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20230109 - EFA
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isaactpetersen committed Jan 9, 2023
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Expand Up @@ -792,7 +792,7 @@ nfactors(

#### Run factor analysis {#runFactorAnalysis-efa}

[Exploratory factor analysis](#efa) (EFA) models were fit using the `fa()` function of the `psych` package [@R-psych] and the `sem()` function of the `lavaan` package [@R-lavaan].
[Exploratory factor analysis](#efa) (EFA) models were fit using the `fa()` function of the `psych` package [@R-psych] and the `sem()` and `efa()` functions of the `lavaan` package [@R-lavaan].

##### Orthogonal (Varimax) rotation {#orthogonal-efa}

Expand Down Expand Up @@ -1037,6 +1037,80 @@ efa9factorOrthogonalLavaan_fit <- sem(
rotation.args = list(orthogonal = TRUE))
```

The `efa()` wrapper can fit multiple [EFA](#efa) models models in one function call:

```{r}
efaOrthogonalLavaan_fit <- efa(
data = HolzingerSwineford1939,
ov.names = vars,
nfactors = 1:5,
rotation = "varimax",
missing = "ML",
estimator = "MLR",
meanstructure = TRUE,
rotation.args = list(orthogonal = TRUE)
)
```

The `efa()` wrapper can also fit individual EFA models (with `output = "lavaan"`):

```{r}
efaFactor1OrthogonalLavaan_fit <- efa(
data = HolzingerSwineford1939,
ov.names = vars,
nfactors = 1,
rotation = "varimax",
missing = "ML",
estimator = "MLR",
meanstructure = TRUE,
rotation.args = list(orthogonal = TRUE)
)
efaFactor2OrthogonalLavaan_fit <- efa(
data = HolzingerSwineford1939,
ov.names = vars,
nfactors = 2,
rotation = "varimax",
missing = "ML",
estimator = "MLR",
meanstructure = TRUE,
rotation.args = list(orthogonal = TRUE)
)
efaFactor3OrthogonalLavaan_fit <- efa(
data = HolzingerSwineford1939,
ov.names = vars,
nfactors = 3,
rotation = "varimax",
missing = "ML",
estimator = "MLR",
meanstructure = TRUE,
rotation.args = list(orthogonal = TRUE)
)
efaFactor4OrthogonalLavaan_fit <- efa(
data = HolzingerSwineford1939,
ov.names = vars,
nfactors = 4,
rotation = "varimax",
missing = "ML",
estimator = "MLR",
meanstructure = TRUE,
rotation.args = list(orthogonal = TRUE)
)
efaFactor5OrthogonalLavaan_fit <- efa(
data = HolzingerSwineford1939,
ov.names = vars,
nfactors = 5,
rotation = "varimax",
missing = "ML",
estimator = "MLR",
meanstructure = TRUE,
rotation.args = list(orthogonal = TRUE)
)
```

##### Oblique (Oblimin) rotation {#oblique-efa}

###### `psych` {#obliquePsych-efa}
Expand Down Expand Up @@ -1104,6 +1178,7 @@ efa9factorOblique <- fa(
The models are fitted below:

```{r}
# settings to mimic Mplus
mplusRotationArgs <-
list(
rstarts = 30,
Expand All @@ -1121,7 +1196,6 @@ efa1factorObliqueLavaan_fit <- sem(
missing = "ML",
estimator = "MLR",
rotation = "geomin",
# mimic Mplus
meanstructure = TRUE,
rotation.args = mplusRotationArgs)
Expand All @@ -1132,7 +1206,6 @@ efa2factorObliqueLavaan_fit <- sem(
missing = "ML",
estimator = "MLR",
rotation = "geomin",
# mimic Mplus
meanstructure = TRUE,
rotation.args = mplusRotationArgs)
Expand All @@ -1143,7 +1216,6 @@ efa3factorObliqueLavaan_fit <- sem(
missing = "ML",
estimator = "MLR",
rotation = "geomin",
# mimic Mplus
meanstructure = TRUE,
rotation.args = mplusRotationArgs)
Expand All @@ -1154,7 +1226,6 @@ efa4factorObliqueLavaan_fit <- sem(
missing = "ML",
estimator = "MLR",
rotation = "geomin",
# mimic Mplus
meanstructure = TRUE,
rotation.args = mplusRotationArgs)
Expand All @@ -1165,7 +1236,6 @@ efa5factorObliqueLavaan_fit <- sem(
missing = "ML",
estimator = "MLR",
rotation = "geomin",
# mimic Mplus
meanstructure = TRUE,
rotation.args = mplusRotationArgs)
Expand All @@ -1176,7 +1246,6 @@ efa6factorObliqueLavaan_fit <- sem(
missing = "ML",
estimator = "MLR",
rotation = "geomin",
# mimic Mplus
meanstructure = TRUE,
rotation.args = mplusRotationArgs)
Expand All @@ -1187,7 +1256,6 @@ efa7factorObliqueLavaan_fit <- sem(
missing = "ML",
estimator = "MLR",
rotation = "geomin",
# mimic Mplus
meanstructure = TRUE,
rotation.args = mplusRotationArgs)
Expand All @@ -1198,7 +1266,6 @@ efa8factorObliqueLavaan_fit <- sem(
missing = "ML",
estimator = "MLR",
rotation = "geomin",
# mimic Mplus
meanstructure = TRUE,
rotation.args = mplusRotationArgs)
Expand All @@ -1209,11 +1276,89 @@ efa9factorObliqueLavaan_fit <- sem(
missing = "ML",
estimator = "MLR",
rotation = "geomin",
# mimic Mplus
meanstructure = TRUE,
rotation.args = mplusRotationArgs)
```

The `efa()` wrapper can fit multiple [EFA](#efa) models models in one function call:

```{r}
efaObliqueLavaan_fit <- efa(
data = HolzingerSwineford1939,
ov.names = vars,
nfactors = 1:5,
rotation = "geomin",
missing = "ML",
estimator = "MLR",
meanstructure = TRUE,
rotation.args = mplusRotationArgs
)
```

The `efa()` wrapper can also fit individual EFA models (with `output = "lavaan"`):

```{r}
efaFactor1ObliqueLavaan_fit <- efa(
data = HolzingerSwineford1939,
ov.names = vars,
nfactors = 1,
rotation = "geomin",
missing = "ML",
estimator = "MLR",
meanstructure = TRUE,
rotation.args = mplusRotationArgs,
output = "lavaan"
)
efaFactor2ObliqueLavaan_fit <- efa(
data = HolzingerSwineford1939,
ov.names = vars,
nfactors = 2,
rotation = "geomin",
missing = "ML",
estimator = "MLR",
meanstructure = TRUE,
rotation.args = mplusRotationArgs,
output = "lavaan"
)
efaFactor3ObliqueLavaan_fit <- efa(
data = HolzingerSwineford1939,
ov.names = vars,
nfactors = 3,
rotation = "geomin",
missing = "ML",
estimator = "MLR",
meanstructure = TRUE,
rotation.args = mplusRotationArgs,
output = "lavaan"
)
efaFactor4ObliqueLavaan_fit <- efa(
data = HolzingerSwineford1939,
ov.names = vars,
nfactors = 4,
rotation = "geomin",
missing = "ML",
estimator = "MLR",
meanstructure = TRUE,
rotation.args = mplusRotationArgs,
output = "lavaan"
)
efaFactor5ObliqueLavaan_fit <- efa(
data = HolzingerSwineford1939,
ov.names = vars,
nfactors = 5,
rotation = "geomin",
missing = "ML",
estimator = "MLR",
meanstructure = TRUE,
rotation.args = mplusRotationArgs,
output = "lavaan"
)
```

#### Factor Loadings {#factorLoadings-efa}

##### Orthogonal (Varimax) rotation {#orthogonalFactorLoadings-efa}
Expand All @@ -1239,6 +1384,9 @@ efa9factorOrthogonal
The factor loadings and summaries of the model results are below:

```{r}
summary(
efaOrthogonalLavaan_fit)
summary(
efa1factorOrthogonalLavaan_fit,
fit.measures = TRUE,
Expand Down Expand Up @@ -1317,6 +1465,9 @@ efa9factorOblique
The factor loadings and summaries of the model results are below:

```{r}
summary(
efaObliqueLavaan_fit)
summary(
efa1factorObliqueLavaan_fit,
fit.measures = TRUE,
Expand Down Expand Up @@ -1372,6 +1523,36 @@ summary(
rsquare = TRUE)
```

#### Estimates of Model Fit {#fitEstimates-efa}

##### Orthogonal (Varimax) rotation {#fitEstimatesOrthogonal-efa}

```{r}
fitMeasures(
efaOrthogonalLavaan_fit,
fit.measures = c(
"chisq", "df", "pvalue",
"chisq.scaled", "df.scaled", "pvalue.scaled",
"chisq.scaling.factor",
"baseline.chisq","baseline.df","baseline.pvalue",
"rmsea", "cfi", "tli", "srmr",
"rmsea.robust", "cfi.robust", "tli.robust"))
```

##### Oblique (Oblimin) rotation {#fitEstimatesOblique-efa}

```{r}
fitMeasures(
efaObliqueLavaan_fit,
fit.measures = c(
"chisq", "df", "pvalue",
"chisq.scaled", "df.scaled", "pvalue.scaled",
"chisq.scaling.factor",
"baseline.chisq","baseline.df","baseline.pvalue",
"rmsea", "cfi", "tli", "srmr",
"rmsea.robust", "cfi.robust", "tli.robust"))
```

#### Factor Scores {#factorScores-efa}

##### Orthogonal (Varimax) rotation {#factorScoresOrthogonal-efa}
Expand Down Expand Up @@ -2668,7 +2849,7 @@ lapply(equivalentDAGs(dagModelBifactor, n = 4), plot)

##### Specify the model {#esemModelSyntax}

To specify an ESEM model, you use the factor loadings from an [EFA](#efa) model as the starting values.
To specify an ESEM model, you use the factor loadings from an [EFA](#efa) model as the starting values in a [structural equation model](#sem).
In this example, I use the factor loadings from the three-factor [EFA](#efa) model, as specified in Section \@ref(obliqueLavaan-efa).

```{r}
Expand All @@ -2692,7 +2873,7 @@ I specify an anchor item for each latent factor below:
anchors <- c(f1 = "x3", f2 = "x5", f3 = "x7")
```

The `petersenlab` package [@R-petersenlab] includes the `make_esem_model()` function that creates `lavaan` syntax for an ESEM model from the factor loadings of an [EFA](#efa) model, as adapted from Mateus Silvestrin: https://msilvestrin.me/post/esem/
The `petersenlab` package [@R-petersenlab] includes the `make_esem_model()` function that creates `lavaan` syntax for an ESEM model from the factor loadings of an [EFA](#efa) model, as adapted from Mateus Silvestrin: https://msilvestrin.me/post/esem

```{r}
esemModel_syntax <- make_esem_model(
Expand Down

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