proc surveylogistic AIC

[bikashten]

Hi all;

I am looking for help. I am reading this paper from Thomas Lumley & Alastair Scott.

https://www.stat.colostate.edu//graybillconference2013/Presentations/Scott.pdf

They mentioned about AIC, BIC and new AIC and BIC value that scaled to sample size.

Output from the SAS SURVEYLOGISTIC Procedure
Model Fit Statistics
Criterion Intercept Intercept
Only and Covariates
AIC 201153424 159489290
SC 201153431 159489396
-2 Log L 201153422 159489262
Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 41664159.2 13 <.0001
Score 38579687.9 13 <.0001
Wald 1344.6 13 <.0001

Notice that the output contains values for quantities labelled AIC,
SC (aka BIC) and Likelihood Ratio.
These mean very little as they stand. However, we can adapt them
to produce something useful.
Part of the problem is that we have used the published weights,
summing to the population size N = 246750000.
We get more reasonable values if we re-scale to the sample size
n = 13,957:

Output from PROC SURVEYLOGISTIC
Model Fit Statistics
Criterion Intercept Intercept
Only and Covariates
AIC 12800.7 10173.8
SC 12807.7 10281.8
-2 Log L 12798.7 10147.8
Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 2356.7 13 <.0001
Score 2182.2 13 <.0001
Wald 1344.6 13 <.0001

I am not sure how they got the AIC value scale to sample size. It will be helpful if someone send me a code to calculate new aic value based on sample size.

Thank you,

Bikash

[ballardw]

---

@bikashten wrote:

Hi all;

I am looking for help. I am reading this paper from Thomas Lumley & Alastair Scott.

https://www.stat.colostate.edu//graybillconference2013/Presentations/Scott.pdf

They mentioned about AIC, BIC and new AIC and BIC value that scaled to sample size.

Output from the SAS SURVEYLOGISTIC Procedure
Model Fit Statistics
Criterion Intercept Intercept
Only and Covariates
AIC 201153424 159489290
SC 201153431 159489396
-2 Log L 201153422 159489262
Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 41664159.2 13 <.0001
Score 38579687.9 13 <.0001
Wald 1344.6 13 <.0001

Notice that the output contains values for quantities labelled AIC,
SC (aka BIC) and Likelihood Ratio.
These mean very little as they stand. However, we can adapt them
to produce something useful.
Part of the problem is that we have used the published weights,
summing to the population size N = 246750000.
We get more reasonable values if we re-scale to the sample size
n = 13,957:

Output from PROC SURVEYLOGISTIC
Model Fit Statistics
Criterion Intercept Intercept
Only and Covariates
AIC 12800.7 10173.8
SC 12807.7 10281.8
-2 Log L 12798.7 10147.8
Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 2356.7 13 <.0001
Score 2182.2 13 <.0001
Wald 1344.6 13 <.0001

I am not sure how they got the AIC value scale to sample size. It will be helpful if someone send me a code to calculate new aic value based on sample size.

Thank you,

Bikash

---

It would help others if you had mentioned that everything you show as text was copied from the PDF, so you have no data or code to start from.

The authors did not show any code or actual data though one could download the public NHANES data set they mention and possibly duplicate the result.

One approach could have been to reduce the sample weight variable by some ratio or log of the weight variable or similar. I recommend if you want specifics to contact the authors.

[bikashten]

Hi Ballardw,

Thank you so much for replying this thread.

There is also a paper suggesting that scaling the weights to sum to sample size (n) (page 12-http://www.isr.umich.edu/src/smp/asda/J%20Surv%20Stat%20Methodol-2015-Lumley-jssam_smu021.pdf). I am also assuming that if we divide the individuals weight by mean of all weight in order to get new weight scaled to sample size, But I am not sure it is right or not.

Thanks,

Bikash