stata如何处理结构方程模型(SEM)中具有缺失值的协变量
作者:互联网
原文链接:http://tecdat.cn/?p=6349
本周我正和一位朋友讨论如何在结构方程模型(SEM)软件中处理具有缺失值的协变量。我的朋友认为某些包中某些SEM的实现能够使用所谓的“完全信息最大可能性”自动适应协变量中的缺失。在下文中,我将描述我后来探索Stata的sem命令如何处理协变量中的缺失。
为了研究如何处理丢失的协变量,我将考虑最简单的情况,其中我们有一个结果Y和一个协变量X,Y遵循给定X的简单线性回归模型。首先我们将模拟一个大数据集,所以我们知道真正的参数值:
gen x = rnormal()
gen y = x + rnormal()
这里真正的截距参数为0,真实斜率参数为1.残差误差为方差1。接下来,让我们设置一些缺少的协变量值。为此,我们将使用缺失机制,其中缺失的概率取决于(完全观察到的)结果Y.这意味着缺失机制将满足所谓的随机假设缺失。具体来说,我们将根据逻辑回归模型计算观察X的概率,其中Y作为唯一的协变量进入:
gen rxb = -2 + 2 * y
gen r =(runiform()<rpr)
现在我们可以应用Stata的sem命令来适应SEM:
(7270 observations with missing values excluded)
Endogenous variables
Observed: y
Exogenous variables
Observed: x
Fitting target model:
Iteration 0: log likelihood = -6732.1256
Iteration 1: log likelihood = -6732.1256
Structural equation model Number of obs = 2730
Estimation method = ml
Log likelihood = -6732.1256
------------------------------------------------------------------------------
| OIM
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Structural |
y <- |
x | .6179208 .0179671 34.39 0.000 .582706 .6531355
_cons | .999025 .0200306 49.88 0.000 .9597658 1.038284
-------------+----------------------------------------------------------------
var(e.y)| .6472101 .0175178 .6137707 .6824714
------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(0) = 0.00, Prob > chi2 = .
在没有缺失值的情况下,sem命令默认使用最大似然来估计模型参数。
但是sem还有另一个选项,它将使我们能够使用来自所有10,000条记录的观察数据来拟合模型。从命令行,我们可以通过以下方式选择它:
*output cut
Structural equation model Number of obs = 10000
Estimation method = mlmv
Log likelihood = -20549.731
------------------------------------------------------------------------------
| OIM
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Structural |
y <- |
x | .9804851 .0156235 62.76 0.000 .9498637 1.011107
_cons | -.0145543 .025363 -0.57 0.566 -.0642649 .0351562
-------------+----------------------------------------------------------------
mean(x)| .0032305 .0257089 0.13 0.900 -.047158 .0536189
-------------+----------------------------------------------------------------
var(e.y)| 1.02696 .0324877 .9652191 1.09265
var(x)| .9847265 .0314871 .924907 1.048415
------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(0) = 0.00, Prob > chi2 = .
估计现在是无偏的。
因此,我们获得无偏估计(对于此数据生成设置),因为Stata的sem命令(在此正确)假设Y和X的联合正态性,并且缺失满足MAR假设。
非正态X
让我们现在重新运行模拟,但现在让X在一个自由度上遵循卡方分布,通过平方rnormal()绘制:
clear
set seed 6812312
set obs 10000
gen x=(rnormal())^2
gen y=x+rnormal()
gen rxb=-2+*y
gen rpr=(rxb)/(1+exp(rxb))
gen r=(() rpr)
x=. if r==0
使用缺少值选项运行sem,我们获得:
*output cut
Structural equation model Number of obs = 10000
Estimation method = mlmv
Log likelihood = -25316.281
------------------------------------------------------------------------------
| OIM
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Structural |
y <- |
x | .8281994 .0066085 125.32 0.000 .815247 .8411518
_cons | .4792567 .0161389 29.70 0.000 .447625 .5108883
-------------+----------------------------------------------------------------
mean(x)| .5842649 .0224815 25.99 0.000 .5402019 .6283279
-------------+----------------------------------------------------------------
var(e.y)| .7537745 .0157842 .7234643 .7853546
var(x)| 3.073801 .0551011 2.96768 3.183717
------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(0) = 0.00, Prob > chi2 = .
现在我们再次有偏差估计,因为Y和X的联合常态假设不再成立。因此,如果我们使用此选项,当我们缺少协变量时,我们会发现联合正态假设是至关重要的。
完全随机缺失
让我们最后一次运行模拟,再次使用X卡方形分布,但现在X随机完全丢失(MCAR):
gen x=(rnormal())^2
gen y=x+rnormal()
replace x=if (()<0.5)
*output cut
Structural equation model Number of obs = 10000
Estimation method = mlmv
Log likelihood = -25495.152
------------------------------------------------------------------------------
| OIM
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Structural |
y <- |
x | .9985166 .0093366 106.95 0.000 .9802173 1.016816
_cons | -.0092478 .0158659 -0.58 0.560 -.0403445 .0218488
-------------+----------------------------------------------------------------
mean(x)| .9738369 .0158113 61.59 0.000 .9428474 1.004826
-------------+----------------------------------------------------------------
var(e.y)| 1.033884 .020162 .9951133 1.074166
var(x)| 1.83369 .0330307 1.77008 1.899585
------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(0) = 0.00, Prob > chi2 = .
尽管联合正态性假设被违反,现在我们再次进行无偏估计。我认为这是因为当数据是MCAR时,即使违反了正态性假设,也可以一致地估计均值和协方差结构.
标签:gen,rnormal,sem,stata,SEM,我们,缺失,Structural 来源: https://blog.51cto.com/u_15198753/2770985