multilevel.cfa: Multilevel Confirmatory Factor Analysis

In misty: Miscellaneous Functions 'T. Yanagida'

Multilevel Confirmatory Factor Analysis

Description

This function conducts multilevel confirmatory factor analysis to investigate different types of constructs with distinct construct meanings at the individual and cluster level (Stapleton et al., 2016) by calling the cfa function in the R package lavaan. By default, the function specifies and estimates a measurement model for an individual and configural construct to provides a table with univariate sample statistics, model fit information, and parameter estimates. Additionally, variance-covariance coverage of the data, modification indices, residual correlation matrix, and relative Opdyke distribution percentile matrix can be requested by specifying the argument print.

Usage

multilevel.cfa(data, ..., cluster, model = NULL, rescov = NULL,
               model.w = NULL, model.b = NULL, rescov.w = NULL, rescov.b = NULL,
               const = c("within", "shared", "config", "shareconf"),
               fix.resid = NULL, ident = c("marker", "var", "effect"),
               ls.fit = FALSE, estimator = c("ML", "MLR"),
               test = c("none", "standard", "yuan.bentler", "yuan.bentler.mplus"),
               se = c("none", "standard", "robust.huber.white"),
               optim.method = c("nlminb", "em"), missing = c("listwise", "fiml"),
               print = c("all", "summary", "coverage", "descript", "fit", "est",
                         "modind", "resid", "opdyke"),
               mod.minval = 6.63, resid.minval = 0.1, opdyke.prec = 1,
               opdyke.minmax = c(0.40, 0.60), color = "b.red",
               style = c("regular", "bold", "italic"), digits = 3, p.digits = 3,
               as.na = NULL, write = NULL, append = TRUE, check = TRUE, output = TRUE)

