日本版総合的社会調査共同研究拠点研究論文集 [10] JGSS Research Seres No.7 JGSS 2009 JGSS JGSS Statstcal Analyss Semnar: Causalty Analyss based on the Propensty Score Kana MIWA JGSS Research Center Osaka Unversty of Commerce akayuk SUGASAWA Career Path Creaton Center Kyushu Unversty JGSS Research Center hosted a statstcal analyss semnar on the theme of causalty analyss based on the propensty score. Propensty score s one methodology to analyss causal effect when a random samplng data s not avalable. Although causalty analyss usng the propensty score s known as to avod the sample selecton bas whch we cannot deal wth by normal multvarable analyss, there are few studes that employed ths approach n Japan. hs paper ams to explan how to do the causalty analyss based on the propensty score, and show examples by usng JGSS data. Key Words: JGSS, causalty analyss, propensty score, satsfacton of famly lfe JGSS 2009 propensty score JGSS JGSS 285
日本版総合的社会調査共同研究拠点研究論文集 [10] JGSS Research Seres No.7 1 JGSS 2009 8 27 28 2 2007 2008 2009 propensty score sample selecton bas Japanese General Socal Surveys JGSS 2 3 4 2 2 1 Y X Y 3 X Y (1) emporalty X Y (2) Correlaton X Y (3) Non-spurousness X Y X Y X Y treatment Y counterfactual Y treatment average treatment effect E d E{ Y treatment} E{ Y no treatment} 286
日本版総合的社会調査共同研究拠点研究論文集 [10] JGSS Research Seres No.7 E{ Y treatment} E{ Y no treatment} treatment group control group C d d = E{ Y treatment} E{ Y no treatment} 1 2 d E{ Y no treatment} = E{ Y no treatment} E{ Y treatment} E{ Y no treatment} Y d s d = E{ Y = E{ Y treatment} E{ Y treatment} E{ Y C C C no treatment } no treatment } d Rosenbaum and Rubn 1983 propensty score strongly gnorable treatment assgnment { Z } X P P C { E[ Y treatment, P( Z)] E[ Y no treatment, P( )]} E{ Y Y } = E Z Y, Y C C ( Y Y ) 2009 X Y Rubn 1985 Imbens 2000 nverse probablty treatment estmaton IPE s 287
日本版総合的社会調査共同研究拠点研究論文集 [10] JGSS Research Seres No.7 (1) IPE P 1/ P 1/(1 P) X P P P X X X X Y IPE 2 2 IPE X 2 1 X P X = α + β Z + v 2 P P = exp[ ˆ α + βˆ Z ]/(1 + exp[ ˆ α + βˆ Z ]) ˆα, βˆ 3 X 1/ P /(1 P) 1 4 X 3 5 Y Y = δ + Weghted[ η X + γ Z ] + u 1 4 5 3 X {Z} Y { Z } X P IPE P X Y { Z } a Y X {Z} b IPE P X X Y X doubly robust estmator a ab 2009 JGSS 288
日本版総合的社会調査共同研究拠点研究論文集 [10] JGSS Research Seres No.7 3 JGSS SPSS General Socal Survey GSS JGSS JGSS 2000 2003 JGSS-2000 JGSS-2001 JGSS-2002 JGSS-2003 4 20 69 10,063 1 1 JGSS-2000~2003 JGSS-2000 JGSS-2001 JGSS-2002 JGSS-2003 2000 10 11 2001 10 11 2002 10 11 2003 10 11 2000 6 25 20 89 2001 9 1 20 89 2002 9 1 20 89 2003 9 1 20 89 4,500 4,500 5,000 7,000 2 2 2 2 ( A B 2 ) 2,893 2,790 2,953 A 1,957 B 1,706 64.9 63.1 62.3 A 55.0 B 48.0 JGSS 4 JGSS-2000 2003 4 X 2 3 2 2 4 1 Y1 1 5 5 X1 1 0 2 2 2.2 1 3 PX1 3 1 (2) 289
日本版総合的社会調査共同研究拠点研究論文集 [10] JGSS Research Seres No.7 PX1 exp[ ˆ α + βˆ Z ] = 1+ exp[ ˆ α + βˆ Z ] exp = 1+ exp [ 0.769 0.399 + 2.056 30 + 2.770 40 +... + 1.548 60 ] [ 0.769 0.399 + 2.056 30 + 2.770 40 +... + 1.548 60 ] 1 3 1 PX1 W1 X1 (1 X1) W1= + 2 PX1 (1 PX1) 2 1 5 1 0 1 0 30 30 10 40 40 10 50 50 10 60 60 10 10 10 10 10 2001 2001 10 2002 2002 10 2003 2003 10 30 30 10 40 40 10 50 50 10 60 60 10 290
日本版総合的社会調査共同研究拠点研究論文集 [10] JGSS Research Seres No.7 3 0.769 *** 0.125 0.399 *** 0.117 20 30 2.056 *** 0.111 40 2.770 *** 0.125 50 2.475 *** 0.113 60 1.847 *** 0.110 0.332 *** 0.078 0.146 * 0.086 0.312 *** 0.082 0.113 * 0.067 2000 2001 0.022 0.077 2002 0.013 0.075 2003 0.012 0.072 30 0.257 0.162 40 0.096 0.177 50 0.668 *** 0.168 60 1.548 *** 0.169 2 9241.075 Cox & Snell R 2 0.177 Nagelkerke R 2 0.263 10063 * 10 ** 5 *** 1 X1 WX1 4 4 WX1 WX1C 0.001 4 10,063 X1 1 0 0 1 7601 0.755 0.430 WX1 W1 X1 0.00 4.85 10056.42 0.999 0.729 WX1 C W1 (1 X1) 0.00 13.92 10040.09 0.998 2.269 4 WX1 7601 WX1 ADJ _ W1 = + 10056.42 C (10063 7601) 10040.09 291
