マルチレベル＋ウェイト？
Carle 2009 Fitting multilevel models in complex survey data with design weights: Recommendations
Kline 2010 Principles and Practice of SEM
p.336
The reference variable for A is X1, and the reference variable for B is X3.
X3ではなく、W1。
Singer & Willet おすすめ文献
誤差共分散構造についての文献
Van Leeuwen 1997 A Note on the Covariance Structure in a Linear Model
Goldstein, healy & Rasbash 1994 Multilevel time series models with applications to repeated measures data.
Wolfinger 1993 Covariance structure selection in general mixed models
縦断データの分析 1 変化についてのマルチレベルモデリング
- 作者: ジュディスシンガー,ジョンウィレット,Judith D. Singer,John B. Willett,菅原ますみ
- 出版社/メーカー: 朝倉書店
- 発売日: 2012/09/01
- メディア: 単行本
- クリック: 1回
- この商品を含むブログを見る
typo:
p.44 ここではより実質的に使いでのある
p.67 表3.3 固定効果の変化率の位置がおかしい。これは2つめの切片の横に来るはず（たぶん）。
p.113 SUS PROC→SAS PROC
Principles and Practice of Structural Equation Modeling Ch.8
clear all ssd init exercise hardy fitness stress illness ssd set obs 373 ssd set cov 4422.25 \ -75.81 1444 \ 954.408 97.888 1354.24 \ -222.775 -585.58 -320.528 4489 \ -332.3936 -379.8784 -666.7866 1423.294 3903.7504 ssd list sem (illness<- fitness stress) (fitness<-exercise) (stress<-hardy), cov(exercise*hardy) estat gof, stats(all) estat mindices
Endogenous variables
Observed: illness fitness stress
Exogenous variables
Observed: exercise hardy
Fitting target model:
Iteration 0: log likelihood = -9944.2736
Iteration 1: log likelihood = -9944.2736
Structural equation model Number of obs = 373
Estimation method = ml
Log likelihood = -9944.2736
------------------------------------------------------------------------------------
| OIM
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------------+----------------------------------------------------------------
Structural |
illness <- |
fitness | -.4244997 .0804313 -5.28 0.000 -.5821422 -.2668573
stress | .286752 .0441772 6.49 0.000 .2001664 .3733377
-----------------+----------------------------------------------------------------
fitness <- |
exercise | .2158195 .0263842 8.18 0.000 .1641074 .2675316
-----------------+----------------------------------------------------------------
stress <- |
hardy | -.4055263 .0888454 -4.56 0.000 -.57966 -.2313926
-------------------+----------------------------------------------------------------
var(e.illness)| 3203.954 234.6102 2775.6 3698.416
var(e.fitness)| 1145.182 83.85616 992.0761 1321.916
var(e.stress)| 4240.134 310.4846 3673.247 4894.507
var(exercise)| 4410.394 322.952 3820.744 5091.043
var(hardy)| 1440.129 105.4537 1247.59 1662.382
-------------------+----------------------------------------------------------------
cov(exercise,hardy)| -75.60676 130.551 -0.58 0.562 -331.4821 180.2685
------------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(5) = 11.11, Prob > chi2 = 0.0493
. estat gof, stats(all)
----------------------------------------------------------------------------
Fit statistic | Value Description
---------------------+------------------------------------------------------
Likelihood ratio |
chi2_ms(5) | 11.107 model vs. saturated
p > chi2 | 0.049
chi2_bs(9) | 165.608 baseline vs. saturated
p > chi2 | 0.000
---------------------+------------------------------------------------------
Population error |
RMSEA | 0.057 Root mean squared error of approximation
90% CI, lower bound | 0.003
upper bound | 0.103
pclose | 0.336 Probability RMSEA <= 0.05
---------------------+------------------------------------------------------
Information criteria |
AIC | 19908.547 Akaike's information criterion
BIC | 19947.763 Bayesian information criterion
---------------------+------------------------------------------------------
Baseline comparison |
CFI | 0.961 Comparative fit index
TLI | 0.930 Tucker-Lewis index
---------------------+------------------------------------------------------
Size of residuals |
SRMR | 0.051 Standardized root mean squared residual
CD | 0.197 Coefficient of determination
----------------------------------------------------------------------------
. estat mindices
Modification indices
----------------------------------------------------------------------
| Standard
| MI df P>MI EPC EPC
-----------------------+----------------------------------------------
Structural |
fitness <- |
illness | 4.386 1 0.04 -.125466 -.2108351
stress | 5.372 1 0.02 -.0606954 -.1105053
---------------------+----------------------------------------------
stress <- |
fitness | 5.110 1 0.02 -.2074007 -.1139156
-----------------------+----------------------------------------------
cov(e.fitness,e.stress)| 3.907 1 0.05 -225.5115 -.1023391
