------------------------------------------------------------------------------------------------------------------------------- name: log: c:\acdbookrevision\stata_final_programs_2013\racd13.txt log type: text opened on: 19 Jan 2013, 16:35:28 . . ********** OVERVIEW OF racd13.do ********** . . * STATA Program . * copyright C 2013 by A. Colin Cameron and Pravin K. Trivedi . * used for "Regression Analyis of Count Data" SECOND EDITION . * by A. Colin Cameron and Pravin K. Trivedi (2013) . * Cambridge University Press . . * This STATA program estimates measurement error models for chapter 13 . * 13.7 SIMULATION EXAMPLE: POISSON WITH MISMEASURED REGRESSOR . . * To run you need no data (the data are generated) . * and user-written Stata addons . * rcal, simex, qvf, cme, and gllamm (cme is a wappper for gllamm) . * in your directory . . ********** SETUP ********** . . set more off . version 12 . clear all . * set linesize 82 . set scheme s1mono /* Graphics scheme */ . * set maxvar 100 width 1000 . . ************ . . * This STATA program estimates some measurement error models . * TRUE: Poisson model with true regressor x1star . * NAIVE: Poisson model with observed x1 with measurement error . * RCAL: Regression calibration with duplicate observation z for x1star . * SIMEX: SIMEX with duplicate observation z for x1star . * NL2SLS: NLIV with instrument z for x1star . * IVAPPROX: Carroll's IV with duplicate observation (instrument) z for x1star . * MLE STRUCTURAL: Maximum likelihood of normal structural model . . * NOTE: SIMEX and MLE STRUCTURAL commented out as take a long time. . * But results from these commands are included in comments below. . * Can speed up SIMEX by reducing number of bootstrap replications . . ********** DATA DESCRIPTION . . * The data are generated . * y ~ Poisson(mu) . * mu = 0 + 1*x1star + 1*x2 . . * For normally distibuted data . * x1star ~ N[0, .4^2] . * x1 = x1star + e1 where e1 ~ N[0, .2^2] . * z1 = x1star + e2 where e2 ~ N[0, .2^2] . * x2 ~ N[0, .4^2] . . * For rescaled chisquare data . * x1star ~ (0.4/sqrt(2)) x (w-1) where w ~ chi2(1) . * x1 = x1star + e1 where e1 ~ (0.4/sqrt(2)) x (w-1) where w ~ chi2(1) . * z1 = x1star + e2 where e2 ~ (0.4/sqrt(2)) x (w-1) where w ~ chi2(1) . * x2 ~ (0.4/sqrt(2)) x (w-1) where w ~ chi2(1) . . ********** PART A: NORMALLY DISTRIBUTED DATA . . clear . set obs 10000 obs was 0, now 10000 . set seed 10101 . . generate x1star = rnormal(0, .4) . generate e1 = rnormal(0, .4) . generate e2 = rnormal(0, .4) . generate x2 = rnormal(0, .4) . generate x1 = x1star + e1 . generate z = x1star + e2 . generate mu = 0 + 1*x1star + 1*x2 . generate y = rpoisson(exp(mu)) . generate ynox2 = rpoisson(exp(0 + 1*x1star)) . generate ylinear = mu + rnormal(0,1) . generate xgamma = rgamma(1,1) . generate munegbin = xgamma*exp(mu) . generate ynegbin = rpoisson(munegbin) . . /* > lowess ynox2 x1, msize(tiny) lineopts(lwidth(medthick)) lstyle(solid) saving(graph1, replace) xlabel(#6) > lpoly ynox2 x1star, msize(tiny) lineopts(lwidth(medthick)) saving(graph2, replace) xlabel(#6) > graph combine graph1.gph graph2.gph iscale(0.7) ysize(5) xsize(6) xcommon > */ . . summarize Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- x1star | 10000 -.0026665 .39794 -1.433627 1.763537 e1 | 10000 -.003983 .3995721 -1.523171 1.548638 e2 | 10000 -.0044249 .4002048 -1.596938 1.504384 x2 | 10000 -.0044088 .3987985 -1.725232 1.627055 x1 | 10000 -.0066495 .5637038 -2.111444 1.982391 -------------+-------------------------------------------------------- z | 10000 -.0070913 .5660889 -2.212548 2.194387 mu | 10000 -.0070753 .5636274 -2.355915 2.077965 y | 10000 1.157 1.28067 0 10 ynox2 | 10000 1.0726 1.123679 