sample size and the replacment of pearson chi-square with likelihood ratio

[Wang Xu-4]

Dear list members,

I recently read a book on statistics, in which the book said when sample size is large then the pearson chi-sqaure could be equal and replaced by likelihood ratio value. But I don't know if there is any rule of thumb say if there is a specific threshold value for such replacement? Thanks a lot!

 

Wang Xu  

[Bruce Weaver]

One way to think of the likelihood ratio chi-square is as the test on the change in -2LL from a logistic regression model with only the intercept to a model that includes the one predictor variable.  This suggests that you should use the same sample size guidelines as you would for logistic regression.  

For binary logistic regression, simulations by Peduzzi et al. (1996, IIRC) suggest that one should have at least 10 events per variable, where an event is defined as the less frequently occurring category for the outcome variable.  (Some people argue 20 events per variable would be preferred.)  If one of the two variables in your contingency table is dichotomous, you could use this rule as a guideline.  But bear in mind that a categorical variable with k levels would be counted as k-1 (indicator) variables.

If both of your variables have more than two categories, you'll have to look a similar rule of thumb for multinomial (or ordinal) logistic regression.  I don't have one at my fingertips.  

Having too many empty or sparsely populated cells would also be problematic.  IIRC, logistic regression issues a warning about this, but I don't have SPSS on this machine, so cannot check the documentation.

Wang Xu-4 wrote

Dear list members,
I recently read a book on statistics, in which the book said when sample size is large then the pearson chi-sqaure could be equal and replaced by likelihood ratio value. But I don't know if there is any rule of thumb say if there is a specific threshold value for such replacement? Thanks a lot!

Wang Xu

[Wang Xu-4]

Thanks a lot, Bruce Weaver!

在2010-04-05 02:45:11，"Bruce Weaver" <[hidden email]> 写道：
>One way to think of the likelihood ratio chi-square is as the test on the
>change in -2LL from a logistic regression model with only the intercept to a
>model that includes the one predictor variable.  This suggests that you
>should use the same sample size guidelines as you would for logistic
>regression.
>
>For binary logistic regression, simulations by Peduzzi et al. (1996, IIRC)
>suggest that one should have at least 10 events per variable, where an event
>is defined as the less frequently occurring category for the outcome
>variable.  (Some people argue 20 events per variable would be preferred.)
>If one of the two variables in your contingency table is dichotomous, you
>could use this rule as a guideline.  But bear in mind that a categorical
>variable with k levels would be counted as k-1 (indicator) variables.
>
>If both of your variables have more than two categories, you'll have to look
>a similar rule of thumb for multinomial (or ordinal) logistic regression.  I
>don't have one at my fingertips.
>
>Having too many empty or sparsely populated cells would also be problematic.
>IIRC, logistic regression issues a warning about this, but I don't have SPSS
>on this machine, so cannot check the documentation.
>
>
>
>Wang Xu-4 wrote:
>>
>> Dear list members,
>> I recently read a book on statistics, in which the book said when sample
>> size is large then the pearson chi-sqaure could be equal and replaced by
>> likelihood ratio value. But I don't know if there is any rule of thumb say
>> if there is a specific threshold value for such replacement? Thanks a lot!
>>
>> Wang Xu
>>
>
>
>-----
>--
>Bruce Weaver
>[hidden email]
>http://sites.google.com/a/lakeheadu.ca/bweaver/
>"When all else fails, RTFM."
>
>NOTE:  My Hotmail account is not monitored regularly.
>To send me an e-mail, please use the address shown above.
>--
>View this message in context: http://old.nabble.com/sample-size-and-the-replacment-of-pearson-chi-square-with-likelihood-ratio-tp28133480p28133664.html
>Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>
>=====================
>To manage your subscription to SPSSX-L, send a message to
>[hidden email] (not to SPSSX-L), with no body text except the
>command. To leave the list, send the command
>SIGNOFF SPSSX-L
>For a list of commands to manage subscriptions, send the command
>INFO REFCARD