Arguments

data	a data frame. If model, model.w, and model.b are NULL, multilevel confirmatory factor analysis based on a measurement model with one factor labeled wf at the Within level and one factor labeled bf at the Between level comprising all variables in the data frame is conducted. Note that the cluster variable specified in cluster is excluded from data when specifying the argument cluster using the variable name of the cluster variable. If model or mode.w and model.b is specified, the data frame needs to contain all variables used in the model argument(s).
...	an expression indicating the variable names in data. Note that the operators +, -, ~, :, ::, and ! can also be used to select variables, see 'Details' in the df.subset function.
cluster	either a character string indicating the variable name of the cluster variable in data or data, or a vector representing the nested grouping structure (i.e., group or cluster variable).
model	a character vector for specifying the same factor structure with one factor at the Within and Between Level, or a list of character vectors for specifying the same measurement model with more than one factor at the Within and Between Level, e.g.,model = c("x1", "x2", "x3", "x4") for specifying a measurement model with one factor labeled wf at the Within level and a measurement model with one factor labeled bf at the Between level each comprising four indicators, or model = list(factor1 = c("x1", "x2", "x3", "x4"), factor2 = c("x5", "x6", "x7", "x8")) for specifying a measurement model with two latent factors labeled wfactor1 and wfactor2 at the Within level and a measurement model with two latent factors labeled bfactor1 and bfactor2 at the Between level each comprising four indicators. Note that the name of each list element is used to label factors, where prefixes w and b are added the labels to distinguish factor labels at the Within and Between level, i.e., all list elements need to be named, otherwise factors are labeled with "wf1", "wf2", "wf3" for labels at the Within level and "bf1", "bf2", "bf3" for labels at the Between level and so on.
rescov	a character vector or a list of character vectors for specifying residual covariances at the Within level, e.g. rescov = c("x1", "x2") for specifying a residual covariance between indicators x1 and x2 at the Within level or rescov = list(c("x1", "x2"), c("x3", "x4")) for specifying residual covariances between indicators x1 and x2, and indicators x3 and x4 at the Within level. Note that residual covariances at the Between level can only be specified by using the arguments model.w, model.b, and model.b.
model.w	a character vector specifying a measurement model with one factor at the Within level, or a list of character vectors for specifying a measurement model with more than one factor at the Within level.
model.b	a character vector specifying a measurement model with one factor at the Between level, or a list of character vectors for specifying a measurement model with more than one factor at the Between level.
rescov.w	a character vector or a list of character vectors for specifying residual covariances at the Within level.
rescov.b	a character vector or a list of character vectors for specifying residual covariances at the Between level.
const	a character string indicating the type of construct(s), i.e., "within" for within-cluster constructs, "shared" for shared cluster-level constructs, "config" (default) for configural cluster constructs, and "shareconf" for simultaneous shared and configural cluster constructs.
fix.resid	a character vector for specifying residual variances to be fixed at 0 at the Between level, e.g., fix.resid = c("x1", "x3") to fix residual variances of indicators x1 and x2 at the Between level at 0. Note that it is also possible to specify fix.resid = "all" which fixes all residual variances at the Between level at 0 in line with the strong factorial measurement invariance assumption across cluster.
ident	a character string indicating the method used for identifying and scaling latent variables, i.e., "marker" for the marker variable method fixing the first factor loading of each latent variable to 1, "var" for the fixed variance method fixing the variance of each latent variable to 1, or "effect" for the effects-coding method using equality constraints so that the average of the factor loading for each latent variable equals 1.
ls.fit	logical: if TRUE (default) level-specific fit indices are computed when specifying a model using the arguments model.w and model.b given the model does not contain any cross-level equality constraints.
estimator	a character string indicating the estimator to be used: "ML" for maximum likelihood with conventional standard errors and "MLR" (default) for maximum likelihood with Huber-White robust standard errors and a scaled test statistic that is asymptotically equal to the Yuan-Bentler test statistic. Note that by default, full information maximum likelihood (FIML) method is used to deal with missing data when using "ML" (missing = "fiml"), whereas incomplete cases are removed listwise (i.e., missing = "listwise") when using "MLR".
test	a character string indicating the test statistics, i.e., "none" for no test statistic, "standard" for a conventional chi-square test, "yuan.bentler" for a Yuan-Bentler scaled test statistic, and "yuan.bentler.mplus" for a test statistic which is asymptotically equivalent to the Yuan-Bentler T2-star test statistic. Note that the default setting is depending on the argument estimator, i.e., test = "standard" when estimator = "ML" and test = "yuan.bentler.mplus" when estimator = "MLR".
