Statistical Analysis: Post Estimation Analysis

LIMDEP and NLOGIT offer many statistical tools for post estimation analysis including partial effects for all models, analysis of coefficients, two step estimation, a variety of hypothesis tests, simulation, extrapolation of predictions and more.

Retained Estimation Results

Retained estimation results are all accessible by name in subsequent operations.

  • Coefficient vector
  • Asymptotic covariance matrix
  • Ancillary parameter vectors
  • Predicted values
  • Residuals or generalized residuals
  • Log likelihood and other scalar statistics
  • Partial effects for all models
  • List predictions with confidence intervals and residuals
  • Extrapolate predictions to out of sample values
  • Analysis of coefficients, linear combinations and nonlinear functions, standard errors and test statistics

Example

Results shown will differ by model. The following shows the analysis of fit and listing of predictions for a binomial logit model.

+----------------------------------------+
| Fit Measures for Binomial Choice Model |
| Probit   model for variable LFP        |
+----------------------------------------+
|                 Y=0       Y=1     Total|
| Proportions  .43161    .56839   1.00000|
| Sample Size     325       428       753|
+----------------------------------------+
| Log Likelihood Functions for BC Model  |
|              P=0.50    P=N1/N   P=Model|
| LogL =      -521.94   -514.87   -499.43|
+----------------------------------------+
| Fit Measures based on Log Likelihood   |
| McFadden = 1-(L/L0)          =   .03000|
| Estrella = 1-(L/L0)^(-2L0/n) =   .04080|
| R-squared (ML)               =   .04020|
| Akaike Information Crit.     =  1.33712|
| Schwartz Information Crit.   =  1.36168|
+----------------------------------------+
| Fit Measures Based on Model Predictions|
| Efron                        =   .04069|
| Ben Akiva and Lerman         =   .52908|
| Veall and Zimmerman          =   .06823|
| Cramer                       =   .04023|
+----------------------------------------+
+---------------------------------------------------------+
|Predictions for Binary Choice Model.  Predicted value is |
|1 when probability is greater than  .500000, 0 otherwise.|
|Note, column or row total percentages may not sum to     |
|100% because of rounding. Percentages are of full sample.|
+------+---------------------------------+----------------+
|Actual|         Predicted Value         |                |
|Value |       0                1        | Total Actual   |
+------+----------------+----------------+----------------+
|  0   |     91 ( 12.1%)|    234 ( 31.1%)|    325 ( 43.2%)|
|  1   |     53 (  7.0%)|    375 ( 49.8%)|    428 ( 56.8%)|
+------+----------------+----------------+----------------+
|Total |    144 ( 19.1%)|    609 ( 80.9%)|    753 (100.0%)|
+------+----------------+----------------+----------------+
+---------------------------------------------------------+
|Crosstab for Binary Choice Model.  Predicted probability |
|vs. actual outcome. Entry = Sum[Y(i,j)*Prob(i,m)] 0,1.   |
|Note, column or row total percentages may not sum to     |
|100% because of rounding. Percentages are of full sample.|
+------+---------------------------------+----------------+
|Actual|      Predicted Probability      |                |
|Value |    Prob(y=0)        Prob(y=1)   | Total Actual   |
+------+----------------+----------------+----------------+
| y=0  |    147 ( 19.5%)|    177 ( 23.5%)|    325 ( 43.0%)|
| y=1  |    177 ( 23.5%)|    250 ( 33.2%)|    428 ( 56.7%)|
+------+----------------+----------------+----------------+
|Total |    325 ( 43.0%)|    427 ( 56.7%)|    753 ( 99.7%)|
+------+----------------+----------------+----------------+

-----------------------------------------------------------------------
Analysis of Binary Choice Model Predictions Based on Threshold =  .5000
-----------------------------------------------------------------------
Prediction Success
-----------------------------------------------------------------------
Sensitivity = actual 1s correctly predicted                     58.411%
Specificity = actual 0s correctly predicted                     45.231%
Positive predictive value = predicted 1s that were actual 1s    58.548%
Negative predictive value = predicted 0s that were actual 0s    45.231%
Correct prediction = actual 1s and 0s correctly predicted       52.722%
-----------------------------------------------------------------------
Prediction Failure
-----------------------------------------------------------------------
False pos. for true neg. = actual 0s predicted as 1s            54.462%
False neg. for true pos. = actual 1s predicted as 0s            41.355%
False pos. for predicted pos. = predicted 1s actual 0s          41.452%
False neg. for predicted neg. = predicted 0s actual 1s          54.462%
False predictions = actual 1s and 0s incorrectly predicted      47.012%
-----------------------------------------------------------------------
The following shows the analysis of predicted probabilities given a change in income.
+-------------------------------------------------------------+
|Scenario 1. Effect on aggregate proportions. Logit    Model  |
|Threshold T* for computing Fit = 1[Prob > T*] is  .50000     |
|Variable changing = INCOME  , Operation = *, value =   1.250 |
+-------------------------------------------------------------+
|Outcome           Base case       Under Scenario   Change    |
|      0       185 =  24.57%       157 =   20.85%      -28    |
|      1       568 =  75.43%       596 =   79.15%       28    |
|  Total       753 = 100.00%       753 =  100.00%        0    |
+-------------------------------------------------------------+
The figure shows the behavior of the predicted probability over the sample range of education.

 Post estimation analysis of binomial logit model using LIMDEP statistical software