----------------------------------------------------------------------
EPC = expected parameter change
Principles and practice of Structural Equation Modeling Ch.7
今年4版が出て、Stataのコードもついてくる模様。
今のところraw dataはないので、共分散行列を入力してそれを分析することになる。
共分散行列は、サポートページでしめされている標準偏差と相関行列から計算することができる。
Rの場合はcor2cov()で相関行列と標準偏差を共分散行列に書き換えてくれる。
基本的にxとyの相関＝（xとyの共分散）/（xの標準偏差）(yの標準偏差)なので、
相関にxとyの標準誤差をかければ、共分散は求められるので、エクセルでも計算できる。
clear all ssd init coercive burnout support tpi experien somatic ssd set obs 109 ssd set cov 69.009572 \ 28.868204 95.447038 \ -22.427279 -49.071453 110.695649 \ -16.805466 1.011164 9.805758 25 \ -4.987848 3.406984 2.808509 12.160924 13.822037 \ -15.269773 -0.68495 8.707448 19.179989 9.728453 27.787658 ssd list sem (burnout<-coercive support) (tpi<-coercive support burnout) (experien<-tpi) (somatic<-tpi), cov(coercive*support) estat gof, stats(all)
Endogenous variables
Observed: burnout tpi experien somatic
Exogenous variables
Observed: coercive support
Fitting target model:
Iteration 0: log likelihood = -2052.8451
Iteration 1: log likelihood = -2052.8451
Structural equation model Number of obs = 109
Estimation method = ml
Log likelihood = -2052.8451
--------------------------------------------------------------------------------
| OIM
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------+----------------------------------------------------------------
Structural |
burnout <- |
coercive | .2935851 .0984724 2.98 0.003 .1005828 .4865873
support | -.3838194 .0777506 -4.94 0.000 -.5362078 -.231431
-------------+----------------------------------------------------------------
tpi <- |
burnout | .1424866 .0510318 2.79 0.005 .0424661 .2425072
coercive | -.2717027 .0545622 -4.98 0.000 -.3786426 -.1647629
support | .0966997 .0458219 2.11 0.035 .0068904 .1865089
-------------+----------------------------------------------------------------
experien <- |
tpi | .486437 .0538653 9.03 0.000 .3808629 .5920111
-------------+----------------------------------------------------------------
somatic <- |
tpi | .7671996 .0692629 11.08 0.000 .6314468 .9029524
---------------+----------------------------------------------------------------
var(e.burnout)| 67.51208 9.14499 51.77024 88.04055
var(e.tpi)| 19.16417 2.595923 14.69565 24.99144
var(e.experien)| 7.833977 1.061168 6.007324 10.21606
var(e.somatic)| 12.95285 1.754555 9.932622 16.89143
var(coercive)| 68.37646 9.262076 52.43307 89.16776
var(support)| 109.6801 14.85695 84.10591 143.0306
---------------+----------------------------------------------------------------
cov(coercive,|
support)| -22.22152 8.563488 -2.59 0.009 -39.00565 -5.437396
--------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(7) = 3.93, Prob > chi2 = 0.7877
. estat gof, stats(all)
----------------------------------------------------------------------------
Fit statistic | Value Description
---------------------+------------------------------------------------------
Likelihood ratio |
chi2_ms(7) | 3.931 model vs. saturated
p > chi2 | 0.788
chi2_bs(14) | 211.718 baseline vs. saturated
p > chi2 | 0.000
---------------------+------------------------------------------------------
Population error |
RMSEA | 0.000 Root mean squared error of approximation
90% CI, lower bound | 0.000
upper bound | 0.078
pclose | 0.882 Probability RMSEA <= 0.05
---------------------+------------------------------------------------------
Information criteria |
AIC | 4133.690 Akaike's information criterion
BIC | 4171.369 Bayesian information criterion
---------------------+------------------------------------------------------
Baseline comparison |
CFI | 1.000 Comparative fit index
TLI | 1.031 Tucker-Lewis index
---------------------+------------------------------------------------------
Size of residuals |
SRMR | 0.034 Standardized root mean squared residual
CD | 0.447 Coefficient of determination
----------------------------------------------------------------------------
JGSSの職種をリコードする
Stataでリコードする場合，
JGSS2010コードブックの職業コードを参照して，リコードしてみる．
以下のコードで一応，管理(1)・事務(2)・熟練(3)・専門(4)・農林(5)・半熟練(6)・販売(7)・非熟練(8)のリコードができる．
分類不能は欠損とした．範囲指定をすれば，もっとエレガントにできるのだろう．
generate tjob=.
replace tjob = 1 if XXJOB = 545
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重回帰分析の係数の標準化
通常のソフトウェアでは重回帰分析の係数の非標準解と標準解を同時に出力する．しかし，それらが出力されない場合，
もしくは手計算の場合は，非標準解にローデータの独立変数の標準偏差をかけて，従属変数の標準偏差で割ると，
標準解が得られるとされている．
まず，標準化されていない回帰式は以下のように書ける．
簡便のため，単回帰を想定する．
標準化されている回帰式は以下のように書ける．
ただし，は{tex:Y}のローデータにおける標準偏差を表すとする．
標準化された係数はのように*をつけてあらわす．
これを変形すると，
となる．これを定数部分と係数の部分に整理をすると．
よって係数の部分は，
となる．
したがって，
となる．
