5分 stata面板数据分析

Longitudinal/Panel Data Analysis Raymond Duch University of Oxford Nuffield College raymond.duch@nuffield.ox.ac.uk raymondduch.com/trinity10/paneldata April 27, 2010 1 / 26 Readings 1 Gellman, Andrew and Jennifer Hill. 2007. Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press 2 Stata 11.0 Manual Longitudinal/Panel Data 3 Rabe-Hesketh, Sophia and Anders Skrondal. 2005. Multilevel and Longitudinal Modeling Using Stata. Stata Press 2 / 26 What is longitudinal panel data? 1 Marriage of regression and time-series analysis 2 A broad cross-section of subjects observed over time 3 Individuals surveyed repeatedly over time (American National Election Study; U.S. Panel Study of Income Dynamics) 4 Statistics compiled over time for a particular geo-political entity (Divorce Rates and welfare rates collected annually from U.S. States) 5 Statistics compiled on hospital patients over time 3 / 26 Modeling Panel Data (Repeated) cross-sectional regression analysis generates the following model y it = α+ βx it + � it (1) y it = α+ x′ it B+ � it (2) 1 Heterogeneity or uniqueness of subjects captured in � it 2 The cross-sectional units (individuals, firms, cities) are represented by i 3 Repeated time units are represented by t 4 / 26 Varying Intercept Model y it = α j + βx it + � it (3)   Group D  Group C  Group B  Group A  Y  X  5 / 26 Varying Slope Model y it = α+ β j x it + � it (4)   Group C  Group B  Group A  Group D  Y  X  6 / 26 Varying Intercepts and Slopes Model y it = α j + β j x it + � it (5) Group C    Group B  Group A  Y  Group D  X  7 / 26 Data Preparation in Stata: Australian Smoking Study 1 data is available at http://www.stat.columbia.edu/ gelman/arm/ 2 variables: newid (identifies each unique respondent) sex (1=female) parsmk (1=parents smoke) wave (identifies each of 6 waves) smkreg (is respondent regular smoker) 8 / 26 . list +-------------------------------------------+ | newid sex_1_f_ parsmk wave smkreg | |-------------------------------------------| 1. | 1 1 0 1 0 | 2. | 1 1 0 2 0 | 3. | 1 1 0 4 0 | 4. | 1 1 0 5 0 | 5. | 1 1 0 6 0 | |-------------------------------------------| 6. | 2 0 0 1 0 | 7. | 2 0 0 2 0 | 8. | 2 0 0 3 0 | 9. | 2 0 0 4 0 | 10. | 2 0 0 5 0 | |-------------------------------------------| 11. | 2 0 0 6 0 | 12. | 3 1 0 1 0 | 13. | 3 1 0 2 0 | 14. | 3 1 0 3 0 | 15. | 3 1 0 4 0 | |-------------------------------------------| 16. | 3 1 0 5 0 | 17. | 3 1 0 6 0 | 18. | 4 1 0 1 0 | 19. | 4 1 0 2 0 | 20. | 4 1 0 3 0 | |-------------------------------------------| 21. | 4 1 0 4 0 | 22. | 4 1 0 5 0 | 23. | 4 1 0 6 0 | 24. | 5 0 0 1 0 | 25. | 5 0 0 2 0 | |-------------------------------------------| 26. | 5 0 0 3 0 | 27. | 5 0 0 4 0 | 28. | 5 0 0 5 0 | 29. | 5 0 0 6 0 | 30. | 6 0 0 1 0 | 9 / 26 Smoking by Sex over Panel Waves girls boys 0 50 10 0 15 0 pr op or tio n sm ok er s in p op ul at io n 1 2 3 4 5 6 wave 10 / 26 Modeling the Smoking Longitudinal Data Pr(y jt = 1) = logit−1(β 0 + β 1 psmoke jt + β 2 female jt + (6) β 3 t + β 4 female jt ∗ t + α j + � jt ), t = 1, ....T j , j = 1, ...., n. (7) α j ∼ N(µα, σ2α) (8) 11 / 26 Estimation with Gllamm in Stata . use "e:\Oxford08\Department08\Trinity_Panel\Data\gelman\smoke_pub.dta", clear . . tsset newid wave panel variable: newid (unbalanced) time variable: wave, 1 to 6, but with gaps delta: 1 unit . gllamm smkreg parsmk wave, i(newid) link(logit) family(binom) 12 / 26 Estimation with Gllamm in Stata gllamm model log likelihood = -2074.7563 ------------------------------------------------------------------------------ smkreg | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- parsmk | 1.270422 .1998237 6.36 0.000 .8787746 1.662069 wave | .4195264 .0365132 11.49 0.000 .3479619 .4910909 _cons | -7.24026 .2742149 -26.40 0.000 -7.777711 -6.702808 ------------------------------------------------------------------------------ Variances and covariances of random effects ------------------------------------------------------------------------------ ***level 2 (newid) var(1): 13.679018 (.88531601) ------------------------------------------------------------------------------ 13 / 26 Estimation with Gllamm in Stata: Incorporating Time Trend . . gen male_time=wave*(1-sex_1_f) . gen female_time=wave*sex_1_f . gen sex_time=wave*sex_1_f . gllamm smkreg parsmk wave sex_time, i(newid) link(logit) family(binom) 14 / 26 Estimation with Gllamm in Stata: Incorporating Time Trend . . gen male_time=wave*(1-sex_1_f) . gen female_time=wave*sex_1_f . gen sex_time=wave*sex_1_f . gllamm smkreg parsmk wave sex_time, i(newid) link(logit) family(binom) 15 / 26 Estimation with Gllamm in Stata: Incorporating Time Trend number of level 1 units = 8730 number of level 2 units = 1760 Condition Number = 17.565231 gllamm model log likelihood = -2071.4531 ------------------------------------------------------------------------------ smkreg | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- parsmk | 1.314832 .2278361 5.77 0.000 .8682812 1.761382 wave | .3598051 .0432529 8.32 0.000 .275031 .4445792 sex_time | .10706 .0424822 2.52 0.012 .0237965 .1903235 _cons | -7.263204 .2767673 -26.24 0.000 -7.805658 -6.72075 ------------------------------------------------------------------------------ Variances and covariances of random effects ------------------------------------------------------------------------------ ***level 2 (newid) var(1): 13.797342 (.90193295) ------------------------------------------------------------------------------ 16 / 26 Estimation with Gllamm in Stata: Incorporating Time Trend +--------------------------------------------+ | newid constant reffm1 inter_eb | |--------------------------------------------| 1. | 1 -7.263204 -1.1592099 -8.422414 | 2. | 1 -7.263204 -1.1592099 -8.422414 | 3. | 1 -7.263204 -1.1592099 -8.422414 | 4. | 1 -7.263204 -1.1592099 -8.422414 | 5. | 1 -7.263204 -1.1592099 -8.422414 | +--------------------------------------------+ . list newid constant reffm1 inter_eb in 1090/1095 +--------------------------------------------+ | newid constant reffm1 inter_eb | |--------------------------------------------| 1090. | 202 -7.263204 -.76498347 -8.028188 | 1091. | 203 -7.263204 7.1519595 -.1112444 | 1092. | 203 -7.263204 7.1519595 -.1112444 | 1093. | 203 -7.263204 7.1519595 -.1112444 | 1094. | 203 -7.263204 7.1519595 -.1112444 | |--------------------------------------------| 1095. | 203 -7.263204 7.1519595 -.1112444 | +--------------------------------------------+ . list newid constant reffm1 inter_eb in 1160/1165 +--------------------------------------------+ | newid constant reffm1 inter_eb | |--------------------------------------------| 1160. | 215 -7.263204 6.0917393 -1.171465 | 1161. | 215 -7.263204 6.0917393 -1.171465 | 1162. | 215 -7.263204 6.0917393 -1.171465 | 1163. | 215 -7.263204 6.0917393 -1.171465 | 1164. | 216 -7.263204 -1.4855779 -8.748782 | |--------------------------------------------| 1165. | 216 -7.263204 -1.4855779 -8.748782 | +--------------------------------------------+ 17 / 26 Data Preparation in Stata: Growth Curve Modeling 1 data is available with following command: net from http://www.stata-press.com/data/mlmus2/ 2 variables: id (child identifier) weight (weight in Kg) age (age in years) gender (1 male; 2 female) 18 / 26 . list +-------------------------------------------------+ | id occ age weight brthwt gender | |-------------------------------------------------| 1. | 45 1 .136893 5.171 4140 boy | 2. | 45 2 .657084 10.86 4140 boy | 3. | 45 3 1.21834 13.15 4140 boy | 4. | 45 4 1.42916 13.2 4140 boy | 5. | 45 5 2.27242 15.88 4140 boy | |-------------------------------------------------| 6. | 258 1 .19165 5.3 3155 girl | 7. | 258 2 .687201 9.74 3155 girl | 8. | 258 3 1.12799 9.98 3155 girl | 9. | 258 4 2.30527 11.34 3155 girl | 10. | 287 1 .134155 4.82 3850 boy | |-------------------------------------------------| 11. | 287 2 .70089 9.09 3850 boy | 12. | 287 3 1.16906 11.1 3850 boy | 13. | 287 4 2.2423 16.8 3850 boy | 14. | 483 1 .747433 5.76 2875 girl | 15. | 483 2 1.01848 6.92 2875 girl | |-------------------------------------------------| 16. | 483 3 2.24504 9.53 2875 girl | 17. | 725 1 .120465 4.4 3280 girl | 18. | 725 2 2.30527 12.25 3280 girl | 19. | 800 1 1.12252 10.89 3900 boy | 20. | 800 2 2.26146 12.7 3900 boy | 19 / 26 Observed growth trajectories for boys and girls 5 10 15 20 0 1 2 3 0 1 2 3 boy girl W ei gh t i n Kg Age in years Graphs by gender 20 / 26 Modeling the Growth Trajectory Data y jt = β 0 + β 1 age jt + β 2 age 2 jt + α j + � jt , (9) t = 1, ....T j , j = 1, ...., n. (10) α j ∼ N(µα, σ2α) (11) 21 / 26 Estimation with xtmixed in Stata . gen age2=age^2 . xtmixed weight age age2 || id:, mle Performing EM optimization: Performing gradient-based optimization: Iteration 0: log likelihood = -276.83266 Iteration 1: log likelihood = -276.83266 Computing standard errors: Mixed-effects ML regression Number of obs = 198 Group variable: id Number of groups = 68 Obs per group: min = 1 avg = 2.9 max = 5 Wald chi2(2) = 2623.63 Log likelihood = -276.83266 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ weight | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- age | 7.817918 .2896529 26.99 0.000 7.250209 8.385627 age2 | -1.705599 .1085984 -15.71 0.000 -1.918448 -1.49275 _cons | 3.432859 .1810702 18.96 0.000 3.077968 3.78775 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ id: Identity | sd(_cons) | .9182256 .0973788 .7458965 1.130369 -----------------------------+------------------------------------------------ sd(Residual) | .7347063 .0452564 .6511507 .8289837 ------------------------------------------------------------------------------ LR test vs. linear regression: chibar2(01) = 78.07 Prob >= chibar2 = 0.0000 . end of do-file 22 / 26 Incorporating Gender Differences to the Growth Model y jt = β 0 + β 1 age jt + β 2 age 2 jt + β 3 girl jt + β4girl ∗ age jt (12) α j + � jt , t = 1, ....T j , j = 1, ...., n. (13) α j ∼ N(µα, σ2α) (14) 23 / 26 Estimation with xtmixed in Stata . xtmixed weight age age2 girl age_girl || id:, mle Iteration 1: log likelihood = -270.7967 Mixed-effects ML regression Number of obs = 198 Group variable: id Number of groups = 68 Obs per group: min = 1 avg = 2.9 max = 5 Wald chi2(4) = 2705.20 Log likelihood = -270.7967 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ weight | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- age | 7.932362 .2935717 27.02 0.000 7.356973 8.507752 age2 | -1.70546 .1069802 -15.94 0.000 -1.915138 -1.495783 girl | -.4889737 .2752022 -1.78 0.076 -1.02836 .0504127 age_girl | -.2289743 .1377625 -1.66 0.096 -.4989839 .0410353 _cons | 3.676974 .2212291 16.62 0.000 3.243373 4.110575 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ id: Identity | sd(_cons) | .8470338 .0921964 .6843065 1.048457 -----------------------------+------------------------------------------------ sd(Residual) | .7261711 .0446575 .6437132 .8191916 ------------------------------------------------------------------------------ LR test vs. linear regression: chibar2(01) = 69.16 Prob >= chibar2 = 0.0000 24 / 26 Also D-in-D Model With two periods and strict exogeneity, y it = β 0 + β 1 D i2 + β 2 T t + β 3 T t D it + � it (15) 1 D i2 = dummy variable for a treatment that takes place between time 1 and time 2 for some of the individuals 2 T t =a time dummy variable, 0 in period 1, 1 in period 2 3 This is a classic regression model. If there are no regressors, using least squares, β 3 = (y 2 − y 1 ) D=1 − (y2 − y1)D=0 (16) 25 / 26 Readings for Week 2 Gellman, Andrew and Jennifer Hill. 2007. Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press, Chapter 13 and 14 Stata 11.0 Manual Longitudinal/Panel Data, xtmixed, xtreg, xtregar Rabe-Hesketh, Sophia and Anders Skrondal. 2005. Multilevel and Longitudinal Modeling Using Stata. Stata Press, Chapter 3 and 4 Halaby, Charles. 2004. "Panel Models in Sociological Research: Theory and Practice." Annual Review of Sociology. 30: 507-44 Wooldridge, J.M. 2002. "Econometric Analysis of Cross Section and Panel Data Cambridge, MA : MIT Press (especially chapters 13 and 14). 26 / 26 Readings Introduction: What is Panel Data? Data Preparation and Exploratory Data Analysis: Smoking Study