or`Matlab`

perhaps you can export your`SPSS`

solution.

- How to evaluate a fit?

- Check the last slides of lecture 8 in which the technique is summarised.
- The cusp has to outperform the
`pre-post`

model.