長格式 (lme4) 和寬格式 (lavaan) 的估計是相同的¶

2026-03-19
jw

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system('sudo apt install r-cran-lavaan r-cran-lme4')
system('sudo apt install r-cran-lavaan r-cran-lme4')

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library(lavaan)
library(lme4)
library(tidyverse)
library(lavaan)
library(lme4)
library(tidyverse)

── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr     1.2.0     ✔ readr     2.2.0
✔ forcats   1.0.1     ✔ stringr   1.6.0
✔ ggplot2   4.0.2     ✔ tibble    3.3.1
✔ lubridate 1.9.5     ✔ tidyr     1.3.2
✔ purrr     1.2.1     
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ tidyr::expand() masks Matrix::expand()
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
✖ tidyr::pack()   masks Matrix::pack()
✖ tidyr::unpack() masks Matrix::unpack()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

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data_wide <- HolzingerSwineford1939[c(1, 7:9)]
data_wide <- HolzingerSwineford1939[c(1, 7:9)]

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head(data_wide)
head(data_wide)

A data.frame: 6 × 4
	id	x1	x2	x3
	<int>	<dbl>	<dbl>	<dbl>
1	1	3.333333	7.75	0.375
2	2	5.333333	5.25	2.125
3	3	4.500000	5.25	1.875
4	4	5.333333	7.75	3.000
5	5	4.833333	4.75	0.875
6	6	5.333333	5.00	2.250

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data_long <- pivot_longer(data_wide, cols = -id )
data_long <- pivot_longer(data_wide, cols = -id )

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  head(data_long)
  head(data_long)

A tibble: 6 × 3
id	name	value
<int>	<chr>	<dbl>
1	x1	3.333333
1	x2	7.750000
1	x3	0.375000
2	x1	5.333333
2	x2	5.250000
2	x3	2.125000

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## wide data (sem)

model <- "
F =~ 1*x1 + 1*x2 + 1*x3
x1 ~~ resvar*x1
x2 ~~ resvar*x2
x3 ~~ resvar*x3

x1 ~ 0*1
x2 ~ 1
x3 ~ 1
F ~ 1
"

fit_sem <- sem(model, data_wide, meanstructure=T)
summary(fit_sem)
## wide data (sem)

model <- "
F =~ 1*x1 + 1*x2 + 1*x3
x1 ~~ resvar*x1
x2 ~~ resvar*x2
x3 ~~ resvar*x3

x1 ~ 0*1
x2 ~ 1
x3 ~ 1
F ~ 1
"

fit_sem <- sem(model, data_wide, meanstructure=T)
summary(fit_sem)

lavaan 0.6-10 ended normally after 23 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                         7
  Number of equality constraints                     2
                                                      
  Number of observations                           301
                                                      
Model Test User Model:
                                                      
  Test statistic                                 7.422
  Degrees of freedom                                 4
  P-value (Chi-square)                           0.115

Parameter Estimates:

  Standard errors                             Standard
  Information                                 Expected
  Information saturated (h1) model          Structured

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  F =~                                                
    x1                1.000                           
    x2                1.000                           
    x3                1.000                           

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)
   .x1                0.000                           
   .x2                1.152    0.076   15.253    0.000
   .x3               -2.685    0.076  -35.547    0.000
    F                 4.936    0.067   74.021    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .x1      (rsvr)    0.859    0.050   17.349    0.000
   .x2      (rsvr)    0.859    0.050   17.349    0.000
   .x3      (rsvr)    0.859    0.050   17.349    0.000
    F                 0.479    0.065    7.426    0.000

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## data long

fit_lmer <- lmer(value ~ (1|id) + name, data_long, REML=F)
summary(fit_lmer)
## data long

fit_lmer <- lmer(value ~ (1|id) + name, data_long, REML=F)
summary(fit_lmer)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: value ~ (1 | id) + name
   Data: data_long

      AIC       BIC    logLik -2*log(L)  df.resid 
   2731.4    2755.4   -1360.7    2721.4       898 

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.94955 -0.62068 -0.02622  0.55642  2.58217 

Random effects:
 Groups   Name        Variance Std.Dev.
 id       (Intercept) 0.4794   0.6924  
 Residual             0.8589   0.9268  
Number of obs: 903, groups:  id, 301

Fixed effects:
            Estimate Std. Error t value
(Intercept)  4.93577    0.06668   74.02
namex2       1.15227    0.07554   15.25
namex3      -2.68535    0.07554  -35.55

Correlation of Fixed Effects:
       (Intr) namex2
namex2 -0.566       
namex3 -0.566  0.500

固定效果：觀察 lavaan- Intercepts 部分 vs lme4- Fixed effects 部分¶

結構方程式估計如下

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)
   .x1                0.000                           
   .x2                1.152    0.076   15.253    0.000
   .x3               -2.685    0.076  -35.547    0.000
    F                 4.936    0.067   74.021    0.000

多層次模式估計如下：

Fixed effects:
            Estimate Std. Error t value
(Intercept)  4.93577    0.06668   74.02
namex2       1.15227    0.07554   15.25
namex3      -2.68535    0.07554  -35.55

隨機效果：觀察 lavaan- Variances 部分 vs lme4- Random effects: 部分¶

結構方程式估計如下

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .x1      (rsvr)    0.859    0.050   17.349    0.000
   .x2      (rsvr)    0.859    0.050   17.349    0.000
   .x3      (rsvr)    0.859    0.050   17.349    0.000
    F                 0.479    0.065    7.426    0.000

多層次模式估計如下：

Random effects:
 Groups   Name        Variance Std.Dev.
 id       (Intercept) 0.4794   0.6924  
 Residual             0.8589   0.9268  
Number of obs: 903, groups:  id, 301