se	a character string indicating the standard errors, i.e., "none" for no standard errors, "standard" for conventional standard error based on inverting the expected observed or first.order information matrix, and "robust.huber.white" for the 'MLR' (aka pseudo ML, Huber-White) approach. Note that the default setting is depending on the argument estimator, i.e., test = "standard" when estimator = "ML" and test = "robust.huber.white" when estimator = "MLR".
optim.method	a character string indicating the optimizer, i.e., "nlminb" (default) for the unconstrained and bounds-constrained quasi-Newton method optimizer and "em" for the Expectation Maximization (EM) algorithm.
missing	a character string indicating how to deal with missing data, i.e., "listwise" (default) for listwise deletion or "fiml" for full information maximum likelihood (FIML) method. Note that FIML method is only available when estimator = "ML", that it takes longer to estimate the model using FIML, and that FIML is prone to convergence issues which might be resolved by switching to listwise deletion.
print	a character string or character vector indicating which results to show on the console, i.e. "all" for all results, "summary" for a summary of the specification of the estimation method and missing data handling in lavaan, "coverage" for the variance-covariance coverage of the data, "descript" for descriptive statistics, "fit" for model fit, "est" for parameter estimates, "modind" for modification indices, "resid" for the residual correlation matrix and standardized residual means, and "opdyke" for the discrepancy between model-implied and observed correlation expressed in terms of the relative percentile of an Opdyke distribution (McNeish, 2025). By default, a summary of the specification, model fit, and parameter estimates are printed. By default, a summary of the specification, descriptive statistics, model fit, and parameter estimates are printed.
mod.minval	numeric value to filter modification indices and only show modifications with a modification index value equal or higher than this minimum value. By default, modification indices equal or higher 6.63 are printed. Note that a modification index value of 6.63 is equivalent to a significance level of \alpha = .01.
resid.minval	numeric value indicating the minimum absolute residual correlation coefficients and standardized means to highlight. By default, absolute residual correlation coefficients and standardized means equal or higher 0.1 are highlighted. Note that highlighting can be disabled by setting the minimum value to 1 or by setting the argument color to "default".
opdyke.prec	a numeric value indicating the precision of the probability density function calculations of the Opdyke distribution. The default is 1 which calculates the PDF for polar angles between (0, pi) in 0.01 increments. Specifying 10 calculates the PDF polar angles between (0, pi) in 0.001 increments, which takes considerably longer, especially if there are many correlation elements.
opdyke.minmax	a numeric vector with two elements indicating the minimum and maximum percentile of the Opdyke distribution that is considered to be acceptably close to the observed correlation represented by the Opdyke distribution median. Predicted correlation outside the range will be color highlighted in line with to the argument color.
color	a character string indicating the text color for highlighting absolute residual correlation coefficients and standardized means equal or higher resid.minval and predicted correlations outside the minimum and maximum percentile of the Opdyke distribution, i.e., i.e., "default" for the default text color without color coding and various text colors for highlighting "red", "b.red" (default), "green", "b.green", "blue", or "b.blue", see the help page of the chr.color function. Note that this option is not supported when using R Markdown and when writing the output into a text file (.txt).
style	a character vector indicating the font style for highlighting absolute residual correlation coefficients and standardized means equal or higher resid.minval, i.e., "regular" (default) for regular text, "bold" for bold text, and "italic" for italic text. Note that the font style "bold" and "italic" can be combined, i.e., style = c("bold", "italic") provides a bold and italic text. Note that the argument color needs to be specified to change the style of the text, e.g. color = "black" and style = "bold" to for bold text.
digits	an integer value indicating the number of decimal places to be used for displaying results. Note that loglikelihood, information criteria and chi-square test statistic is printed with digits minus 1 decimal places.
p.digits	an integer value indicating the number of decimal places to be used for displaying the p-value.
as.na	a numeric vector indicating user-defined missing values, i.e. these values are converted to NA before conducting the analysis. Note that as.na() function is only applied to data but not to cluster.
write	a character string naming a file for writing the output into either a text file with file extension ".txt" (e.g., "Output.txt") or Excel file with file extension ".xlsx" (e.g., "Output.xlsx"). If the file name does not contain any file extension, an Excel file will be written.
append	logical: if TRUE (default), output will be appended to an existing text file with extension .txt specified in write, if FALSE existing text file will be overwritten.
check	logical: if TRUE (default), argument specification, convergence and model identification is checked.
output	logical: if TRUE (default), output is shown.

