1. Discrete Choice Modeling William Greene Stern School of Business New York University Lab Sessions

2. Lab Session 2 Analyzing Binary Choice Data

3. Data Set: Load PANELPROBIT.LPJ

4. Fit Basic Models

5. Partial Effects for Interactions

6. Partial Effects  Build the interactions into the model statement PROBIT ; Lhs = Doctor ; Rhs = one,age,educ,age^2,age*educ $  Built in computation for partial effects PARTIALS ; Effects: Age & Educ = 8(2)20 ; Plot(ci) $

7. Average Partial Effects --------------------------------------------------------------------- Partial Effects Analysis for Probit Probability Function --------------------------------------------------------------------- Partial effects on function with respect to AGE Partial effects are computed by average over sample observations Partial effects for continuous variable by differentiation Partial effect is computed as derivative = df(.)/dx --------------------------------------------------------------------- df/dAGE Partial Standard (Delta method) Effect Error |t| 95% Confidence Interval --------------------------------------------------------------------- Partial effect.00441.00059 7.47.00325.00557 EDUC = 8.00.00485.00101 4.80.00287.00683 EDUC = 10.00.00463.00068 6.80.00329.00596 EDUC = 12.00.00439.00061 7.18.00319.00558 EDUC = 14.00.00412.00091 4.53.00234.00591 EDUC = 16.00.00384.00138 2.78.00113.00655 EDUC = 18.00.00354.00192 1.84 -.00023.00731 EDUC = 20.00.00322.00250 1.29 -.00168.00813

8. Useful Plot

9. More Elaborate Partial Effects  PROBIT ; Lhs = Doctor ; Rhs = one,age,educ,age^2,age*educ, female,female*educ,income $  PARTIAL ; Effects: income @ female = 0,1 ? Do for each subsample | educ = 12,16,20 ? Set 3 fixed values & age = 20(10)50 ? APE for each setting

10. Constructed Partial Effects

11. Predictions List and keep predictions Add ; List ; Prob = PFIT to the probit or logit command (Tip: Do not use ;LIST with large samples!) Sample ; 1-100 $ PROBIT ; Lhs=ip ; Rhs=x1 ; List ; Prob=Pfit $ DSTAT ; Rhs = IP,PFIT $

12. Testing a Hypothesis – Wald Test SAMPLE ; All $ PROBIT ; Lhs = IP ; RHS = Sectors,X1 $ MATRIX ; b1 = b(1:3) ; v1 = Varb(1:3,1:3) $ MATRIX ; List ; Waldstat = b1' b1 $ CALC ; List ; CStar = CTb(.95,3) $

13. Testing a Hypothesis – LM Test PROBIT ; LHS = IP ; RHS = X1 $ PROBIT ; LHS = IP ; RHS = X1,Sectors ; Start = b,0,0,0 ; MAXIT = 0 $

14. Results of an LM test Maximum iterations reached. Exit iterations with status=1. Maxit = 0. Computing LM statistic at starting values. No iterations computed and no parameter update done. +---------------------------------------------+ | Binomial Probit Model | | Dependent variable IP | | Number of observations 6350 | | Iterations completed 1 | | LM Stat. at start values 163.8261 | | LM statistic kept as scalar LMSTAT | | Log likelihood function -4228.350 | | Restricted log likelihood -4283.166 | | Chi squared 109.6320 | | Degrees of freedom 6 | | Prob[ChiSqd > value] =.0000000 | +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ Constant -.01060549.04902957 -.216.8287 IMUM.43885789.14633344 2.999.0027.25275054 FDIUM 2.59443123.39703852 6.534.0000.04580618 SP.43672968.11922200 3.663.0002.07428482 RAWMTL.000000.06217590.000 1.0000.08661417 INVGOOD.000000.03590410.000 1.0000.50236220 FOOD.000000.07923549.000 1.0000.04724409 Note: Wald equaled 163.236.

15. Likelihood Ratio Test PROBIT ; Lhs = IP ; Rhs = X1,Sectors $ CALC ; LOGLU = Logl $ PROBIT ; Lhs = IP ; Rhs = X1 $ CALC ; LOGLR = Logl $ CALC ; List ; LRStat = 2*(LOGLU – LOGLR) $ Result is 164.878.