0 8 ylinear | 10000 -.0078468 1.14627 -5.075897 4.553571 -------------+-------------------------------------------------------- xgamma | 10000 1.00228 1.013867 .0000238 11.05992 munegbin | 10000 1.172875 1.521178 .0000254 25.49255 ynegbin | 10000 1.1694 1.849391 0 22 . summarize y, detail y ------------------------------------------------------------- Percentiles Smallest 1% 0 0 5% 0 0 10% 0 0 Obs 10000 25% 0 0 Sum of Wgt. 10000 50% 1 Mean 1.157 Largest Std. Dev. 1.28067 75% 2 9 90% 3 9 Variance 1.640115 95% 4 10 Skewness 1.547291 99% 5 10 Kurtosis 6.607161 . tabulate y y | Freq. Percent Cum. ------------+----------------------------------- 0 | 3,735 37.35 37.35 1 | 3,210 32.10 69.45 2 | 1,717 17.17 86.62 3 | 791 7.91 94.53 4 | 342 3.42 97.95 5 | 116 1.16 99.11 6 | 51 0.51 99.62 7 | 15 0.15 99.77 8 | 15 0.15 99.92 9 | 6 0.06 99.98 10 | 2 0.02 100.00 ------------+----------------------------------- Total | 10,000 100.00 . . * Linear model with truth - not in book . regress ylinear x1star x2 Source | SS df MS Number of obs = 10000 -------------+------------------------------ F( 2, 9997) = 1618.41 Model | 3213.39251 2 1606.69625 Prob > F = 0.0000 Residual | 9924.63757 9997 .992761585 R-squared = 0.2446 -------------+------------------------------ Adj R-squared = 0.2444 Total | 13138.0301 9999 1.3139344 Root MSE = .99637 ------------------------------------------------------------------------------ ylinear | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1star | 1.029784 .0250396 41.13 0.000 .9807012 1.078866 x2 | .9813376 .0249857 39.28 0.000 .9323607 1.030315 _cons | -.0007743 .0099646 -0.08 0.938 -.0203069 .0187582 ------------------------------------------------------------------------------ . * Linear model with observed - not in book . regress ylinear x1 x2 Source | SS df MS Number of obs = 10000 -------------+------------------------------ F( 2, 9997) = 1073.98 Model | 2323.58619 2 1161.79309 Prob > F = 0.0000 Residual | 10814.4439 9997 1.08176892 R-squared = 0.1769 -------------+------------------------------ Adj R-squared = 0.1767 Total | 13138.0301 9999 1.3139344 Root MSE = 1.0401 ------------------------------------------------------------------------------ ylinear | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1 | .4984598 .0184532 27.01 0.000 .4622879 .5346317 x2 | .9908689 .0260836 37.99 0.000 .9397398 1.041998 _cons | -.0001637 .0104022 -0.02 0.987 -.0205541 .0202267 ------------------------------------------------------------------------------ . . * TRUE: Poisson model with true regressor x1star . poisson y x1star x2 Iteration 0: log likelihood = -13035.343 Iteration 1: log likelihood = -13035.343 Poisson regression Number of obs = 10000 LR chi2(2) = 3653.13 Prob > chi2 = 0.0000 Log likelihood = -13035.343 Pseudo R2 = 0.1229 ------------------------------------------------------------------------------ y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1star | .989535 .0235534 42.01 0.000 .9433712 1.035699 x2 | 1.006646 .0233194 43.17 0.000 .9609411 1.052352 _cons | -.0052865 .0106147 -0.50 0.618 -.026091 .015518 ------------------------------------------------------------------------------ . estimates store NTrue . . * NAIVE: Poisson model with observed x1 with measurement error . poisson y x1 x2 Iteration 0: log likelihood = -13415.789 Iteration 1: log likelihood = -13415.789 Poisson regression Number of obs = 10000 LR chi2(2) = 2892.24 Prob > chi2 = 0.0000 Log likelihood = -13415.789 Pseudo R2 = 0.0973 ------------------------------------------------------------------------------ y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1 | .5232958 .0164709 31.77 0.000 .4910134 .5555782 x2 | 1.01995 .0233884 43.61 0.000 .9741098 1.06579 _cons | .0288349 .01033 2.79 0.005 .0085885 .0490813 ------------------------------------------------------------------------------ . estimates store NNaive . . * RCAL: Regression calibration with duplicate observation z for x1star . * Standard errors vary with the seed . rcal (y = x2) (w1: x1 z), family(poisson) bstrap brep(400) seed(10101) Regression calibration No. of obs = 10000 Bootstrap reps = 400 Residual df = 9997 Wald F(2,9997) = 1417.20 Prob > F = 0.0000 (IRLS EIM) Scale param = 1.043864 Variance Function: V(u) = u [Poisson] Link Function : g(u) = ln(u) [Log] ------------------------------------------------------------------------------ | Bootstrap y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x2 | 1.012936 .0240201 42.17 0.000 .9658518 1.06002 w1 | .9999429 .0306092 32.67 0.000 .9399427 1.059943 _cons | .0223918 .0105701 2.12 0.034 .0016722 .0431113 ------------------------------------------------------------------------------ . estimates store NRCAL . . * SIMEX: SIMEX with duplicate observation z for x1star . * Commented out as takes a long time . * matrix theta=(0,.5,1,1.5,2,2.5,3,3.5) . * simex (y = x2) (w1: x1 z), family(poisson) theta(theta) median bstrap brep(400) seed(10101) . * Estimated coefficients vary with the seed . * simex (y = x2) (w1: x1 z), family(poisson) theta(theta) median bstrap brep(400) seed(12345) . . /* SIMEX Results. SIMEX commented out as takes a long time > . * SIMEX: SIMEX with duplicate observation z for x1star > . matrix theta=(0,.5,1,1.5,2,2.5,3,3.5) > . simex (y = x2) (w1: x1 z), family(poisson) theta(theta) median bstrap brep(400) seed(10101) > Estimated time to perform bootstrap: 15.5 minutes. > Simulation extrapolation No. of obs = 10000 > Bootstraps reps = 400 > Residual df = 9997 Wald F(2,9997) = 1501.29 > Prob > F = 0.0000 > Variance Function: V(u) = u [Poisson] > Link Function : g(u) = ln(u) [Log] > ------------------------------------------------------------------------------ > | Bootstrap > y | Coef. Std. Err. t P>|t| [95% Conf. Interval] > -------------+---------------------------------------------------------------- > x2 | 1.012512 .0240066 42.18 0.000 .9654542 1.05957 > w1 | .858099 .0238988 35.91 0.000 .8112526 .9049454 > _cons | .0062725 .009817 0.64 0.523 -.0129708 .0255157 > ------------------------------------------------------------------------------ > */ . . * NL2SLS: NLIV with instrument z for x1star . gmm (y - exp({xb:x1 x2} + {b0})), instruments(z x2) onestep Step 1 Iteration 0: GMM criterion Q(b) = .34138844 Iteration 1: GMM criterion Q(b) = .29895765 Iteration 2: GMM criterion Q(b) = .00095572 Iteration 3: GMM criterion Q(b) = 2.944e-07 Iteration 4: GMM criterion Q(b) = 2.614e-14 Iteration 5: GMM criterion Q(b) = 2.118e-28 GMM estimation Number of parameters = 3 Number of moments = 3 Initial weight matrix: Unadjusted Number of obs = 10000 ------------------------------------------------------------------------------ | Robust | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- /xb_x1 | .9607275 .0363876 26.40 0.000 .8894091 1.032046 /xb_x2 | 1.025419 .0269247 38.08 0.000 .9726474 1.07819 /b0 | -.0715327 .0150407 -4.76 0.000 -.1010118 -.0420535 ------------------------------------------------------------------------------ Instruments for equation 1: z x2 _cons . estimates store NNL2SLS . . * IVAPPROX: Carroll's IV with duplicate observation (instrument) z for x1star . qvf y x1 x2 (z x2), family(poisson) IV Generalized linear models No. of obs = 10000 Optimization : MQL Fisher scoring Residual df = 9997 (IRLS EIM) Scale param = 1 Deviance = 11861.55151 (1/df) Deviance = 1.186511 