Details

Stapleton et al. (2016) identified different types of constructs when data are collected from individuals nested within clusters characterized by different interpretations of construct meaning. At the individual level, the hypothesized construct is expected to be relevant to individual item responses, i.e., scores on the measure reflect individual variability. At the cluster level, there are two types of constructs measured using item responses from individuals: shared construct, a characteristic of the cluster itself and configural construct, which reflects a construct at the individual level. Marsh et al. (2012) introduced the terms climate construct and contextual construct, while Lüdtke et al., (2011) used the term reflective construct and formative construct to differentiate between shared and configural constructs.

Five types of confirmatory factor analysis (CFA) models were proposed for construct validation with nested data, depending on whether the construct of interest exists solely at the individual level or is also relevant at the cluster level (Stapleton et al., 2016).

Model 1: Individual Constructs, Single-Level Model

Model 1 is a single-level CFA model whose parameter estimates provide an aggregate of the relationship between item responses and the individual construct. A design-based estimation approach is used to adjust the standard error estimates, chi-square test statistic, and fit indices to account for the dependency of item responses among individuals within clusters. Note that this model is estimated using the item.cfa with specifying the cluster argument.

This model is appropriate when a positive ICC(1) is spurious, resulting from a selection process. For example, lactose intolerance is an entirely individual characteristic, unaffected by environment. However, item responses measuring lactose intolerance might exhibit a non-negligible ICC(1) due to the selection of individuals across different clusters, rather than reflecting a true cluster-level construct. That is, lactose intolerance is a completely individual measure, not able to be influenced by environmental effect.

The model is designed for application across a broad population that may or may not be nested within clusters in a single-level model. However, if the measure aims to compare the relative positions of individuals within a cluster, a within-cluster approach is more suitable.

Model 2: Within-Cluster Constructs

Model 2 is a two-level CFA model specified by const = "within" that includes a within-cluster construct representing an individual's standing within the cluster. The model does not assume the existence of a cluster-level construct but allows for cluster-level variability in each measure through a saturated variance-covariance model.

The model is designed for application within clusters to compare individuals and their relative positions within a specific cluster, while between-cluster constructs are not meaningful or not of interest.

Model 3: Shared Cluster-Level Constructs

Model 3 is a two-level CFA model specified by const = "shared" that includes a between-cluster construct representing a cluster-level characteristic that is measured using individuals within a cluster as the information source. The model does not assume the existence of an individual-level construct but allows for individual-level variability in each measure through a saturated variance-covariance model.

For a shared construct, individual item responses should be interchangeable, reflecting perfect interrater reliability and complete within-cluster agreement. However, within-cluster variation can exist for shared constructs, as these constructs stem from the experiences, attitudes, perceptions, values, or cognitions of individual cluster members. Given evidence of adequate agreement within clusters, the aggregate value of the measure can be assigned to the cluster, i.e., the shared perceptions of individuals in a cluster are interpreted as a proxy for the cluster-level characteristic (Jak et al., 2023). From this perspective, the greater the agreement within the cluster, the more reliably the shared construct is measured, although perfect agreement is not required. A reasonable step in the shared construct modeling process is to examine the ICC(2) values for each item measuring the shared construct. Klein et al. (2000) suggested that ICC(2) values of at least 0.7 indicate acceptable reliability of the measured shared construct, values between 0.5 and 0.7 indicate marginal reliability, and values below 0.5 are considered poor.

Note that the wording of questionnaire items plays a crucial role in the context of multilevel measurement. For example, the statement "The instructor presents materials in ways that keep it interesting." would likely to elicit responses reflecting the instructor's qualities, whereas the statement "I find the class meeting interest." would likely to reflect both a characteristic of the cluster and the individual's intrinsic interest in the class topic. Accordingly, an argument should be made regarding how the item wording targets cluster characteristics.

Model 4: Individual and Configural Constructs

Model 4 is a two-level CFA model specified by const = "config" that includes a within-cluster construct representing an individual's standing within the cluster and a between-cluster construct representing an aggregate of the measurements of individuals within the cluster. The configural cluster construct model requires cross-level measurement invariance of factor loadings to interpret the individual- and cluster-level common factors as reflecting the individual- and cluster-level components of the same construct (Jak et al., 2023).

For a configural construct, individual item responses are not interchangeable, and it is not expected that individuals within a cluster respond similarly to the items. Marsh et al. (2012) noted that if item responses have an ICC(1) of zero, there is little justification for continuing to examine the configural cluster-level construct. However, Stapleton et al. (2016) argued that it may still be of interest to investigate the variability in individual hypothetical latent scores across clusters, i.e., the dispersion of the construct may differ across clusters and represent an important cluster characteristic.

Model 5: Simultaneous Shared and Configural Constructs

Model 5 is a two-level CFA model specified by const = "shareconf" that includes a within-cluster construct representing an individual's standing within the cluster and two between-cluster constructs: a configural construct representing the individual-level construct, and a shared construct modeling additional covariation among cluster-average item responses, representing rater effects. The factor loadings of the configural construct are constrained to be equal across levels, i.e., metric cross-level measurement invariance.

For example, suppose that teachers have provided ratings of their students' motivation using multiple items for each child. It is possible that some teachers rate more positively compared to others, resulting in two sources of covariation at the cluster level: variation due to the fact that students in some classes are truly more motivated on average than those in other classes, and variation due to rater effects, because some teachers tend to rate their students more positively or more negatively on average.

