+---------------------------------------------+
| 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

+---------+--------------+----------------+--------+---------+----------+
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

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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