* Bivariate Probit Model in SAS; * Copyright 2013 by Ani Katchova; proc import out= work.data datafile= "C:\Econometrics\Data\bivariate_health.csv" dbms=csv replace; getnames=yes; datarow=2; run; %let ylist1=hlthe; %let ylist2=dmdu; %let xlist= age linc ndisease; proc means data=data; var &ylist1 &ylist2 &xlist; run; proc freq data=data; tables &ylist1 &ylist2; run; *Probit models; proc qlim data=data; model &ylist1 = &xlist / discrete (dist=normal); run; proc qlim data=data; model &ylist2 = &xlist / discrete (dist=normal); run; *Bivariate probit; proc qlim data=data; model &ylist1 &ylist2 = &xlist; endogenous &ylist1 &ylist2 ~ discrete; output out=mfx marginal; run; *Bivariate probit allowing different set of regressors; proc qlim data=data method=qn; model &ylist1 = &xlist; model &ylist2 = &xlist; endogenous &ylist2 &ylist1 ~ discrete; output out=mfx marginal; run; /*Marginal effects; proc means data=mfx n mean std; var Meff_P2_hlthe_age Meff_P2_hlthe_linc Meff_P2_hlthe_ndisease Meff_P2_dmdu_age Meff_P2_dmdu_linc Meff_P2_dmdu_ndisease; run;

The SAS System The MEANS Procedure Variable

N

Mean

Std Dev

Minimum

Maximum

hlthe

5574

0.5412630

0.4983392

0

1.0000000

dmdu

5574

0.6713312

0.4697715

0

1.0000000

age

5574

25.5761339

16.7301105

0.0253251

63.2751500

linc

5574

8.6969290

1.2205920

0

10.2832400

ndisease

5574

11.2052651

6.7889585

0

58.6000000

The SAS System The FREQ Procedure hlthe Frequency Percent Cumulative Cumulative Frequency Percent 0

2557

45.87

2557

45.87

1

3017

54.13

5574

100.00

dmdu Frequency Percent Cumulative Cumulative Frequency Percent 0

1832

32.87

1832

32.87

1

3742

67.13

5574

100.00

The SAS System The QLIM Procedure Discrete Response Profile of hlthe Total Frequency

Index

Value

1

0

2557

2

1

3017

Model Fit Summary Number of Endogenous Variables

1

Endogenous Variable

hlthe

Number of Observations

5574

Log Likelihood

-3554

Maximum Absolute Gradient

0.00358

Number of Iterations Optimization Method

9 Quasi-Newton

AIC

7116

Schwarz Criterion

7143

Goodness-of-Fit Measures Measure

Value Formula

Likelihood Ratio (R) 580.81 2 * (LogL - LogL0) Upper Bound of R (U) 7689.2 - 2 * LogL0 Aldrich-Nelson Cragg-Uhler 1

0.0944 R / (R+N) 0.099 1 - exp(-R/N)

Cragg-Uhler 2

0.1322 (1-exp(-R/N)) / (1-exp(-U/N))

Estrella

0.1027 1 - (1-R/U)^(U/N)

Adjusted Estrella

0.1013 1 - ((LogL-K)/LogL0)^(-2/N*LogL0)

McFadden's LRI

0.0755 R / U

Veall-Zimmermann

0.1628 (R * (U+N)) / (U * (R+N))

McKelvey-Zavoina

0.1567

N = # of observations, K = # of regressors Algorithm converged. Parameter Estimates Parameter DF

Estimate Standard Error t Value

Approx Pr > |t|

Parameter Estimates Parameter DF

Estimate Standard Error t Value

Approx Pr > |t|

Intercept

1 -0.230438

0.133559

-1.73

0.0845

age

1 -0.017819

0.001083

-16.46

<.0001

linc

1

0.132508

0.014975

8.85

<.0001

ndisease

1 -0.032653

0.002759

-11.84

<.0001

The SAS System The QLIM Procedure

The SAS System The QLIM Procedure Discrete Response Profile of dmdu Total Frequency

Index

Value

1

0

1832

2

1

3742

Model Fit Summary Number of Endogenous Variables

1

Endogenous Variable

dmdu

Number of Observations

5574

Log Likelihood

-3405

Maximum Absolute Gradient

0.0000120

Number of Iterations Optimization Method

8 Quasi-Newton

AIC

6817

Schwarz Criterion

6844

Goodness-of-Fit Measures Measure

Value Formula

Likelihood Ratio (R) 249.98 2 * (LogL - LogL0) Upper Bound of R (U) 7059.3 - 2 * LogL0 Aldrich-Nelson

