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analysis of survey data part 10
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Tài sản của (a) dự toán không đúng trực tiếp, (b) ước tính hiệp phương sai trực tiếp, (c) dự toán không đúng trực tiếp và (d) ước tính hồi quy trực tiếp (Ã, 1000) trên 100 lần nhắc lại.  €  €  € (a) LLTI (1)  78X6, (2)  0X979, yy  79X6 yy yy (1) Syy (2) Syy | SIMULATION STUDIES 337 Table 20.2 Properties of estimates c direct variance over 100 replications. x T T TT V 1 no Z V 2 a LLTI p1 - 78.6 p1 a direct variance estimates b direct covariance estimates and d direct regression estimates x 1000 - 0.979 Pyy - 79.6 s v S2 yy yy Data Mean SD Mean SD m. - 371 n0 - 18 880 79.6 0.834 128 9.365 m. - 371 n0 - 3776 79.6 1.845 88.5 6.821 m. - 371 n0 - 378 79.3 5.780 m0 - 371 n0 - 38 77.8 18.673 u T T TT f A T rv P 1 00 2 P 2 1 2 A P 04 7 b LL I CARO 2- yx - 22-8 2- yx - 1-84 yx - 24-7 Data S 1 yx S 2 yx Mean SD Mean SD m. - 371 n - 18 880 24.7 0.645 115 14.227 m. - 371 n0 - 3776 24.5 1.480 41.1 6.626 m. - 371 n0 - 378 24.8 4.856 0 - 371 n0 - 38 23.2 14.174 c CARO p 1 90 5 P c CARO 2_ xx - 90-5 2 xx - 6.09 Pxx - 96.6 S1 xx s xx Data Mean SD Mean SD m0 - 371 n0 - 18 880 96.6 1.167 399 32.554 m0 - 371 n0 - 3776 96.5 2.264 152 12.511 m0 - 371 n0 - 378 96.6 7.546 m0 - 371 n0 - 38 92.0 22.430 d LLTI vs. CARO pyx - 252 pyx - 302 Pyx - 255 By B y2x Data Mean SD Mean SD m0 - 371 n0 - 18 880 255 6.155 288 26.616 m0 - 371 n0 - 3776 254 14.766 270 36.597 m0 - 371 n0 - 378 256 45.800 m0 - 371 n0 - 38 258 155.517 338 ANALYSIS OF SURVEY AND GEOGRAPHICALLY AGGREGATED DATA 20.5. USING AUXILIARY VARIABLES TO REDUCE AGGREGATION EFFECTS In Section 20.3 it was shown how individual-level data on y and x can be used in combination with aggregate data. In some cases individual-level data may not be available for y and x but may be available for some auxiliary variables. Steel and Holt 1996a suggested introducing extra variables to account for the correlations within areas. Suppose that there is a set of auxiliary variables z that partially characterize the way in which individuals are clustered within the groups and conditional on z the observations for individuals in area g are influenced by random group-level effects. The auxiliary variables in z may only have a small effect on the individual-level relationships and may not be of any direct interest.