Pearson = 10881.85446 (1/df) Pearson = 1.088512 Variance Function: V(u) = u [Poisson] Link Function : g(u) = ln(u) [Log] Standard Errors : OIM Sandwich ------------------------------------------------------------------------------ y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- x2 | 1.025686 .0258009 39.75 0.000 .9751169 1.076254 x1 | .95795 .0349921 27.38 0.000 .8893668 1.026533 _cons | .0388165 .0108394 3.58 0.000 .0175717 .0600613 ------------------------------------------------------------------------------ . estimates store NIVApprox . . * MLE STRUCTURAL: Maximum likelihood of normal structural model . * Takes a long time to run so commented out . * cme y x2 (x1true: x1 z), link(log) family(poisson) robust . . /* CME RESULTS. CME commented out as takes a long time > . * MLE STRUCTURAL: Maximum likelihood of normal structural model > . cme y x2 (x1true: x1 z), link(log) family(poisson) robust > Running adaptive quadrature > Iteration 0: log likelihood = -29442.215 > Iteration 1: log likelihood = -28836.534 > Iteration 2: log likelihood = -28802.87 > Iteration 3: log likelihood = -28802.777 > Iteration 4: log likelihood = -28802.777 > Adaptive quadrature has converged, running Newton-Raphson > Iteration 0: log likelihood = -28802.777 > Iteration 1: log likelihood = -28802.777 > Iteration 2: log likelihood = -28802.776 > gllamm covariate measurement error model No. of obs = 10000 > log likelihood = -28802.776 > OUTCOME MODEL > ------------------------------------------------------------------------------ > | Robust > y | Coef. Std. Err. z P>|z| [95% Conf. Interval] > -------------+---------------------------------------------------------------- > y | > x2 | 1.01163 .0248953 40.64 0.000 .9628365 1.060424 > x1true | .9904211 .02921 33.91 0.000 .9331706 1.047672 > _cons | -.0026743 .0110999 -0.24 0.810 -.0244297 .0190811 > ------------------------------------------------------------------------------ > TRUE COVARIATE MODEL > ------------------------------------------------------------------------------ > x1true | Coef. Std. Err. z P>|z| [95% Conf. Interval] > -------------+---------------------------------------------------------------- > x1true | > x2 | -.0033133 .0122784 -0.27 0.787 -.0273785 .020752 > _cons | -.006885 .0048946 -1.41 0.160 -.0164782 .0027082 > -------------+---------------------------------------------------------------- > res. var. | .1603168 .003648 .1532465 .1675466 > ------------------------------------------------------------------------------ > MEASUREMENT MODEL > ------------------------------------------------------------------------------ > error var. | .1587588 .0022676 .1543761 .163266 > reliability | .5024414 .0075969 .4875535 .5173258 > ------------------------------------------------------------------------------ > */ . . *** TABLE 13.1 RESULTS: PANEL A: POISSON MODEL AND NORMAL DGP . . estimates table NTrue NNaive NRCAL NNL2SLS NIVApprox, b(%9.3f) se equations(1) -------------------------------------------------------------------------- Variable | NTrue NNaive NRCAL NNL2SLS NIVApprox -------------+------------------------------------------------------------ #1 | x1star | 0.990 | 0.024 x2 | 1.007 1.020 1.013 1.026 | 0.023 0.023 0.024 0.026 x1 | 0.523 0.958 | 0.016 0.035 w1 | 1.000 | 0.031 _cons | -0.005 0.029 0.022 0.961 0.039 | 0.011 0.010 0.011 0.036 0.011 -------------+------------------------------------------------------------ xb_x2 | _cons | 1.025 | 0.027 -------------+------------------------------------------------------------ b0 | _cons | -0.072 | 0.015 -------------------------------------------------------------------------- legend: b/se . . . ********** PART