Statistical Analysis: Simulations
Model Simulation for Any Model, Built In or User Created
- Average prediction with standard errors and confidence intervals
- Prediction at the sample means
- Analyze scenarios
- Extrapolate to out of sample simulations
- Fully accounts for all interactions and nonlinearities
Example
The following shows an ordered probit model for health satisfaction - the variable is coded 0-10. Some nonlinearity and two interaction terms are built into the model. The estimates are obtained for married individuals. The predicted probabilities for the 11 outcomes are simulated for the individuals in the sample. In a second simulation, the same predictions are computed for the unmarried individuals using the model estimated for married individuals. The third simulation examines the effect of age on the probability of the highest outcome. The simulation is listed then plotted with confidence limits for the simulation.
ORDERED ; If[married = 1] ; Lhs = hsat ; Rhs = one,age,age*educ,female,female*educ,hhkids $ Normal exit: 23 iterations. Status=0, F= 43080.05 ----------------------------------------------------------------------------- Ordered Probability Model Dependent variable HSAT Log likelihood function -43080.05498 Restricted log likelihood -43815.85243 Chi squared [ 5 d.f.] 1471.59489 Significance level .00000 McFadden Pseudo R-squared .0167930 Estimation based on N = 20730, K = 15 Inf.Cr.AIC = 86190.1 AIC/N = 4.158 Underlying probabilities based on Normal --------+-------------------------------------------------------------------- | Standard Prob. 95% Confidence HSAT| Coefficient Error z |z|>Z* Interval --------+-------------------------------------------------------------------- |Index function for probability Constant| 3.22007*** .04254 75.70 .0000 3.13670 3.30345 AGE| -.03177*** .00127 -25.06 .0000 -.03425 -.02928 AGE*EDUC| .00091*** .8924D-04 10.24 .0000 .00074 .00109 FEMALE| -.12656* .07517 -1.68 .0923 -.27389 .02077 |Interaction FEMALE*EDUC Intrct02| .00769 .00666 1.15 .2484 -.00537 .02075 HHKIDS| .03937** .01701 2.31 .0207 .00603 .07272 |Threshold parameters for index Mu(1)| .20742*** .01208 17.18 .0000 .18375 .23109 Mu(2)| .52526*** .01276 41.16 .0000 .50025 .55027 Mu(3)| .86479*** .01149 75.27 .0000 .84227 .88731 Mu(4)| 1.13613*** .01049 108.29 .0000 1.11556 1.15669 Mu(5)| 1.70965*** .00919 186.01 .0000 1.69163 1.72766 Mu(6)| 1.98584*** .00887 223.76 .0000 1.96844 2.00323 Mu(7)| 2.39664*** .00893 268.29 .0000 2.37913 2.41415 Mu(8)| 3.05476*** .00985 310.22 .0000 3.03546 3.07406 Mu(9)| 3.51443*** .01182 297.21 .0000 3.49125 3.53760 --------+-------------------------------------------------------------------- Note: nnnnn.D-xx or D+xx => multiply by 10 to -xx or +xx. Note: ***, **, * ==> Significance at 1%, 5%, 10% level. ----------------------------------------------------------------------------- SIMULATE ; Scenario: @ Married = 1 ; Outcome = * $ --------------------------------------------------------------------- Model Simulation Analysis for Ordered Probit Prob[Y = 10] --------------------------------------------------------------------- Simulations are computed by average over sample observations --------------------------------------------------------------------- User Function Function Standard (Delta method) Value Error |t| 95% Confidence Interval --------------------------------------------------------------------- Subsample