16. Using the Binary Choice Simulator Fit the model with MODEL ; Lhs = … ; Rhs = … Simulate the model with BINARY CHOICE ; ; Start = B (coefficients) ; Model = the kind of model (Probit or Logit) ; Scenario: variable = value / (may repeat) ; Plot: Variable ( range of variation is optional) ; Limit = P* (is optional, 0.5 is the default) $ E.g.: Probit ; Lhs = IP ; Rhs = One,LogSales,Imum,FDIum $ BinaryChoice ; Lhs = IP ; Rhs = One,LogSales,IMUM,FDIUM ; Model = Probit ; Start = B ; Scenario: LogSales * = 1.1 ; Plot: LogSales $

17. Estimated Model for Innovation +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ Index function for probability Constant -1.89382186.20520881 -9.229.0000 LOGSALES.16345837.01766902 9.251.0000 10.5400961 IMUM.99773826.14091020 7.081.0000.25275054 FDIUM 3.66322280.37793285 9.693.0000.04580618 +---------------------------------------------------------+ |Predictions for Binary Choice Model. Predicted value is | |1 when probability is greater than.500000, 0 otherwise.| |------+---------------------------------+----------------+ |Actual| Predicted Value | | |Value | 0 1 | Total Actual | +------+----------------+----------------+----------------+ | 0 | 531 ( 8.4%)| 2033 ( 32.0%)| 2564 ( 40.4%)| | 1 | 454 ( 7.1%)| 3332 ( 52.5%)| 3786 ( 59.6%)| +------+----------------+----------------+----------------+ |Total | 985 ( 15.5%)| 5365 ( 84.5%)| 6350 (100.0%)| +------+----------------+----------------+----------------+

18. Effect of logSales on Probability

19. Model Simulation: logSales Increases by 10% for all Firms in the Sample +-------------------------------------------------------------+ |Scenario 1. Effect on aggregate proportions. Probit Model | |Threshold T* for computing Fit = 1[Prob > T*] is.50000 | |Variable changing = LOGSALES, Operation = *, value = 1.100 | +-------------------------------------------------------------+ |Outcome Base case Under Scenario Change | | 0 985 = 15.51% 300 = 4.72% -685 | | 1 5365 = 84.49% 6050 = 95.28% 685 | | Total 6350 = 100.00% 6350 = 100.00% 0 | +-------------------------------------------------------------+

20. Lab Session 3 Bivariate Extensions of the Probit Model

21. Bivariate Probit Model Two equation model General usage of LHS = the set of dependent variables RH1 = one set of independent variables RH2 = a second set of variables Economical use of namelists is useful here Namelist ; x1=one,age,female,educ,married,working $ Namelist ; x2=one,age,female,hhninc,hhkids $ BivariateProbit ;lhs=doctor,hospital ;rh1=x1 ;rh2=x2;marginal effects $

22. Heteroscedasticity in the Bivariate Probit Model General form of heteroscedasticity in LIMDEP/NLOGIT: Exponential σ i = σ exp(γ’z i ) so that σ i > 0 γ = 0 returns the homoscedastic case σ i = σ Easy to specify Namelist ; x1=one,age,female,educ,married,working ; z1 = … $ Namelist ; x2=one,age,female,hhninc,hhkids ; z2 = … $ BivariateProbit ;lhs=doctor,hospital ;rh1=x1 ; hf1 = z1 ;rh2=x2 ; hf2 = z2$

23. Heteroscedasticity in Marginal Effects Univariate case: If the variables are the same in x and z, these terms are added. Sign and magnitude are ambiguous Vastly more complicated for the bivariate probit case. NLOGIT handles it internally.

24. Marginal Effects: Heteroscedasticity +------------------------------------------------------+ | Partial Effects for Ey1|y2=1 | +----------+---------------------+---------------------+ | | Regression Function | Heteroscedasticity | | +---------------------+---------------------+ | | Direct | Indirect | Direct | Indirect | | Variable | Efct x1 | Efct x2 | Efct h1 | Efct h2 | +----------+----------+----------+----------+----------+ | AGE |.00190 | -.00012 |.00000 |.00000 | | FEMALE |.10215 |.20688 | -.05880 | -.30944 | | EDUC | -.00247 |.00000 |.00000 |.00000 | | MARRIED |.00103 |.00000 |.00064 |.00476 | | WORKING | -.02139 |.00000 |.00000 |.00000 | | HHNINC |.00000 |.00154 |.00000 |.00000 | | HHKIDS |.00000 |.00005 |.00000 |.00000 | +----------+----------+----------+----------+----------+

