Introdução ao Lavaan

Bibliotecas

  library(knitr)
  library(semPlot)
  library(tidyverse)

Instale o lavaan

  install.packages("lavaan")

Exemplo do Cap 2 do livro de (Beaujean, 2014)

# Ative o lavaan
  library(lavaan)

# Cria uma matriz de correlação
  rs <- c(1.0,0.20,1,0.24,0.30,1,0.70,0.80,0.30,1)
  R <- lower2full(rs)
  

# Nomeie as variáveis
  colnames(R) <- c("X1", "X2", "X3", "Y") 
  rownames(R) <- c("X1", "X2", "X3", "Y") 
  
  kable(R)

	X1	X2	X3	Y
X1	1.00	0.2	0.24	0.7
X2	0.20	1.0	0.30	0.8
X3	0.24	0.3	1.00	0.3
Y	0.70	0.8	0.30	1.0

# Sintaxe do modelo
  
  regr_model <-"
    Y ~ a*X1 + b*X2 + c*X3
    Y ~~ z*Y
  "

# fit the model
  fit <- sem(regr_model, sample.cov=R, sample.nobs=1000)
  summary(fit, rsquare=TRUE)

## lavaan (0.5-23.1097) converged normally after  25 iterations
## 
##   Number of observations                          1000
## 
##   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 ~                                                 
##     X1         (a)    0.571    0.008   74.539    0.000
##     X2         (b)    0.700    0.008   89.724    0.000
##     X3         (c)   -0.047    0.008   -5.980    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .Y          (z)    0.054    0.002   22.361    0.000
## 
## R-Square:
##                    Estimate
##     Y                 0.946

# desenha o modelo (http://sachaepskamp.com/semPlot/examples)
  semPaths(fit, whatLabels = "est")

# imprime tabela

  kable(
    parameterEstimates(fit, standardized=TRUE)[,c(1:3,5:6,12)], 
    digits = 2
    )

lhs	op	rhs	est	se	std.all
Y	~	X1	0.57	0.01	0.57
Y	~	X2	0.70	0.01	0.70
Y	~	X3	-0.05	0.01	-0.05
Y	~~	Y	0.05	0.00	0.05
X1	~~	X1	1.00	0.00	1.00
X1	~~	X2	0.20	0.00	0.20
X1	~~	X3	0.24	0.00	0.24
X2	~~	X2	1.00	0.00	1.00
X2	~~	X3	0.30	0.00	0.30
X3	~~	X3	1.00	0.00	1.00

Como testar mediação/efeitos indiretos? (2.4.1 de Beaujean (2014))

Abre base e examina variáveis

# Abre base do enade 
  load(
    url("http://www.labape.com.br/rprimi/SEM/exerc18/bd_enade.RData")
    )
# Inspeciona base 
 names(bd_enade)

##  [1] "nt_obj_fg"  "nt_dis_fg"  "nt_obj_ce"  "nt_dis_ce"  "cd_catad"  
##  [6] "ENEM.OBJ.7" "ENEM.RED.7" "in_noturno" "esc_pai7"   "esc_mae7"  
## [11] "Renda7"     "trab_07"

# Descrve variáveis 
  library(psych)
 
  describe(bd_enade) %>%
    kable(digits = 2)

	vars	n	mean	sd	median	trimmed	mad	min	max	range	skew	kurtosis	se
nt_obj_fg	1	6368	48.34	18.64	50.00	48.27	18.53	12.5	100.0	87.5	0.05	-0.50	0.23
nt_dis_fg	2	5598	48.53	16.15	50.00	48.79	18.53	2.5	95.0	92.5	-0.15	-0.47	0.22
nt_obj_ce	3	6470	44.16	14.68	45.00	44.10	14.83	5.0	90.0	85.0	0.01	-0.35	0.18
nt_dis_ce	4	5475	26.89	15.03	25.00	26.09	17.35	1.7	83.3	81.6	0.46	-0.38	0.20
cd_catad	5	6764	1.81	0.39	2.00	1.89	0.00	1.0	2.0	1.0	-1.60	0.54	0.00
ENEM.OBJ.7	6	6764	63.21	15.30	63.49	63.69	16.47	0.0	100.0	100.0	-0.29	-0.44	0.19
ENEM.RED.7	7	6659	65.27	13.14	65.00	65.42	14.83	25.0	100.0	75.0	-0.11	-0.24	0.16
in_noturno	8	6764	0.60	0.49	1.00	0.62	0.00	0.0	1.0	1.0	-0.40	-1.84	0.01
esc_pai7	9	5870	3.28	2.00	4.00	3.19	2.97	0.0	7.0	7.0	0.22	-1.14	0.03
esc_mae7	10	6071	3.58	2.04	4.00	3.53	2.97	0.0	7.0	7.0	0.07	-1.18	0.03
Renda7	11	6085	3.12	1.14	3.00	3.05	1.48	1.0	7.0	6.0	0.60	0.64	0.01
trab_07	12	6034	1.66	0.70	2.00	1.57	1.48	1.0	3.0	2.0	0.59	-0.81	0.01

# Correlaciona
  bd_enade %>% 
    select(nt_obj_ce, ENEM.OBJ.7, cd_catad) %>%
    pairs.panels(pch =4, cex=0.5)

Testa modelo IES publica -> enem -> enade

# Modelo cat_adm -> enem -> enade
 mod <- "
    nt_obj_ce ~ a*publ  + c*ENEM.OBJ.7
    ENEM.OBJ.7 ~ b*publ
    ind:= b*c
  "
 