B: RESCALED CHISQUARE DISTRIBUTED DATA . . clear . set obs 10000 obs was 0, now 10000 . set seed 10101 . . generate x1star = 0.4*(rchi2(1)-1)/sqrt(2) . generate e1 = 0.4*(rchi2(1)-1)/sqrt(2) . generate e2 = 0.4*(rchi2(1)-1)/sqrt(2) . generate x2 = 0.4*(rchi2(1)-1)/sqrt(2) . . generate x1 = x1star + e1 . generate z = x1star + e2 . generate mu = 0 + 1*x1star + 1*x2 . generate y = rpoisson(exp(mu)) . generate ynox2 = rpoisson(exp(0 + 1*x1star)) . generate ylinear = mu + rnormal(0,1) . generate xgamma = rgamma(1,1) . generate munegbin = xgamma*exp(mu) . generate ynegbin = rpoisson(munegbin) . . /* > lowess ynox2 x1, msize(tiny) lineopts(lwidth(medthick)) lstyle(solid) saving(graph1, replace) xlabel(#6) > lpoly ynox2 x1star, msize(tiny) lineopts(lwidth(medthick)) saving(graph2, replace) xlabel(#6) > graph combine graph1.gph graph2.gph iscale(0.7) ysize(5) xsize(6) xcommon > */ . . summarize Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- x1star | 10000 .0029802 .4087211 -.2828427 3.859689 e1 | 10000 -.0010369 .3980761 -.2828427 3.471328 e2 | 10000 -.0020615 .3934839 -.2828427 3.519124 x2 | 10000 -.0021314 .4045407 -.2828427 4.583592 x1 | 10000 .0019433 .5705487 -.5656648 4.456134 -------------+-------------------------------------------------------- z | 10000 .0009187 .5649666 -.5656725 4.09623 mu | 10000 .0008488 .5805357 -.5656208 4.882773 y | 10000 1.324 2.806637 0 118 ynox2 | 10000 1.1516 1.713683 0 51 ylinear | 10000 -.0077314 1.171113 -3.818903 5.461312 -------------+-------------------------------------------------------- xgamma | 10000 1.011231 1.015599 .0002631 8.811442 munegbin | 10000 1.337701 4.323259 .0003677 244.9276 ynegbin | 10000 1.3504 4.500694 0 241 . summarize y, detail y ------------------------------------------------------------- Percentiles Smallest 1% 0 0 5% 0 0 10% 0 0 Obs 10000 25% 0 0 Sum of Wgt. 10000 50% 1 Mean 1.324 Largest Std. Dev. 2.806637 75% 2 62 90% 3 94 Variance 7.877212 95% 4 98 Skewness 18.76434 99% 9 118 Kurtosis 610.5811 . tabulate y y | Freq. Percent Cum. ------------+----------------------------------- 0 | 3,812 38.12 38.12 1 | 3,220 32.20 70.32 2 | 1,660 16.60 86.92 3 | 636 6.36 93.28 4 | 261 2.61 95.89 5 | 137 1.37 97.26 6 | 75 0.75 98.01 7 | 47 0.47 98.48 8 | 37 0.37 98.85 9 | 20 0.20 99.05 10 | 19 0.19 99.24 11 | 13 0.13 99.37 12 | 8 0.08 99.45 13 | 11 0.11 99.56 14 | 3 0.03 99.59 15 | 4 0.04 99.63 16 | 6 0.06 99.69 17 | 2 0.02 99.71 18 | 4 0.04 99.75 19 | 4 0.04 99.79 20 | 3 0.03 99.82 21 | 2 0.02 99.84 23 | 1 0.01 99.85 24 | 2 0.02 99.87 26 | 1 0.01 99.88 28 | 2 0.02 99.90 29 | 1 0.01 99.91 31 | 1 0.01 99.92 33 | 1 0.01 99.93 43 | 1 0.01 99.94 44 | 1 0.01 99.95 49 | 1 0.01 99.96 62 | 1 0.01 99.97 94 | 1 0.01 99.98 98 | 1 0.01 99.99 118 | 1 0.01 100.00 ------------+----------------------------------- Total | 10,000 100.00 . . * Linear model with truth - not in book . regress ylinear x1star x2 Source | SS df MS Number of obs = 10000 -------------+------------------------------ F( 2, 9997) = 1723.45 Model | 3516.06716 2 1758.03358 Prob > F = 0.0000 Residual | 10197.6248 9997 1.0200685 R-squared = 0.2564 -------------+------------------------------ Adj R-squared = 0.2562 Total | 13713.692 9999 1.37150635 Root MSE = 1.01 ------------------------------------------------------------------------------ ylinear | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1star | .9761178 .0247166 39.49 0.000 .9276683 1.024567 x2 | 1.065811 .024972 42.68 0.000 1.016861 1.114761 _cons | -.0083688 .0101003 -0.83 0.407 -.0281673 .0114298 ------------------------------------------------------------------------------ . * Linear model with observed - not in book . regress ylinear x1 