# Re: st: Tiao-Goldberger test

 From Michael Stobernack To statalist@hsphsun2.harvard.edu Subject Re: st: Tiao-Goldberger test Date Mon, 16 Feb 2009 18:01:27 +0100

```At 16.02.2009 16:47, you wrote:
```
```--- On Mon, 16/2/09, Michael Stobernack wrote:
> Another possibility could be to incorporate dummy variables
> and interaction terms for the different groups of interest.
> Since I have got four different groups I need three dummies
> and many interactions terms, so I loose (to) many degrees of
> freedom (n=50).

By estimating separate models for each group you actually
estimate 4 extra coefficients, i.e. loose 4 degrees of
freedom,
```
```

I estimate the following model 4 times, i.e. once for each of the four groups:

```
y = b0 + b1*x1 + b2 * x2 + b3*x3 + e, so I have to estimate 4*4 = 16 coefficients.
```
```
If I estimate one model for all 4 groups together and D1 is a dummy four group1 etc, I use
```
y = b0 + b1*x1 + b2*x2 + b3*x3 +
```
b4*D1 + b5*D2 + b6*D3 + (to see, whether the intercept differs between the groups) b7*D1*x1 + b8*D2*x1 + b9*D3*x1 + (to see, whether the slope of x1 differs between the groups) b10*D1*x2 + b11*D2*x2 + b12*D3*x2 + (to see, whether the slope of x2 differs between the groups) b13*D1*x3 + b14*D2*x3 + b15*D3*x3 + epsilon (to see, whether the slope of x3 differs between the groups)
```
So I have to estimate 16 coefficients.

```
What do you mean by 'estimate 4 extra coefficients'? Do you mean 4 extra values of the residual variance?
```
Michael

```
``` compared to a model with all the interaction
effects. The reason is that in the interaction model you
constrain the residual variance to be equal across groups.

-- Maarten

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

Buitenveldertselaan 3 (Metropolitan), room N515

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

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```
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