12. 估计方法，标准误差和缺失值

12.1 估计方法

如果所有数据都是连续的，默认估计方法是最大似然法，还有一些其他方法：

• "GLS": generalized least squares. 只能用于完整数据
• "WLS": weighted least squares (sometimes called ADF estimation). 只能用于完整数据
• "DWLS": diagonally weighted least squares
• "ULS": unweighted least squares

许多估计方法都有“稳健”变体，意味着它们提供稳健标准误差和缩放的检验统计量。例如，对于最大似然，lavaan提供如下稳健变体：

• "MLM": maximum likelihood estimation with robust standard errors and a Satorra-Bentler scaled test statistic. 只能用于完整数据
• "MLMVS": maximum likelihood estimation with robust standard errors and a mean- and variance adjusted test statistic (aka the Satterthwaite approach). 只能用于完整数据
• "MLMV": maximum likelihood estimation with robust standard errors and a mean- and variance adjusted test statistic (using a scale-shifted approach). 只能用于完整数据
• "MLF": for maximum likelihood estimation with standard errors based on the first-order derivatives, and a conventional test statistic. 可以用于完整和非完整数据
• "MLR": maximum likelihood estimation with robust (Huber-White) standard errors and a scaled test statistic that is (asymptotically) equal to the Yuan-Bentler test statistic. 可以用于完整和非完整数据

12.2 最大似然估计

lavaan默认使用有偏样本协方差矩阵，与Mplus所使用方法相似(“normal”)。我们也可以使用likelihood = "wishart"来使用无偏协方差用以接近EQS, LISREL或AMOS的计算结果(“Wishart”)：

fit <- cfa(HS.model,
           data = HolzingerSwineford1939,
fit

12.3 缺失值

默认为列表状态删除，在进行统计量的计算时，把含有缺失值的记录删除，这种方法可以用于计算全体无缺失值数据的均数、协方差和标准差。

13. 间接效应和中介分析

设想一个典型的中介分析，X->M->Y，随机生成人工数据，示例如下：

set.seed(1234)
X <- rnorm(100)
M <- 0.5*X + rnorm(100)
Y <- 0.7*M + rnorm(100)
Data <- data.frame(X = X, Y = Y, M = M)
model <- '# direct effect
            Y ~ c*X
          # mediator
            M ~ a*X
            Y ~ b*M
          # indirect effect (a*b)
            ab := a*b
          # total effect
            total := c + (a*b)'
            
fit <- sem(model, data = Data)
summary(fit)

结果如下：

lavaan (0.5-23.1097) converged normally after  12 iterations

  Number of observations                           100

  Estimator                                         ML
  Minimum Function Test Statistic                0.000
  Degrees of freedom                                 0
  Minimum Function Value               0.0000000000000

Parameter Estimates:

  Information                                 Expected
  Standard Errors                             Standard

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)
  Y ~                                                 
    X          (c)    0.036    0.104    0.348    0.728
  M ~                                                 
    X          (a)    0.474    0.103    4.613    0.000
  Y ~                                                 
    M          (b)    0.788    0.092    8.539    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .Y                 0.898    0.127    7.071    0.000
   .M                 1.054    0.149    7.071    0.000

Defined Parameters:
                   Estimate  Std.Err  z-value  P(>|z|)
    ab                0.374    0.092    4.059    0.000
    total             0.410    0.125    3.287    0.001

14. 修正指标

可以通过在summary()函数中增加参数modindices = TRUE，来得出修正指标，例如：

fit <- cfa(HS.model,
           data = HolzingerSwineford1939)
mi <- modindices(fit)
mi[mi$op == "=~",]

结果为：