Example
use http://www.gseis.ucla.edu/courses/data/hsb2, clear
generate mathhi = math>=54
generate write2 = write^2
tabulate mathhi
mathhi | Freq. Percent Cum.
------------+-----------------------------------
0 | 108 54.00 54.00
1 | 92 46.00 100.00
------------+-----------------------------------
Total | 200 100.00
logit mathhi write, nolog
Logit estimates Number of obs = 200
LR chi2(1) = 59.60
Prob > chi2 = 0.0000
Log likelihood = -108.18989 Pseudo R2 = 0.2160
------------------------------------------------------------------------------
mathhi | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
write | .1422945 .0222105 6.41 0.000 .0987627 .1858262
_cons | -7.796827 1.224831 -6.37 0.000 -10.19745 -5.396203
------------------------------------------------------------------------------
predict p2
(option p assumed; Pr(mathhi))
fitstat, saving(0)
Measures of Fit for logit of mathhi
Log-Lik Intercept Only: -137.989 Log-Lik Full Model: -108.190
D(198): 216.380 LR(1): 59.598
Prob > LR: 0.000
McFadden's R2: 0.216 McFadden's Adj R2: 0.201
Maximum Likelihood R2: 0.258 Cragg & Uhler's R2: 0.344
McKelvey and Zavoina's R2: 0.356 Efron's R2: 0.286
Variance of y*: 5.109 Variance of error: 3.290
Count R2: 0.725 Adj Count R2: 0.402
AIC: 1.102 AIC*n: 220.380
BIC: -832.687 BIC': -54.299
linktest
Logit estimates Number of obs = 200
LR chi2(2) = 65.54
Prob > chi2 = 0.0000
Log likelihood = -105.21668 Pseudo R2 = 0.2375
------------------------------------------------------------------------------
mathhi | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_hat | 1.270807 .2018605 6.30 0.000 .8751672 1.666446
_hatsq | .2662515 .1057033 2.52 0.012 .0590768 .4734262
_cons | -.3040576 .2107231 -1.44 0.149 -.7170672 .1089521
------------------------------------------------------------------------------
logit mathhi write write2, nolog
Logit estimates Number of obs = 200
LR chi2(2) = 65.54
Prob > chi2 = 0.0000
Log likelihood = -105.21668 Pseudo R2 = 0.2375
------------------------------------------------------------------------------
mathhi | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
write | -.4099542 .2153784 -1.90 0.057 -.8320882 .0121797
write2 | .005391 .0021403 2.52 0.012 .0011962 .0095858
_cons | 5.97325 5.316722 1.12 0.261 -4.447334 16.39383
------------------------------------------------------------------------------
postgr3 write, asis(write write2) gen(p1)
Variables left asis: write write2
(option p assumed; Pr(mathhi))
linktest
Logit estimates Number of obs = 200
LR chi2(2) = 65.70
Prob > chi2 = 0.0000
Log likelihood = -105.14092 Pseudo R2 = 0.2380
------------------------------------------------------------------------------
mathhi | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_hat | 1.001082 .1450353 6.90 0.000 .7168177 1.285345
_hatsq | -.0459454 .116897 -0.39 0.694 -.2750592 .1831685
_cons | .0639112 .2373879 0.27 0.788 -.4013605 .529183
------------------------------------------------------------------------------
fitstat, using(0)
Measures of Fit for logit of mathhi
Current Saved Difference
Model: logit logit
N: 200 200 0
Log-Lik Intercept Only: -137.989 -137.989 0.000
Log-Lik Full Model: -105.217 -108.190 2.973
D: 210.433(197) 216.380(198) 5.946(1)
LR: 65.544(2) 59.598(1) 5.946(1)
Prob > LR: 0.000 0.000 0.015
McFadden's R2: 0.237 0.216 0.022
McFadden's Adj R2: 0.216 0.201 0.014
Maximum Likelihood R2: 0.279 0.258 0.022
Cragg & Uhler's R2: 0.373 0.344 0.029
McKelvey and Zavoina's R2: 0.362 0.356 0.006
Efron's R2: 0.297 0.286 0.011
Variance of y*: 5.155 5.109 0.046
Variance of error: 3.290 3.290 0.000
Count R2: 0.740 0.725 0.015
Adj Count R2: 0.435 0.402 0.033
AIC: 1.082 1.102 -0.020
AIC*n: 216.433 220.380 -3.946
BIC: -833.335 -832.687 -0.648
BIC': -54.948 -54.299 -0.648
Difference of 0.648 in BIC' provides weak support for current model.