日本版総合的社会調査共同研究拠点研究論文集 [10] JGSS Research Seres No.7 5 1 0.95 1.05 5 ADJ _W1 0.30 3.66 10063.00 1.000 0.493 6 X 6 Pearson 0.464 *** 0.002 0.000 0.820 10063 10063 *** 1 ADJ _W1 OLS 7 OLS 7 2.2 Y X {Z} 292
日本版総合的社会調査共同研究拠点研究論文集 [10] JGSS Research Seres No.7 7 3.250 *** 0.051 3.128 *** 0.053 1 0 0.401 *** 0.025 0.413 *** 0.023 0.022 0.052 0.277 *** 0.052 20 30 0.275 *** 0.049 0.137 *** 0.048 40 0.364 *** 0.049 0.208 *** 0.047 50 0.266 *** 0.047 0.123 *** 0.045 60 0.145 *** 0.049 0.025 0.047 0.137 *** 0.028 0.101 *** 0.028 0.305 *** 0.032 0.259 *** 0.031 0.032 0.031 0.059 * 0.031 0.048 ** 0.024 0.066 *** 0.024 2000 2001 0.024 0.028 0.016 0.029 2002 0.029 0.028 0.013 0.028 2003 0.050 0.027 0.037 0.027 30 0.080 0.070 0.154 ** 0.070 40 0.047 0.068 0.269 *** 0.068 50 0.051 0.065 0.355 *** 0.065 60 0.121 * 0.066 0.037 *** 0.066 R 2 0.037 0.057 10063 10063 * 10 ** 5 *** 1 4 2 2 8,360 1 X 2 1 0 2 4.1 1 2 8 PX 2 3 PX2 exp = 1+ exp [ 2.832 0.300 + 0.385 30 + 0.460 40 +... 1.034 60 ] [ 2.832 0.300 + 0.385 30 + 0.460 40 +... 1.034 60 ] 3 293
日本版総合的社会調査共同研究拠点研究論文集 [10] JGSS Research Seres No.7 8 2.832 *** 0.333 0.300 0.517 20 30 0.385 0.340 40 0.460 0.332 50 1.019 *** 0.321 60 1.727 *** 0.319 0.192 ** 0.124 0.537 *** 0.096 0.169 0.082 0.092 0.067 2000 2001 0.120 0.116 2002 0.055 0.112 2003 0.063 0.106 30 0.483 0.597 40 0.248 0.565 50 0.476 0.540 60 1.034 * 0.535 2 4728.159 Cox & Snell R 2 0.042 Nagelkerke R 2 0.093 8360 * 10 ** 5 *** 1 2 X 2 9 2 3 WX 2 W2 X 2 WX 2 C W2 (1 X 2) WX 2 WX 2C WX2 759 WX2C (8360 759) ADJ _ W2 = + 8289.80 8360.67 9 ADJ _W2 1.000 9 8,360 X 2 1 0 0 1 759 0.090 0.287 WX2 W2 X 2 0.00 45.53 8289.80 0.992 3.817 WX2 C W2 (1 X 2) 0.00 1.39 8360.67 1.000 0.326 ADJ _W2 0.32 4.17 8360.00 1.000 0.211 294
日本版総合的社会調査共同研究拠点研究論文集 [10] JGSS Research Seres No.7 ADJ _W2 OLS 10 0.350 0.476 10 2 3.448 *** 0.071 3.466 *** 0.071 1 0 0.350 *** 0.038 0.476 *** 0.037 0.373 *** 0.094 0.332 *** 0.094 20 30 0.083 0.069 0.084 0.069 40 0.169 ** 0.067 0.172 ** 0.067 50 0.070 0.066 0.081 0.066 60 0.048 0.068 0.022 0.068 0.140 *** 0.030 0.135 *** 0.030 0.289 *** 0.034 0.282 *** 0.034 0.041 0.034 0.053 0.034 0.056 ** 0.026 0.060 ** 0.026 2000 2001 0.032 0.031 0.044 0.031 2002 0.037 0.031 0.034 0.031 2003 0.049 * 0.029 0.050 * 0.029 30 0.203 * 0.108 0.218 ** 0.108 40 0.240 ** 0.105 0.226 ** 0.105 50 0.390 *** 0.102 0.356 *** 0.102 60 0.475 *** 0.102 0.421 *** 0.102 R 2 0.031 0.036 8360 8360 * 10 ** 5 *** 1 295
日本版総合的社会調査共同研究拠点研究論文集 [10] JGSS Research Seres No.7 5 2009 treatment Acknowledgement General Socal Surveys JGSS 1999-2003 SSJ 1 IPE JGSS 20092009 2 SPSS /SAVE=PRED X = 1 pre_1, 2009,,. Imbens, G. W., 2000, he Role of the Propensty Score n Estmatng Dose-response Functons, Bometrka, 87(3), 706 710., 2009, Propensty Score Matchng,, No. 28. http://ssjda.ss.u-tokyo.ac.jp/panel/youthandmddle/dp/paneldp_028kan.pdf, 2010 2 1 Rosenbaum, P. R. and Rubn, D. B., 1983, he Central Role of the Propensty Score n Observatonal Studes for Causal Effects, Bometrka, 70(1), 41-55. Rubn, D. B., 1985, he Use of Propensty Score n Appled Bayesan Inference, Bernardo, J. M., De Groot, M. H., Lndley, D. V., and Smth, A. F. M. (eds.), Bayesan Statstcs, Vol.2, 463-472, North-Holland: Elsever Scence Publsher B. V. 296