Problem with linktest on logistic regression

[Sasi Levy]

Hello,

I want to investigate the determinants of job-education mismatches. I ran logistic regress and then the linktest. The_hatsq value is significant, indicating problem with the model specification. My R-squared is also pretty low.

Y = having mismatch job = 1 and 0 otherwise.
year = dummies of time = year of survey

logit newmatch i.reg i.area i.sex age i.marital i.edule i.status i.subject i.year
linktest

linktest result:

newmatch Coef. Std. Err. z P>z [95% Conf. Interval]

_hat .8927595 .0154203 57.90 0.000 .8625363 .9229826
_hatsq .0897623 .0088951 10.09 0.000 .0723282 .1071964
_cons -.0569142 .0159678 -3.56 0.000 -.0882105 -.0256179

I tried to alter my model by adding interaction between variables. However, I still got the significant _hatsq (P = 0.000). Do you have any recommendations on what I should do/ modify with the model?

logit newmatch i.reg i.area i.sex##i.subject c.age##c.age i.marital i.edule i.status i.year
linktest

linktest result:

newmatch Coef. Std. Err. z P>z [95% Conf. Interval]

_hat .9058087 .0156475 57.89 0.000 .8751401 .9364773
_hatsq .0752449 .0087495 8.60 0.000 .0580962 .0923935
_cons -.0460228 .0157786 -2.92 0.004 -.0769483 -.0150973



Thank you so much in advance .

[Carlo Lazzaro]

Sasi:
1) I'm under the impression that you have too many categorical predictors: this may explain the -linktest- disappointing outcome. I would go for a more parsimonious rtegression specification, run -linktest-, add one predictor at a time till -linktest- outcome, if feasible, does not show a p-value <0.05 for sq_hat;
2) see the cautionary note about -linktest- after -logit- in Example 3, -linktest- entry, Stata .pdf manual;
3) as far as the value of the pseudo_R2 is concerned, being high or low depends on its average value is similar researches.

[Sasi Levy]

Carlo,

Thank you so much for your reply; this is very helpful. I followed your 1)recommendation by adding one predictor at a time in logistic regress and it turned out that i.reg i.area i.year generated -linktest- outcome, with a p-value > 0.05 for sq_hat.

logit newmatch i.reg
logit newmatch i.reg i.area
logit newmatch i.reg i.area
logit newmatch i.reg i.area i.year

I'm not what I should do next. Should I just ignore the results for -linktest- as it may not be sensible to rely on?

Thank you.

[Carlo Lazzaro]

Sasi:
a p-value >0.05 supports the lack of evidence for rejecting the null of -linktest- (the null being: the functional form of the regressand -or, under more general conditions, the whole regression model - is misspecified).
As there's no evidence of misspecification, go -logit newmatch i.reg i.area i.year-.