25. Marginal Effects: Total Effects +-------------------------------------------+ | Partial derivatives of E[y1|y2=1] with | | respect to the vector of characteristics. | | They are computed at the means of the Xs. | | Effect shown is total of 4 parts above. | | Estimate of E[y1|y2=1] =.819898 | | Observations used for means are All Obs. | | Total effects reported = direct+indirect. | +-------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ Constant.000000......(Fixed Parameter)....... AGE.00347726.00022941 15.157.0000 43.5256898 FEMALE.08021863.00535648 14.976.0000.47877479 EDUC -.00392413.00093911 -4.179.0000 11.3206310 MARRIED.00061108.00506488.121.9040.75861817 WORKING -.02280671.00518908 -4.395.0000.67704750 HHNINC.00216510.00374879.578.5636.35208362 HHKIDS.00034768.00164160.212.8323.40273000

26. Imposing Fixed Value and Equality Constraints Used throughout LIMDEP in all models, model parameters appear as a long list: β 1 β 2 β 3 β 4 α 1 α 2 α 3 α 4 σ and so on. M parameters in total. Use ; RST = list of symbols for the model parameters, in the right order This may be used for nonlinear models. Not in REGRESS. Use ;CLS:… for linear models Use the same name for equal parameters Use specific numbers to fix the values

27. BivariateProbit ; lhs=doctor,hospital ; rh1=one,age,female,educ,married,working ; rh2=one,age,female,hhninc,hhkids ; rst = beta1,beta2,beta3,be,bm,bw, beta1,beta2,beta3,bi,bk, 0.4 $ --------+------------------------------------------------------------- Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] Mean of X --------+------------------------------------------------------------- |Index equation for DOCTOR Constant| -1.69181***.08938 -18.928.0000 AGE|.01244***.00167 7.440.0000 44.3352 FEMALE|.38543***.03157 12.209.0000.42277 EDUC|.08144***.00457 17.834.0000 10.9409 MARRIED|.42021***.03987 10.541.0000.84539 WORKING|.03310.03910.847.3972.73941 |Index equation for HOSPITAL Constant| -1.69181***.08938 -18.928.0000 AGE|.01244***.00167 7.440.0000 44.3352 FEMALE|.38543***.03157 12.209.0000.42277 HHNINC| -.98617***.08917 -11.060.0000.34930 HHKIDS| -.09406**.04600 -2.045.0409.45482 |Disturbance correlation RHO(1,2)|.40000......(Fixed Parameter)...... --------+-------------------------------------------------------------

28. Miscellaneous Topics  Two Step Estimation  Robust (Sandwich) Covariance matrix  Matrix Algebra – Testing for Normality

29. Two Step Estimation

30. Murphy and Topel This can usually easily be programmed using the models, CREATE, CALC and MATRIX. Several leading cases are built in.

31. Two Step Estimation: Automated

32. Application: Recursive Probit Hospital = bh ’ xh + c*Doctor + eh Doctor = bd ’ xd + ed Sample ; All $ Namelist ; xD=one,age,female,educ,married,working ; xH=one,age,female,hhninc,hhkids $ Reject ; _Groupti < 7 $ Probit ; lhs=hospital;rhs=xh,doctor$ Probit ; lhs=doctor;rhs=xd;prob=pd;hold$ Probit ; lhs=hospital;rhs=xh,pd;2step=pd$

33. Robust Covariance Matrix

34. ; ROBUST Using the health care data: +---------------------------------------------+ | Binomial Probit Model | +---------------------------------------------+ +---------+--------------+----------------+--------+---------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | +---------+--------------+----------------+--------+---------+ |Index function for probability Constant| -.17336***.05874 -2.951.0032 AGE|.01393***.00074 18.920.0000 43.5257 FEMALE|.32097***.01718 18.682.0000.47877 EDUC| -.01602***.00344 -4.650.0000 11.3206 MARRIED| -.00153.01869 -.082.9347.75862 WORKING| -.09257***.01893 -4.889.0000.67705 Robust VC= G used for estimates. Constant| -.17336***.05881 -2.948.0032 AGE|.01393***.00073 19.024.0000 43.5257 FEMALE|.32097***.01701 18.869.0000.47877 EDUC| -.01602***.00345 -4.648.0000 11.3206 MARRIED| -.00153.01874 -.082.9348.75862 WORKING| -.09257***.01885 -4.911.0000.67705

