Statistical Analysis: Predictions
Retained Estimation Results
Retained estimation results are all accessible by name in subsequent operations.
- Predictions produced by all models
- Retain as a variable in the data set
- List with residuals and confidence intervals
- Extrapolate to out of sample observations
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%
-----------------------------------------------------------------------
Predicted Values (* => observation was not in estimating sample.)
Observation Observed Y Predicted Y Residual x(i)b Prob[Y=1]
1 1.0000000 1.0000000 .000000 .2236725 .5884939
2 1.0000000 1.0000000 .000000 .2682516 .6057472
3 1.0000000 1.0000000 .000000 .2155592 .5853343
4 1.0000000 1.0000000 .000000 .1631414 .5647964
5 1.0000000 1.0000000 .000000 .4736288 .6821177
6 1.0000000 1.0000000 .000000 .0214147 .5085426
7 1.0000000 1.0000000 .000000 .5769710 .7180205
8 1.0000000 1.0000000 .000000 .0187182 .5074671
9 1.0000000 1.0000000 .000000 .0846364 .5337248
10 1.0000000 1.0000000 .000000 .1733737 .5688211