# How to compare parameters between different types of generalized linear model?

I am doing some work on the effects of collinearity on different types of model (OLS, binomial logistic, ordinal logistic, multinomial logistic and maybe others). I have found the perturb package in R, which will be very useful for this. This package shows how small changes in the data affect the parameter estimates of a model. The perturb package perturbs the data that is used to build the model, and then re-runs the model - a little like a bootstrap. In this particular case, I chose to perturb the independent variables, but I could also perturb the dependent variable.

However, I am struggling to figure out the best way to compare these effects. For example, I ran perturb on an OLS model and got

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Impact of perturbations on coefficients:

mean  s.d.    min   max

x0          0.014 0.264 -0.743 0.604

x1          1.451 0.347  0.771 3.772

x2          0.847 0.321  0.308 2.817

x3          2.222 0.243  1.129 2.746
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Then I dichotomized the DV and ran perturb on a logistic model and got

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Impact of perturbations on coefficients:

mean  s.d.    min    max

x0          0.119 0.234 -0.477  0.732

x1          0.918 0.819 -6.612  2.215

x2          0.247 1.008 -9.413  1.175

x3          1.533 2.292  0.574 24.083
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The latter certainly looks like it was affected much more, but I don't know of any more formal ways to compare these parameter estimates and, especially, the size of the sd of the different estimates.

Thanks

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What exactly is perturbed in these simulations? The $y$'s? I'm also trying to understand your tables - for example, the 0.918 in the second table - does this mean the coefficient for $x_1$ was increased by $0.918$ on average? and the max, min and standard deviation of that change was $2.215, -6.612$ and $0.819$, respectively? –  Macro May 23 '12 at 14:58
@Macro I edited the post to (I hope) answer your question. –  Peter Flom May 23 '12 at 15:23
I also don't quite follow what these values indicate. Surely, the sampling distributions of the perturbations would be centered on 0, so what does the mean refer to? It would make sense to take the absolute values first, but the min values are negative. A little more explanation would help, here. On a different note, would you mind including a link to the package, and including the tabular info in the code block so that spacing / columns line up for better readability? –  gung May 23 '12 at 15:55
I'm still confused, Peter. Similarly to @gung, the entries of the table are a bit mysterious to me. Also, I'm still not sure what exactly is being perturbed - the predictors? the response? both? –  Macro May 23 '12 at 16:00