35. Cluster Correction PROBIT ; Lhs = doctor ; Rhs = one,age,female,educ,married,working ; Cluster = ID $ Normal exit: 4 iterations. Status=0. F= 17448.10 +---------------------------------------------------------------------+ | Covariance matrix for the model is adjusted for data clustering. | | Sample of 27326 observations contained 7293 clusters defined by | | variable ID which identifies by a value a cluster ID. | +---------------------------------------------------------------------+ Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] Mean of X --------+------------------------------------------------------------- |Index function for probability Constant| -.17336**.08118 -2.135.0327 AGE|.01393***.00102 13.691.0000 43.5257 FEMALE|.32097***.02378 13.497.0000.47877 EDUC| -.01602***.00492 -3.259.0011 11.3206 MARRIED| -.00153.02553 -.060.9521.75862 WORKING| -.09257***.02423 -3.820.0001.67705 --------+-------------------------------------------------------------

36. Using Matrix Algebra Namelists with the current sample serve 2 major functions: (1) Define lists of variables for model estimation (2) Define the columns of matrices built from the data. NAMELIST ; X = a list ; Z = a list … $ Set the sample any way you like. Observations are now the rows of all matrices. When the sample changes, the matrices change. Lists may be anything, may contain ONE, may overlap (some or all variables) and may contain the same variable(s) more than once

37. Matrix Functions Matrix Product: MATRIX ; XZ = X ’ Z $ Moments and Inverse MATRIX ; XPX = X ’ X ; InvXPX = $ Moments with individual specific weights in variable w. Σ i w i x i x i ’ = X ’ [w]X. [Σ i w i x i x i ’ ] -1 = Unweighted Sum of Rows in a Matrix Σ i x i = 1 ’ X Column of Sample Means (1/n) Σ i x i = 1/n * X ’ 1 or MEAN(X) (Matrix function. There are over 100 others.) Weighted Sum of rows in matrix Σ i w i x i = 1 ’ [w]X

38. Normality Test for Probit Thanks to Joachim Wilde, Univ. Halle, Germany for suggesting this.

39. Normality Test for Probit NAMELIST ; XI = One,... $ CREATE ; yi = the dependent variable $ PROBIT ; Lhs = yi ; Rhs = Xi ; Prob = Pfi $ CREATE ; bxi = b'Xi ; fi = N01(bxi) $ CREATE ; zi3 = -1/2*(bxi^2 - 1) ; zi4 = 1/4*(bxi*(bxi^2+3)) $ NAMELIST ; Zi = Xi,zi3,zi4 $ CREATE ; di = fi/sqr(pfi*(1-pfi)) ; ei = yi - pfi ; eidi = ei*di ; di2 = di*di $ MATRIX ; List ; LM = 1'[eidi]Zi * * Zi'[eidi]1 $

40. Multivariate Probit MPROBIT ; LHS = y1,y2, …,yM ; Eq1 = RHS for equation 1 ; Eq2 = RHS for equation 2 … ; EqM = RHS for equation M $ Parameters are the slope vectors followed by the lower triangle of the correlation matrix

41. Constrained Panel Probit Sample ; 1 - 1270 $ MPROBIT ; LHS = IP84, IP85, IP86 ; MarginalEffects ; Eq1 = One,Fdium84,SP84 ; Eq2 = One,Fdium85,SP85 ; Eq3 = One,Fdium86,SP86 ; Rst = b1,b2,b3,b1,b2,b3,b1,b2,b3,r45, r46, r56 ; Maxit = 3 ; Pts = 15 $ (Reduces time to compute)

42. Estimated Multivariate Probit +---------------------------------------------+ | Multivariate Probit Model: 3 equations. | | Number of observations 1270 | | Log likelihood function -2423.732 | | Number of parameters 6 | | Replications for simulated probs. = 15 | +---------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ Index function for IP84 Constant.13489406.03467525 3.890.0001 FDIUM84.33571101.47118274.712.4762.05055702 SP84.65662961.13801209 4.758.0000.11012047 Index function for IP85 Constant.13489406.03467525 3.890.0001 FDIUM85.33571101.47118274.712.4762.05051809 SP85.65662961.13801209 4.758.0000.11014611 Index function for IP86 Constant.13489406.03467525 3.890.0001 FDIUM86.33571101.47118274.712.4762.05049439 SP86.65662961.13801209 4.758.0000.11016926 Correlation coefficients R(01,02).46759312.03716428 12.582.0000 R(01,03).37251014.03946383 9.439.0000 R(02,03).46215054.03721312 12.419.0000

