Binomial Probit Model Maximum Likelihood Estimates Model estimated

Binomial probit model maximum likelihood estimates

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+---------------------------------------------+ | Binomial Probit Model | | Maximum Likelihood Estimates | | Model estimated: May 05, 2008 at 04:07:03PM.| | Dependent variable FINAL | | Weighting variable None | | Number of observations 2587 | | Iterations completed 6 | | Log likelihood function -825.9472 | | Restricted log likelihood -1284.216 | | Chi squared 916.5379 | | Degrees of freedom 9 | | Prob[ChiSqd > value] = .0000000 | | Hosmer-Lemeshow chi-squared = 22.57308 | | P-value= .00396 with deg.fr. = 8 | +---------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ Index function for probability Constant .8712666323 .24117408 3.613 .0003 AN .2259549490E-01 .94553383E-02 2.390 .0169 10.596830 HC .1585898886E-03 .21039762E-02 .075 .9399 49.974874 DOC .8804040395 .14866411 5.922 .0000 .31774256 COMP .4596088640 .13798168 3.331 .0009 .41785852 LIB .5585267697 .17568141 3.179 .0015 .13567839 CI .1797199200 .90808055E-01 1.979 .0478 1.2311558 CK .1415663447E-01 .13332671 .106 .9154 .91998454 PHD -.2351326125 .10107423 -2.326 .0200 .68612292 NOEVAL -1.928215642 .72363621E-01 -26.646 .0000 .29068419 (Note: E+nn or E-nn means multiply by 10 to + or -nn power.) +-------------------------------------------+ | Partial derivatives of E[y] = F[*] with | | respect to the vector of characteristics. | | They are computed at the means of the Xs. | | Observations used for means are All Obs. | +-------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| William. E. Becker Module One, Part Two: Using LIMDEP Sept. 15, 2008: p. 37
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+---------+--------------+----------------+--------+---------+----------+ Index function for probability Constant .1735365132 .47945637E-01 3.619 .0003 AN .4500509092E-02 .18776909E-02 2.397 .0165 10.596830 HC .3158750180E-04 .41902052E-03 .075 .9399 49.974874 Marginal effect for dummy variable is P|1 - P|0. DOC .1467543687 .21319420E-01 6.884 .0000 .31774256 Marginal effect for dummy variable is P|1 - P|0. COMP .8785901674E-01 .25536388E-01 3.441 .0006 .41785852 Marginal effect for dummy variable is P|1 - P|0. LIB .8672357482E-01 .20661637E-01 4.197 .0000 .13567839 CI .3579612385E-01 .18068050E-01 1.981 .0476 1.2311558 Marginal effect for dummy variable is P|1 - P|0. CK .2839467767E-02 .26927626E-01 .105 .9160 .91998454 Marginal effect for dummy variable is P|1 - P|0. PHD -.4448632109E-01 .18193388E-01 -2.445 .0145 .68612292 Marginal effect for dummy variable is P|1 - P|0. NOEVAL -.5339710749 .19569243E-01 -27.286 .0000 .29068419 (Note: E+nn or E-nn means multiply by 10 to + or -nn power.) +----------------------------------------+ | Fit Measures for Binomial Choice Model | | Probit model for variable FINAL | +----------------------------------------+ | Proportions P0= .197140 P1= .802860 | | N = 2587 N0= 510 N1= 2077 | | LogL = -825.94717 LogL0 = -1284.2161 | | Estrella = 1-(L/L0)^(-2L0/n) = .35481 | +----------------------------------------+ | Efron | McFadden | Ben./Lerman | | .39186 | .35685 | .80450 | | Cramer | Veall/Zim. | Rsqrd_ML | | .38436 | .52510 | .29833 | +----------------------------------------+ | Information Akaike I.C. Schwarz I.C. | | Criteria .64627 1730.47688 | +----------------------------------------+ Frequencies of actual & predicted outcomes Predicted outcome has maximum probability. Threshold value for predicting Y=1 = .5000 Predicted ------ ---------- + ----- Actual 0 1 | Total ------ ---------- + ----- 0 337 173 | 510 1 192 1885 | 2077 ------ ---------- + ----- Total 529 2058 | 2587 For each of these two probits, the first block of coefficients are for the latent variable probit equation. The second block provides the marginal effects. The initial class size (hb) probit coefficient −0.004883, however, is highly significant with a two-tail p -value of 0.0112. On the other hand, the William. E. Becker Module One, Part Two: Using LIMDEP Sept. 15, 2008: p. 38
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end-of-term class size (hc) probit coefficient (0.000159) is insignificant with a two-tail p -value of 0.9399. The overall goodness of fit can be assessed in several ways. The easiest is the proportion of correct 0 and 1 predictions: For the first probit, using initial class size (hb) as an explanatory variable, the proportion of correct prediction is 0.859 = (342+1880)/2587. For the second probit, using end-of-term class size (hc) as an explanatory variable, the proportion of correct prediction is also 0.859 = (337+1885)/2587. The Chi-square (922.95, df =9) for the probit employing the initial class size is slightly higher than that for the end-of-term probit (916.5379, df =9) but they are both highly significant.
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