# Estima modelo

  fit <- 
  bd_enade %>% 
   mutate(
    publ = ifelse(cd_catad==1, 1, 0)
     ) %>%
  sem(mod, data = .)
  
  summary(fit, standardized=TRUE, rsq=TRUE)

## lavaan (0.5-23.1097) converged normally after  35 iterations
## 
##                                                   Used       Total
##   Number of observations                          6470        6764
## 
##   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|)   Std.lv  Std.all
##   nt_obj_ce ~                                                           
##     publ       (a)    0.998    0.469    2.127    0.033    0.998    0.025
##     ENEM.OBJ.7 (c)    0.418    0.011   37.109    0.000    0.418    0.431
##   ENEM.OBJ.7 ~                                                          
##     publ       (b)   11.171    0.498   22.417    0.000   11.171    0.268
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .nt_obj_ce       174.091    3.061   56.877    0.000  174.091    0.808
##    .ENEM.OBJ.7      211.654    3.721   56.877    0.000  211.654    0.928
## 
## R-Square:
##                    Estimate
##     nt_obj_ce         0.192
##     ENEM.OBJ.7        0.072
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     ind               4.674    0.244   19.188    0.000    4.674    0.116

# plota modelo  

  semPaths(fit,
    whatLabels = "std", 
    sizeMan = 12, 
    shapeMan = "rectangle" ,
    edge.label.cex=1.5,
    nodeLabels = c("enade", "enem", "publ"),
    node.width = 2,
    label.prop = .6
    )

Testa modelo enem -> IES pública -> enade

# Modelo cat_adm -> enem -> enade
 mod <- "
    nt_obj_ce ~ a*ENEM.OBJ.7  + c*publ
    publ ~ b*ENEM.OBJ.7
    ind:= b*c
  "
 
# Estima modelo

  fit <- 
  bd_enade %>% 
   mutate(
    publ = ifelse(cd_catad==1, 1, 0)
     ) %>%
  sem(mod, data = .)
  
  summary(fit, standardized=TRUE, rsq=TRUE)

## lavaan (0.5-23.1097) converged normally after  28 iterations
## 
##                                                   Used       Total
##   Number of observations                          6470        6764
## 
##   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|)   Std.lv  Std.all
##   nt_obj_ce ~                                                           
##     ENEM.OBJ.7 (a)    0.418    0.011   37.109    0.000    0.418    0.431
##     publ       (c)    0.998    0.469    2.127    0.033    0.998    0.025
##   publ ~                                                                
##     ENEM.OBJ.7 (b)    0.006    0.000   22.417    0.000    0.006    0.268
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .nt_obj_ce       174.091    3.061   56.877    0.000  174.091    0.808
##    .publ              0.122    0.002   56.877    0.000    0.122    0.928
## 
## R-Square:
##                    Estimate
##     nt_obj_ce         0.192
##     publ              0.072
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     ind               0.006    0.003    2.117    0.034    0.006    0.007

  parameterEstimates(fit, standardized=TRUE) %>%
    kable(digits = 2)

lhs	op	rhs	label	est	se	z	pvalue	ci.lower	ci.upper	std.lv	std.all	std.nox
nt_obj_ce	~	ENEM.OBJ.7	a	0.42	0.01	37.11	0.00	0.40	0.44	0.42	0.43	0.03
nt_obj_ce	~	publ	c	1.00	0.47	2.13	0.03	0.08	1.92	1.00	0.02	0.02
publ	~	ENEM.OBJ.7	b	0.01	0.00	22.42	0.00	0.01	0.01	0.01	0.27	0.02
nt_obj_ce	~~	nt_obj_ce		174.09	3.06	56.88	0.00	168.09	180.09	174.09	0.81	0.81
publ	~~	publ		0.12	0.00	56.88	0.00	0.12	0.13	0.12	0.93	0.93
ENEM.OBJ.7	~~	ENEM.OBJ.7		228.09	0.00	NA	NA	228.09	228.09	228.09	1.00	228.09
ind	:=	b*c	ind	0.01	0.00	2.12	0.03	0.00	0.01	0.01	0.01	0.00

# plota modelo  

  semPaths(fit,
    whatLabels = "std", 
    sizeMan = 12, 
    shapeMan = "rectangle" ,
    edge.label.cex=1.5,
    node.width = 2,
     nodeLabels = c("enade", "publ", "enem"),
    label.prop = .6
    )

Exercício

Faça uma análise de mediação: escolaridade dos pais -> enem -> enade
Veja mais detalhes em http://lavaan.ugent.be/tutorial/mediation.html

Referências

Beaujean, A. A. (2014). Latent Variable Modeling Using R: A Step-By-Step Guide (Edição: 1.). New York: Routledge.

Introdução ao Lavaan

Ricardo Primi

15 de abril de 2018

Bibliotecas

Instale o lavaan

Exemplo do Cap 2 do livro de (Beaujean, 2014)

Como testar mediação/efeitos indiretos? (2.4.1 de Beaujean (2014))

Abre base e examina variáveis

Testa modelo IES publica -> enem -> enade

Testa modelo enem -> IES pública -> enade

Exercício

Referências