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# Which test can I perform o show that one model is better than the other using simulations

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2 weeks ago

I have two models estimating the same number of parameters and using the same data. The models are only different because they are using different different likelihood functions in the proc nlmixed procedure.

I mean this;

```
proc nlmixed data=Surveydata;
parms b0=0 b1=0 ;
mean = exp(b0 + b1*Age);
ll = /*Some codes*/;
model art ~ general(ll);
run;
proc nlmixed data=Surveydata;
parms b0=0 b1=0 ;
mean = exp(b0 + b1*Age);
ll = /*Some codes different from those above*/;
model art ~ general(ll);
run;
```

Therefore expect different estimates for variable Age. So my question is this Apart from AIC or BIC what test can I use especially that I can incorporate with simulation to justify that one model is better than the other. The test may even focus on the ability of the estimates of the parameter Age to best explain the variable art. But most of all I would really want to simulate different data sets to use the test just to justify that for different data sets Model X is better than Model 2.

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Wednesday

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Posted in reply to john1111

a week ago

I assume the different LL represent different models, such as comparing Poisson, Neg Bionomial, ZIP, etc.

In simulation studies, people are often interested in

1. Bias. You can examine the distribution of (theta - theta_hat) where theta_hat is the Monte Carlo estimate

2. If the purpose of the study is to assess a point estimate, then the standard error of the MC estimates are important (precision)

3. If the purpose is to assess a confidence interval, then empirical coverage probability is important.

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Solution

Wednesday

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Posted in reply to john1111

a week ago

I assume the different LL represent different models, such as comparing Poisson, Neg Bionomial, ZIP, etc.

In simulation studies, people are often interested in

1. Bias. You can examine the distribution of (theta - theta_hat) where theta_hat is the Monte Carlo estimate

2. If the purpose of the study is to assess a point estimate, then the standard error of the MC estimates are important (precision)

3. If the purpose is to assess a confidence interval, then empirical coverage probability is important.

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Posted in reply to john1111

a week ago

If the two models can be considered strictly nonnested, then you can use the Vuong or Clarke test which are available from the Vuong macro.