What are the ways to compare the fit of multinomial, ordinal, and stereotype logistic regression to a given dataset with ordinal response data using Stata?
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You can compare the log-likelihood for the ordered logit regression with that of the multinomial logit within which it is nested. A likelihood ratio test will therefore tell you whether simplification from multinomial logit to ordered logit is justified. For example, using the Mroz(1987) data, the test is distributed \(\chi^2(6)\) and yields a tail probability of 0.6%. Therefore, the simplification to an ordered model is rejected.
Output:Code:use https://www3.nd.edu/~rwilliam/statafiles/mroz.dta, clear *CATEGORIZE ANNUAL WORKING HOURS (NON-PARTICIPATION, PART-TIME, FULL-TIME) gen lfstatus= cond(hours==0, 0, cond(inrange(hours, 1, 1249), 1, 2)) lab def lfstatus 0 "non-participation" 1 "part-time work" 2 "full-time work" lab values lfstatus lfstatus mlogit lfstatus kidslt6 kidsge6 age educ exper nwifeinc est sto mlogit ologit lfstatus kidslt6 kidsge6 age educ exper nwifeinc est sto ologit lrtest mlogit ologit, force
Code:. mlogit lfstatus kidslt6 kidsge6 age educ exper nwifeinc Iteration 0: log likelihood = -809.85106 Iteration 1: log likelihood = -682.09452 Iteration 2: log likelihood = -676.45369 Iteration 3: log likelihood = -676.35678 Iteration 4: log likelihood = -676.35676 Multinomial logistic regression Number of obs = 753 LR chi2(12) = 266.99 Prob > chi2 = 0.0000 Log likelihood = -676.35676 Pseudo R2 = 0.1648 ----------------------------------------------------------------------------------- lfstatus | Coef. Std. Err. z P>|z| [95% Conf. Interval] ------------------+---------------------------------------------------------------- non_participation | (base outcome) ------------------+---------------------------------------------------------------- part_time_work | kidslt6 | -1.029752 .2192135 -4.70 0.000 -1.459402 -.6001012 kidsge6 | .1452962 .0810486 1.79 0.073 -.0135561 .3041485 age | -.061935 .0161806 -3.83 0.000 -.0936485 -.0302215 educ | .2352844 .0489108 4.81 0.000 .139421 .3311478 exper | .0836159 .0155026 5.39 0.000 .0532314 .1140004 nwifeinc | -.0191471 .0093588 -2.05 0.041 -.0374899 -.0008043 _cons | -1.051627 .9599877 -1.10 0.273 -2.933168 .8299147 ------------------+---------------------------------------------------------------- full_time_work | kidslt6 | -2.04806 .2883306 -7.10 0.000 -2.613177 -1.482942 kidsge6 | -.0562924 .089552 -0.63 0.530 -.2318111 .1192262 age | -.1267562 .0173295 -7.31 0.000 -.1607214 -.0927911 educ | .2225451 .0508362 4.38 0.000 .1229081 .3221822 exper | .1554865 .0162169 9.59 0.000 .123702 .187271 nwifeinc | -.0218055 .0102905 -2.12 0.034 -.0419746 -.0016364 _cons | 1.552764 .9850566 1.58 0.115 -.3779109 3.48344 ----------------------------------------------------------------------------------- . . est sto mlogit . . ologit lfstatus kidslt6 kidsge6 age educ exper nwifeinc Iteration 0: log likelihood = -809.85106 Iteration 1: log likelihood = -686.68524 Iteration 2: log likelihood = -685.50088 Iteration 3: log likelihood = -685.49686 Iteration 4: log likelihood = -685.49686 Ordered logistic regression Number of obs = 753 LR chi2(6) = 248.71 Prob > chi2 = 0.0000 Log likelihood = -685.49686 Pseudo R2 = 0.1536 ------------------------------------------------------------------------------ lfstatus | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- kidslt6 | -1.390614 .1813509 -7.67 0.000 -1.746055 -1.035172 kidsge6 | -.0341089 .0623172 -0.55 0.584 -.1562484 .0880307 age | -.0916151 .0121459 -7.54 0.000 -.1154207 -.0678096 educ | .158401 .0356408 4.44 0.000 .0885464 .2282557 exper | .1159833 .0112204 10.34 0.000 .0939917 .137975 nwifeinc | -.0153582 .0073408 -2.09 0.036 -.0297459 -.0009705 -------------+---------------------------------------------------------------- /cut1 | -1.75244 .7084357 -3.140949 -.3639319 /cut2 | -.3338748 .7054785 -1.716587 1.048838 ------------------------------------------------------------------------------ . . est sto ologit . . lrtest mlogit ologit, force Likelihood-ratio test LR chi2(6) = 18.28 (Assumption: ologit nested in mlogit) Prob > chi2 = 0.0056 -
Thank you, Andrew! Can I also perform goodness of fit test, residual analysis and sensitivity analysis?Last edited by Carla Jorge; 11 Feb 2020, 09:35.Comment
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You should follow what is done in related studies. For goodness of fit, most researchers within economics report the Pseudo R2 (McFadden's definition is what Stata uses). For more fit statistics, install fitstat from SSC which works both after mlogit and ologit.
Robustness checks require knowledge of the subject matter and availability of data. Then you can ask, for example, what is the effect of adding variable "X" or dropping variable "Y" on some variable "Z", which is the focus of your study. Bottom line is that your analysis must make sense.Code:ssc install fitstat
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Do NOT install fitstat from SSC! The version there is almost 20 years old and horribly outdated. Instead, do
findit spost13_ado
and install it. That will give you the most current version of fitstat, as well as several other useful programs.
For more on spost13, see
https://www.stata.com/bookstore/regr...ent-variables/
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Richard Williams, Notre Dame Dept of Sociology
StataNow Version: 19.5 MP (2 processor)
EMAIL: [email protected]
WWW: https://www3.nd.edu/~rwilliamComment
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Thank you, Andrew and Richard!Comment
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