x2 Source | SS df MS Number of obs = 10000 -------------+------------------------------ F( 2, 9997) = 1262.82 Model | 2765.85198 2 1382.92599 Prob > F = 0.0000 Residual | 10947.84 9997 1.09511253 R-squared = 0.2017 -------------+------------------------------ Adj R-squared = 0.2015 Total | 13713.692 9999 1.37150635 Root MSE = 1.0465 ------------------------------------------------------------------------------ ylinear | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1 | .5083372 .0183464 27.71 0.000 .4723745 .5442999 x2 | 1.069799 .0258751 41.34 0.000 1.019079 1.120519 _cons | -.0064391 .010465 -0.62 0.538 -.0269525 .0140744 ------------------------------------------------------------------------------ . . * TRUE: Poisson model with true regressor x1star . poisson y x1star x2 Iteration 0: log likelihood = -35375.388 Iteration 1: log likelihood = -20529.053 Iteration 2: log likelihood = -13502.43 Iteration 3: log likelihood = -13151.675 Iteration 4: log likelihood = -13145.302 Iteration 5: log likelihood = -13145.3 Iteration 6: log likelihood = -13145.3 Poisson regression Number of obs = 10000 LR chi2(2) = 11796.45 Prob > chi2 = 0.0000 Log likelihood = -13145.3 Pseudo R2 = 0.3097 ------------------------------------------------------------------------------ y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1star | .9746038 .0104697 93.09 0.000 .9540836 .9951241 x2 | .9869814 .0101441 97.30 0.000 .9670993 1.006863 _cons | .0096458 .0101329 0.95 0.341 -.0102144 .029506 ------------------------------------------------------------------------------ . estimates store CTrue . . * NAIVE: Poisson model with observed x1 with measurement error . poisson y x1 x2 Iteration 0: log likelihood = -29491.768 Iteration 1: log likelihood = -18776.217 Iteration 2: log likelihood = -14265.803 Iteration 3: log likelihood = -14054.319 Iteration 4: log likelihood = -14053.53 Iteration 5: log likelihood = -14053.53 Poisson regression Number of obs = 10000 LR chi2(2) = 9979.99 Prob > chi2 = 0.0000 Log likelihood = -14053.53 Pseudo R2 = 0.2620 ------------------------------------------------------------------------------ y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1 | .6923382 .009804 70.62 0.000 .6731228 .7115537 x2 | 1.000488 .0101882 98.20 0.000 .9805198 1.020457 _cons | .0332065 .0101038 3.29 0.001 .0134034 .0530096 ------------------------------------------------------------------------------ . estimates store CNaive . . * RCAL: Regression calibration with duplicate observation z for x1star . * Standard errors vary with the seed . rcal (y = x2) (w1: x1 z), family(poisson) bstrap brep(400) seed(10101) Regression calibration No. of obs = 10000 Bootstrap reps = 400 Residual df = 9997 Wald F(2,9997) = 2736.83 Prob > F = 0.0000 (IRLS EIM) Scale param = 1.113003 Variance Function: V(u) = u [Poisson] Link Function : g(u) = ln(u) [Log] ------------------------------------------------------------------------------ | Bootstrap y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x2 | .9800205 .0167146 58.63 0.000 .9472566 1.012784 w1 | 1.25432 .0246016 50.99 0.000 1.206096 1.302544 _cons | .0148296 .0109865 1.35 0.177 -.0067061 .0363653 ------------------------------------------------------------------------------ . estimates store CRCAL . . * SIMEX: SIMEX with duplicate observation z for x1star . * matrix theta=(0,.5,1,1.5,2,2.5,3,3.5) . * simex (y = x2) (w1: x1 z), family(poisson) theta(theta) median bstrap brep(400) seed(10101) . * Estimated coefficients vary with the seed . * simex (y = x2) (w1: x1 z), family(poisson) theta(theta) median bstrap brep(400) seed(12345) . . /* SIMEX Results. SIMEX commented out as takes a