0.0429 R / (R+N)

Cragg-Uhler 1

0.0439 1 - exp(-R/N)

Cragg-Uhler 2

0.0611 (1-exp(-R/N)) / (1-exp(-U/N))

Estrella

0.0446 1 - (1-R/U)^(U/N)

Adjusted Estrella

0.0432 1 - ((LogL-K)/LogL0)^(-2/N*LogL0)

McFadden's LRI

0.0354 R / U

Veall-Zimmermann

0.0768 (R * (U+N)) / (U * (R+N))

McKelvey-Zavoina

0.078

N = # of observations, K = # of regressors Algorithm converged. Parameter Estimates Parameter DF

Estimate Standard Error t Value

Approx Pr > |t|

Parameter Estimates Parameter DF

Estimate Standard Error t Value

Approx Pr > |t|

Intercept

1 -1.033029

0.129085

-8.00

<.0001

age

1

0.002008

0.001093

1.84

0.0661

linc

1

0.121285

0.014255

8.51

<.0001

ndisease

1

0.034723

0.002891

12.01

<.0001

The SAS System The QLIM Procedure

The SAS System The QLIM Procedure Discrete Response Profile of hlthe Total Frequency

Index

Value

1

0

2557

2

1

3017

Discrete Response Profile of dmdu Total Frequency

Index

Value

1

0

1832

2

1

3742

Model Fit Summary Number of Endogenous Variables

2

Endogenous Variable

hlthe dmdu

Number of Observations

5574

Log Likelihood

-6958

Maximum Absolute Gradient

0.0000756

Number of Iterations

14

Optimization Method

Quasi-Newton

AIC

13934

Schwarz Criterion

13994

Algorithm converged. Parameter Estimates Parameter

DF

Estimate Standard Error t Value

Approx Pr > |t|

hlthe.Intercept

1 -0.229708

0.133452

-1.72

0.0852

hlthe.age

1 -0.017825

0.001083

-16.46

<.0001

hlthe.linc

1

0.132468

0.014963

8.85

<.0001

hlthe.ndisease

1 -0.032666

0.002759

-11.84

<.0001

dmdu.Intercept

1 -1.032527

0.129053

-8.00

<.0001

dmdu.age

1

0.002004

0.001093

1.83

0.0667

dmdu.linc

1

0.121252

0.014251

8.51

<.0001

dmdu.ndisease

1

0.034711

0.002891

12.01

<.0001

_Rho

1

0.028218

0.022809

1.24

0.2160

The SAS System The QLIM Procedure

The SAS System The QLIM Procedure

The SAS System The QLIM Procedure Discrete Response Profile of hlthe Total Frequency

Index

Value

1

0

2557

2

1

3017

Discrete Response Profile of dmdu Total Frequency

Index

Value

1

0

1832

2

1

3742

Model Fit Summary Number of Endogenous Variables

2

Endogenous Variable

hlthe dmdu

Number of Observations

5574

Log Likelihood

-6958

Maximum Absolute Gradient

0.0000756

Number of Iterations

14

Optimization Method

Quasi-Newton

AIC

13934

Schwarz Criterion

13994

Algorithm converged. Parameter Estimates Parameter

DF

Estimate Standard Error t Value

Approx Pr > |t|

hlthe.Intercept

1 -0.229708

0.133452

-1.72

0.0852

hlthe.age

1 -0.017825

0.001083

-16.46

<.0001

hlthe.linc

1

0.132468

0.014963

8.85

<.0001

hlthe.ndisease

1 -0.032666

0.002759

-11.84

<.0001

dmdu.Intercept

1 -1.032527

0.129053

-8.00

<.0001

dmdu.age

1

0.002004

0.001093

1.83

0.0667

dmdu.linc

1

0.121252

0.014251

8.51

<.0001

dmdu.ndisease

1

0.034711

0.002891

12.01

<.0001

_Rho

1

0.028218

0.022809

1.24

0.2160

The SAS System The QLIM Procedure

The SAS System The QLIM Procedure

Bivariate Probit and Logit Models SAS Program and Output.pdf ...

Variable N Mean Std Dev Minimum Maximum. hlthe. dmdu. age. linc. ndisease. 5574. 5574. 5574. 5574. 5574. 0.5412630. 0.6713312. 25.5761339. 8.6969290. 11.2052651. 0.4983392. 0.4697715. 16.7301105. 1.2205920. 6.7889585. 0. 0. 0.0253251. 0. 0. 1.0000000. 1.0000000. 63.2751500. 10.2832400. 58.6000000.

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