44. Endogenous Variable in Probit Model PROBIT ; Lhs = y1, y2 ; Rh1 = rhs for the probit model,y2 ; Rh2 = exogenous variables for y2 $ SAMPLE ; All $ CREATE ; GoodHlth = Hsat > 5 $ PROBIT ; Lhs = GoodHlth,Hhninc ; Rh1 = One,Female,Hhninc ; Rh2 = One,Age,Educ $

45. Lab Session 4 Panel Data Binary Choice Models with Panel Data

46. Telling NLOGIT You are Fitting a Panel Data Model Balanced Panel Model ; … ; PDS = number of periods $ REGRESS ; Lhs = Milk ; Rhs = One,Labor ; Pds = 6 ; Panel $ (Note ;Panel is needed only for REGRESS) Unbalanced Panel Model ; … ; PDS = group size variable $ REGRESS ; Lhs = Milk ; Rhs = One,Labor ; Pds = FarmPrds ; Panel $ FarmPrds gives the number of periods, in every period. (More later about unbalanced panels)

47. Group Size Variables for Unbalanced Panels FarmMilkCowsFarmPrds 123.310.73 123.310.63 1259.43 219.6112 222.2112 324.7114 325.4124 325.313.54 326.114.54 455.4222 463.5222

48. Application to Spanish Dairy Farms Dairy.lpj InputUnitsMeanStd. Dev.MinimumMaximum MilkMilk production (liters) 131,108 92,539 14,110727,281 Cows# of milking cows 2.12 11.27 4.5 82.3 Labor# man-equivalent units 1.67 0.55 1.0 4.0 LandHectares of land devoted to pasture and crops. 12.99 6.17 2.0 45.1 FeedTotal amount of feedstuffs fed to dairy cows (tons) 57,94147,9813,924.14 376,732 N = 247 farms, T = 6 years (1993-1998)

49. Global Setting for Panels SETPANEL ; Group = the name of the ID variable ; PDS = the name of the groupsize variable to create $ Subsequent model commands state ;PANEL with no other specifications requred to set the panel. Some other specifications usually required for the specific model – e.g., fixed vs. random effects.

50. Dialog Boxes for Model Commands

52. Selecting PANEL from the Options Tab

53. Load the Probit Data Set Data for this session are PANELPROBIT.LPJ Various Fixed and Random Effects Models Random Parameters Latent Class

54. Fixed Effects Models ? Fixed Effects Probit. ? Looks like an incidental parameters problem. Sample ; All $ Namelist ; X = IMUM,FDIUM,SP,LogSales $ Probit ; Lhs = IP ; Rhs = X ; FEM ; Marginal ; Pds=5 $ Probit ; Lhs = IP ; Rhs = X,one ; Marginal $

55. Logit Fixed Effects Models Conditional and Unconditional FE ? Logit, conditional vs. unconditional Logit ; Lhs = IP ; Rhs = X ; Pds = 5 $ (Conditional) Logit ; Lhs = IP ; Rhs = X ; Pds = 5 ; Fixed $

56. Hausman Test for Fixed Effects ? Logit: Hausman test for fixed effects ? Logit ; Lhs = IP ; Rhs = X ; Pds = 5 $ Matrix ; Bf = B ; Vf = Varb $ Logit ; Lhs = IP ; Rhs = X,One $ Calc ; K = Col(X) $ Matrix ; Bp = b(1:K) ; Vp = Varb(1:K,1:K) $ Matrix ; Db = Bf - Bp ; DV = Vf - Vp ; List ; Hausman = Db' Db $ Calc ; List ; Ctb(.95,k) $

57. Random Effects and Random Constant ? Random effects ? Quadrature Based (Butler and Moffitt) Estimator Probit ; Lhs = IP ; Rhs = X,One ; Random ; Pds = 5 $ Calc ; List ; RhoQ = rho $ ? Simulation Based Estimator Probit ; Lhs = IP ; Rhs = X,one ; RPM ; Pds = 5 ; Fcn = One(N) ; Halton ; Pts = 25 $ Calc ; List ; RhoRP = b(6)^2/(1+b(6)^2) ; RhoQ $