long time > * SIMEX: SIMEX with duplicate observation z for x1star > . simex (y = x2) (w1: x1 z), family(poisson) theta(theta) median bstrap brep(400) seed(10101) > Estimated time to perform bootstrap: 15.5 minutes. > Simulation extrapolation No. of obs = 10000 > Bootstraps reps = 400 > Residual df = 9997 Wald F(2,9997) = 3289.04 > Prob > F = 0.0000 > Variance Function: V(u) = u [Poisson] > Link Function : g(u) = ln(u) [Log] > ------------------------------------------------------------------------------ > | Bootstrap > y | Coef. Std. Err. t P>|t| [95% Conf. Interval] > -------------+---------------------------------------------------------------- > x2 | .983736 .0178388 55.15 0.000 .9487683 1.018704 > w1 | .956486 .0147981 64.64 0.000 .9274788 .9854933 > _cons | .0078898 .0106569 0.74 0.459 -.0129999 .0287794 > ------------------------------------------------------------------------------ > */ . . * NL2SLS: NLIV with instrument z for x1star . gmm (y - exp({xb:x1 x2} + {b0})), instruments(z x2) onestep Step 1 Iteration 0: GMM criterion Q(b) = 2.239997 Iteration 1: GMM criterion Q(b) = .43695283 Iteration 2: GMM criterion Q(b) = .18524262 Iteration 3: GMM criterion Q(b) = .00003971 Iteration 4: GMM criterion Q(b) = 4.188e-10 Iteration 5: GMM criterion Q(b) = 1.505e-20 GMM estimation Number of parameters = 3 Number of moments = 3 Initial weight matrix: Unadjusted Number of obs = 10000 ------------------------------------------------------------------------------ | Robust | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- /xb_x1 | .9793202 .0227306 43.08 0.000 .9347691 1.023871 /xb_x2 | .993116 .024999 39.73 0.000 .9441189 1.042113 /b0 | -.1076062 .0182696 -5.89 0.000 -.143414 -.0717984 ------------------------------------------------------------------------------ Instruments for equation 1: z x2 _cons . estimates store CNL2SLS . . * IVAPPROX: Carroll's IV with duplicate observation (instrument) z for x1star . qvf y x1 x2 (z x2), family(poisson) IV Generalized linear models No. of obs = 10000 Optimization : MQL Fisher scoring Residual df = 9997 (IRLS EIM) Scale param = 1 Deviance = 13030.90317 (1/df) Deviance = 1.303481 Pearson = 12070.42779 (1/df) Pearson = 1.207405 Variance Function: V(u) = u [Poisson] Link Function : g(u) = ln(u) [Log] Standard Errors : OIM Sandwich ------------------------------------------------------------------------------ y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- x2 | .9755163 .0235816 41.37 0.000 .9292973 1.021735 x1 | 1.356062 .0465995 29.10 0.000 1.264729 1.447396 _cons | .0322457 .0133714 2.41 0.016 .0060383 .058453 ------------------------------------------------------------------------------ . estimates store CIVApprox . . * MLE STRUCTURAL: Maximum likelihood of normal structural model . * Takes a long time to run so commented out . * cme y x2 (x1true: x1 z), link(log) family(poisson) robust . . /* CME RESULTS. CME commented out as takes a long time > . * MLE STRUCTURAL: Maximum likelihood of normal structural model > . cme y x2 (x1true: x1 z), link(log) family(poisson) robust > Running adaptive quadrature > Iteration 0: log likelihood = -29704.418 > Iteration 1: log likelihood = -29107.377 > Iteration 2: log likelihood = -29037.282 > Iteration 3: log likelihood = -29036.541 > Iteration 4: log likelihood = -29036.541 > Adaptive quadrature has converged, running Newton-Raphson > Iteration 0: log likelihood = -29036.541 > Iteration 1: log likelihood = -29036.541 (backed up) > Iteration 2: log likelihood = -29036.538 > Iteration 3: log likelihood = -29036.538 > gllamm covariate measurement error model No. of obs = 10000 > log likelihood = -29036.538 > OUTCOME MODEL > ------------------------------------------------------------------------------ > | Robust > y | Coef. Std. Err. z P>|z| [95% Conf. Interval] > -------------+---------------------------------------------------------------- > y | > x2 | .9698153 .0157735 61.48 0.000 .9388999 1.000731 > x1true | 1.213485 .0215 56.44 0.000 1.171346 1.255624 > _cons | -.0178152 .0115338 -1.54 0.122 -.040421 .0047907 > ------------------------------------------------------------------------------ > TRUE COVARIATE MODEL > ------------------------------------------------------------------------------ > x1true | Coef. Std. Err. z P>|z| [95% Conf. Interval] > -------------+---------------------------------------------------------------- > x1true | > x2 | .0253178 .012859 1.97 0.049 .0001147 .050521 > _cons | .001485 .0049441 0.30 0.764 -.0082053 .0111753 > -------------+---------------------------------------------------------------- > res. var. | .1658849 .0065873 .1532253 .1790469 > ------------------------------------------------------------------------------ > MEASUREMENT MODEL > ------------------------------------------------------------------------------ > error var. | .1563348 .004127 .1484518 .1646365 > reliability | .5148191 .0124117 .4904801 .539103 > ------------------------------------------------------------------------------ > */ . . *** TABLE 13.1 RESULTS: PANEL B: POISSON MODEL AND CHISQUARE DGP . . estimates table CTrue CNaive CRCAL CNL2SLS CIVApprox, b(%9.3f) se equations(1) -------------------------------------------------------------------------- Variable | CTrue CNaive CRCAL CNL2SLS CIVApprox -------------+------------------------------------------------------------ #1 | x1star | 0.975 | 0.010 x2 | 0.987 1.000 0.980 0.976 | 0.010 0.010 0.017 0.024 x1 | 0.692 1.356 | 0.010 0.047 w1 | 1.254 | 0.025 _cons | 0.010 0.033 0.015 0.979 0.032 | 0.010 0.010 0.011 0.023 0.013 -------------+------------------------------------------------------------ xb_x2 | _cons | 0.993 | 0.025 -------------+------------------------------------------------------------ b0 | _cons | -0.108 | 0.018 -------------------------------------------------------------------------- legend: b/se . . /* NOT IN BOOK ..... > > * REPEAT FOR NEGATIVE BINOMIAL D.G.P. - BUT USING POISSON METHODS > > * Negative binomial model with truth > nbreg ynegbin x1star x2 > * Negative binomial model with observed > nbreg ynegbin x1 x2 > > * Regression calibration with duplicate observation z for x1star > rcal (ynegbin = x2) (w1: x1 z), family(poisson) bstrap brep(100) > > * SIMEX with duplicate observation z for x1star > matrix theta=(0,.5,1,1.5,2,2.5,3,3.5) > simex (ynegbin = x2) (w1: x1 z), family(poisson) theta(theta) median bstrap brep(10) > > * Carroll's IV with duplicate observation (instrument) z for x1star > qvf ynegbin x1 x2 (z x2), family(poisson) > > * NLIV with instrument z for x1star > gmm (ynegbin - exp({xb:x1 x2} + {b0})), instruments(z x2) onestep > > * REPEAT FOR NEGATIVE BINOMIAL - BUT USING NBINOMIAL > > * Negative binomial model with truth > nbreg ynegbin x1star x2 > * Negative binomial model with observed > nbreg ynegbin x1 x2 > > * Regression calibration with duplicate observation z for x1star > rcal (ynegbin = x2) (w1: x1 z), family(nbinomial) bstrap brep(100) > > * SIMEX with duplicate observation z for x1star > matrix theta=(0,.5,1,1.5,2,2.5,3,3.5) > simex (ynegbin = x2) (w1: x1 z), family(nbinomial) theta(theta) median bstrap brep(10) > > * Carroll's IV with duplicate observation (instrument) z for x1star > qvf ynegbin x1 x2 (z x2), family(nbinomial) > > */ . . ********** CLOSE OUTPUT . . * log close . * clear . * exit . end of do-file . exit, clear