Note: p-value for difference in LR is only valid if models are nested.
Difference of 0.648 in BIC' provides weak support for saved model.
Note: p-value for difference in LR is only valid if models are nested.
scatter p1 p2 write, con(l l) msym(i i) sort
Next, we will use the fracpoly command to do the polynomial logistic regression.
fracpoly logit mathhi write 1 2, nolog
-> gen double Iwrit__1 = X-5.277 if e(sample)
-> gen double Iwrit__2 = X^2-27.85 if e(sample)
(where: X = write/10)
Logit estimates Number of obs = 200
LR chi2(2) = 65.54
Prob > chi2 = 0.0000
Log likelihood = -105.21668 Pseudo R2 = 0.2375
------------------------------------------------------------------------------
mathhi | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Iwrit__1 | -4.099542 2.153784 -1.90 0.057 -8.320882 .1217973
Iwrit__2 | .5390984 .2140251 2.52 0.012 .1196169 .9585798
_cons | -.6471137 .2288751 -2.83 0.005 -1.095701 -.1985267
------------------------------------------------------------------------------
Deviance: 210.433.
fracplot write
Finally, we will use fracpoly again but this time let it search for the best
fitting polynomial. In this case, it used write and write-2
fracpoly logit mathhi write
........
-> gen double Iwrit__1 = X^-2-.0359 if e(sample)
-> gen double Iwrit__2 = X-5.277 if e(sample)
(where: X = write/10)
Logit estimates Number of obs = 200
LR chi2(2) = 66.01
Prob > chi2 = 0.0000
Log likelihood = -104.98407 Pseudo R2 = 0.2392
------------------------------------------------------------------------------
mathhi | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Iwrit__1 | 86.12373 31.13893 2.77 0.006 25.09256 147.1549
Iwrit__2 | 2.915556 .6256198 4.66 0.000 1.689364 4.141748
_cons | -.5831283 .2112336 -2.76 0.006 -.9971387 -.169118
------------------------------------------------------------------------------
Deviance: 209.9681. Best powers of write among 44 models fit: -2 1.
linktest
Logit estimates Number of obs = 200
LR chi2(2) = 66.02
Prob > chi2 = 0.0000
Log likelihood = -104.98113 Pseudo R2 = 0.2392
------------------------------------------------------------------------------
mathhi | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_hat | 1.001922 .1473193 6.80 0.000 .7131815 1.290663
_hatsq | .0093415 .1219907 0.08 0.939 -.2297559 .2484389
_cons | -.0127298 .238401 -0.05 0.957 -.4799871 .4545275
------------------------------------------------------------------------------
fitstat
Measures of Fit for logit of mathhi
Log-Lik Intercept Only: -137.989 Log-Lik Full Model: -104.984
D(197): 209.968 LR(2): 66.009
Prob > LR: 0.000
McFadden's R2: 0.239 McFadden's Adj R2: 0.217
Maximum Likelihood R2: 0.281 Cragg & Uhler's R2: 0.376
McKelvey and Zavoina's R2: 0.360 Efron's R2: 0.300
Variance of y*: 5.141 Variance of error: 3.290
Count R2: 0.740 Adj Count R2: 0.435
AIC: 1.080 AIC*n: 215.968
BIC: -833.800 BIC': -55.413
Categorical Data Analysis Course
Phil Ender