Model goodness of fit

[miaomiao-alt]

This is the result of my model, and I want to know how well does this model fit? Thank you!

[miaomiao-alt]

The following is my understanding: for this model, whether the chi-square value is the primary criterion for evaluation, and the rest are auxiliary. If the chi-square value is too large, even if other fitting indicators perform better, it cannot be said that the model has a good fit. Is that right?

[cg09]

They are all standard statistical measures of agreement between a sample empirical distribution and an assumption about the family of distributions from which the sample is drawn. No such measure has any guarantee of anything about a finite sample. There best use is comparative, not between these measures but for any particular measure used to compare alternative hypotheses. Take your choice.

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On Sun, Sep 1, 2024 at 10:25 AM miaomiao-alt ***@***.***> wrote: The following is my understanding: for this model, whether the chi-square value is the primary criterion for evaluation, and the rest are auxiliary. If the chi-square value is too large, even if other fitting indicators perform better, it cannot be said that the model has a good fit. Is that right? — Reply to this email directly, view it on GitHub <#1815 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AD4Y3OJCC3RLOHX7HLPY5X3ZUMPVDAVCNFSM6AAAAABNO4B2XGVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDGMRTGM3DGNBYGE> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[miaomiao-alt]

Could you recommend some relevant literature？

[cg09]

The literature is vast and, about fundamentals, not very helpful. Google scholar is your friend, as is Wikipedia. Go to ChatGPT for a start. The basic problem is that you are trying to guess an infinite property from a finite sample. That is the basic problem in most statistical inference. However good the BIC score or p value for a hypothesis test, there is no logical guarantee that the results will not be different, or even reversed in model comparison, in a new, larger sample from the same population. The only logical guarantees that statistic provides are in the infinite limit...where you will never be.

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On Sun, Sep 1, 2024 at 8:29 PM miaomiao-alt ***@***.***> wrote: Could you recommend some relevant literature？ — Reply to this email directly, view it on GitHub <#1815 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AD4Y3OO4OTLZDOYZEHC4YMLZUOWPVAVCNFSM6AAAAABNO4B2XGVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDGMRTGU3DOOBTGY> . You are receiving this because you commented.Message ID: ***@***.***>

[miaomiao-alt]

OK！Thank you so much! At 2024-09-02 08:49:18, "cg09" ***@***.***> wrote: The literature is vast and, about fundamentals, not very helpful. Google scholar is your friend, as is Wikipedia. Go to ChatGPT for a start. The basic problem is that you are trying to guess an infinite property from a finite sample. That is the basic problem in most statistical inference. However good the BIC score or p value for a hypothesis test, there is no logical guarantee that the results will not be different, or even reversed in model comparison, in a new, larger sample from the same population. The only logical guarantees that statistic provides are in the infinite limit...where you will never be.

On Sun, Sep 1, 2024 at 8:29 PM miaomiao-alt ***@***.***> wrote: Could you recommend some relevant literature？ — Reply to this email directly, view it on GitHub <#1815 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AD4Y3OO4OTLZDOYZEHC4YMLZUOWPVAVCNFSM6AAAAABNO4B2XGVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDGMRTGU3DOOBTGY> . You are receiving this because you commented.Message ID: ***@***.***>

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