58. Unbalanced Panel Data Set Load healthcare.lpj Create group size variable Examine Distribution of Group Sizes Sample ; all$ Setpanel ; Group = id ; Pds = ti $ Histogram ; rhs = ti $

59. Group Sizes

60. A Fixed Effects Probit Model Probit ;lhs=doctor ; rhs=age,hhninc,educ,married ; fem ; panel ; Parameters $ +---------------------------------------------+ | Probit Regression Start Values for DOCTOR | | Maximum Likelihood Estimates | | Dependent variable DOCTOR | | Weighting variable None | | Number of observations 27326 | | Iterations completed 10 | | Log likelihood function -17700.96 | | Number of parameters 5 | | Akaike IC=35411.927 Bayes IC=35453.005 | | Finite sample corrected AIC =35411.929 | +---------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ AGE.01538640.00071823 21.423.0000 43.5256898 HHNINC -.09775927.04626475 -2.113.0346.35208362 EDUC -.02811308.00350079 -8.031.0000 11.3206310 MARRIED -.00930667.01887548 -.493.6220.75861817 Constant.02642358.05397131.490.6244 These are the pooled data estimates used to obtain starting values for the iterations to get the full fixed effects model.

61. Fixed Effects Model Nonlinear Estimation of Model Parameters Method=Newton; Maximum iterations=100 Convergence criteria: max|dB|.1000D-08, dF/F=.1000D-08, g g=.1000D-08 Normal exit from iterations. Exit status=0. +---------------------------------------------+ | FIXED EFFECTS Probit Model | | Maximum Likelihood Estimates | | Dependent variable DOCTOR | | Number of observations 27326 | | Iterations completed 11 | | Log likelihood function -9454.061 | | Number of parameters 4928 | | Akaike IC=28764.123 Bayes IC=69250.570 | | Finite sample corrected AIC =30933.173 | | Unbalanced panel has 7293 individuals. | | Bypassed 2369 groups with inestimable a(i). | | PROBIT (normal) probability model | +---------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ Index function for probability AGE.06334017.00425865 14.873.0000 42.8271810 HHNINC -.02495794.10712886 -.233.8158.35402169 EDUC -.07547019.04062770 -1.858.0632 11.3602526 MARRIED -.04864731.06193652 -.785.4322.76348771

62. Computed Fixed Effects Parameters

63. Lab Session 5 Modeling Heterogeneity with Random Parameters and Latent Classes

64. Random Parameters Model ? Random parameters specification ? Logit ; Lhs = IP ; Rhs = One,IMUM,FDIUM,SP,LogSales ; Pds = 5 ; RPM ; Halton ; Pts = 25 ; Cor ; Fcn = One(n),IMUM(n),FDIUM(n) ; Marginal ; Parameters $ Sample ; 1 - 1270 $ Create ; bimum = 0 $ Matrix ; bi = beta_i(1:1270,2:2) $ Create ; bimum = bi $ Kernel ; Rhs = bimum $

65. Random Parameters with Industry Heterogeneity ? Random parameters with industry heterogeneity ? Examine effect of industry heterogeneity. Sample ; All $ Logit ; Lhs = IP ; Rhs = One,IMUM,FDIUM,SP,LogSales ; Pds = 5 ; RPM = InvGood,RawMtl ; Halton ; Pts = 15 ; Cor ; Fcn = One(n),IMUM(n),FDIUM(n) ; Marginal ; Parameters $ Create; Bimum = beta_i(firm,2) $ Regress ; Lhs = Bimum ; Rhs = one,InvGood,RawMtl $

66. Latent Class Models ? Latent class models Sample ; All $ Logit ; Lhs = IP ; Rhs = X ; LCM ; Pds=5 ; Pts = 3 $ Logit ; Lhs = IP ; Rhs = X ; LCM=Invgood,Rawmtl ; Pds=5 ; Pts = 3 $ Logit ; Lhs = IP ; Rhs = X ; LCM ; Pds=5 ; Pts = 4 $ Logit ; Lhs = IP ; Rhs = X ; LCM ; Pds=5 ; Pts = 5 $