for this iteration is MARRIED = 1 Observations: 20730 Avg.Prob(y= 0) .01502 .00031 48.83 .01442 .01563 Avg.Prob(y= 1) .00942 .00068 13.81 .00809 .01076 Avg.Prob(y= 2) .02369 .00170 13.90 .02035 .02703 Avg.Prob(y= 3) .04261 .00280 15.23 .03713 .04810 Avg.Prob(y= 4) .05047 .00383 13.17 .04296 .05798 Avg.Prob(y= 5) .15939 .00479 33.28 .15000 .16877 Avg.Prob(y= 6) .09809 .00608 16.15 .08618 .11000 Avg.Prob(y= 7) .15655 .00619 25.27 .14440 .16869 Avg.Prob(y= 8) .22505 .00548 41.06 .21430 .23579 Avg.Prob(y= 9) .10784 .00468 23.04 .09867 .11701 Avg.Prob(y=10) .11188 .00239 46.85 .10720 .11656 SIMULATE ; Scenario: @ married = 0 ; Outcome = * $ --------------------------------------------------------------------- Model Simulation Analysis for Ordered Probit Prob[Y = 10] --------------------------------------------------------------------- Simulations are computed by average over sample observations --------------------------------------------------------------------- User Function Function Standard (Delta method) Value Error |t| 95% Confidence Interval --------------------------------------------------------------------- Subsample for this iteration is MARRIED = 0 Observations: 6596 Avg.Prob(y= 0) .01236 .00027 45.11 .01183 .01290 Avg.Prob(y= 1) .00786 .00058 13.64 .00673 .00899 Avg.Prob(y= 2) .02001 .00146 13.73 .01715 .02286 Avg.Prob(y= 3) .03665 .00244 15.04 .03188 .04143 Avg.Prob(y= 4) .04428 .00339 13.05 .03763 .05093 Avg.Prob(y= 5) .14482 .00452 32.05 .13597 .15368 Avg.Prob(y= 6) .09250 .00577 16.03 .08119 .10382 Avg.Prob(y= 7) .15294 .00607 25.21 .14104 .16483 Avg.Prob(y= 8) .23308 .00567 41.08 .22196 .24420 Avg.Prob(y= 9) .11940 .00522 22.87 .10917 .12963 Avg.Prob(y=10) .13610 .00354 38.41 .12915 .14304 SIMULATE ; Scenario: @ married = 0,1 & age = 25(5)65 ; Means ; Plot(ci) $ --------------------------------------------------------------------- Model Simulation Analysis for Ordered Probit Prob[Y = 10] --------------------------------------------------------------------- Simulations are computed at sample means of all variables --------------------------------------------------------------------- User Function Function Standard (Delta method) Value Error |t| 95% Confidence Interval --------------------------------------------------------------------- Subsample for this iteration is MARRIED = 0 Observations: 6596 Func. at means .12968 .01364 9.51 .10294 .15641 AGE = 25.00 .25400 .01871 13.58 .21733 .29066 AGE = 30.00 .20588 .01707 12.06 .17242 .23933 AGE = 35.00 .16363 .01533 10.68 .13359 .19367 AGE = 40.00 .12746 .01352 9.43 .10096 .15395 AGE = 45.00 .09726 .01169 8.32 .07435 .12017 AGE = 50.00 .07267 .00989 7.35 .05328 .09206 AGE = 55.00 .05315 .00818 6.50 .03712 .06919 AGE = 60.00 .03804 .00660 5.76 .02510 .05099 AGE = 65.00 .02664 .00520 5.12 .01644 .03683 --------------------------------------------------------------------- Subsample for this iteration is MARRIED = 1 Observations: 20730 Func. at means .10122 .01223 8.28 .07725 .12519 AGE = 25.00 .25878 .01898 13.63 .22158 .29599 AGE = 30.00 .21014 .01744 12.05 .17596 .24432 AGE = 35.00 .16733 .01576 10.62 .13644 .19821 AGE = 40.00 .13059 .01397 9.35 .10320 .15797 AGE = 45.00 .09984 .01214 8.23 .07605 .12363 AGE = 50.00 .07475 .01031 7.25 .05454 .09496 AGE = 55.00 .05478 .00856 6.40 .03801 .07155 AGE = 60.00 .03929 .00693 5.67 .02571 .05287 AGE = 65.00 .02757 .00547 5.04 .01685 .03828