Note that what may appear to be an additional shared construct could instead reflect a spurious contextual effect. Specifically, when constraining factor loadings across levels results in a relatively poor fit compared to a model with unconstrained loadings in a configural model, this suggests that the apparent additional shared construct is actually due to measurement noninvariance at the within-cluster level.

Value

Returns an object of class misty.object, which is a list with following entries:

call	function call
type	type of analysis
data	data frame used for the current analysis
args	specification of function arguments
model	specified model
model.fit	fitted lavaan object (mod.fit)
check	results of the convergence and model identification check
result	list with result tables, i.e., summary for the summary of the specification of the estimation method and missing data handling in lavaan, coverage for the variance-covariance coverage of the data, descript for descriptive statistics, fit for model fit, est for a list with parameter estimates for Within and Between, score fir a list with modification indices for parameter constraints for Within and Between, resid for a list with residual correlation matrices and standardized residual means for the Within and Between level, and opdyke for the relative Opdyke distribution percentile matrix for the Within and Between level.

Note

The function uses the functions cfa, lavInspect, lavTech, modindices, parameterEstimates, and standardizedsolution provided in the R package lavaan by Yves Rosseel (2012). The relative Opdyke distribution percentile matrix is based on the functions opdyke and opdyke.percentiles provided in the R package opddyke by Dan McNeish (2026).

Author(s)

Takuya Yanagida [e-mail]

References

Jak, S., Jorgensen, T. D., ten Hove, D., & Nevicka, B. (2023). Modeling cluster-level constructs measured by individual responses: Configuring a shared approach. Advances in Methods and Practices in Psychological Science, 6(3), Article 25152459231182319. https://doi.org/10.1177/25152459231182319

Klein, K. J., & Kozlowski, S. W. (2000). Multilevel theory, research, and methods in organizations: Foundations, extensions, and new directions. Jossey-Bass.

Lüdtke, O., Marsh, H. W., Robitzsch, A., & Trautwein, U. (2011). A 2x2 taxonomy of multilevel latent contextual models: Accuracy-bias trade-offs in full and partial error correction models. Psychological Methods, 16, 444-467. https://doi.org/10.1037/a0024376

Marsh, H. W., Ludtke, O., Nagengast, B., Trautwein, U., Morin, A. J. S., Abduljabbar, A. S., & Koller, O. (2012). Classroom climate and contextual effects: Conceptual and methodological issues in the evaluation of group-level effects. Educational Psychologist, 47, 106-124. https://doi.org/10.1080/00461520.2012.670488

McNeish, D. (2025). Less Heuristic Approximate Local Fit Evaluation in Structural Equation Models. Structural Equation Modeling: A Multidisciplinary Journal, 32(4), 590-605. https://doi.org/10.1080/10705511.2025.2473342

McNeish D (2026). opdyke: Opdyke Percentiles for Approximate Local Fit in Structural Equation Models. R package version 1.0.0. Retrieved from https://github.com/dmcneish18/opdyke

Rosseel, Y. (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48, 1-36. https://doi.org/10.18637/jss.v048.i02

Stapleton, L. M., Yang, J. S., & Hancock, G. R. (2016). Construct meaning in multilevel settings. Journal of Educational and Behavioral Statistics, 41, 481-520. http://dx.doi.org/10.3102/1076998616646200

See Also

item.cfa, multilevel.fit, multilevel.invar, multilevel.omega, multilevel.cor, multilevel.descript

Examples

## Not run: 

# Load data set "Demo.twolevel" in the lavaan package
data("Demo.twolevel", package = "lavaan")

#————————————————————————————————————————————————————————————————————————————
# Model Specification Using 'data' for a One-Factor Model
#
# Same factor structure with one factor at the Within and Between Level

#——————————————————————————————————————
## Cluster Variable Specification

# Example 1a: Specification using the argument '...'
multilevel.cfa(Demo.twolevel, y1:y4, cluster = "cluster")

# Example 1b: Alternative specification with cluster variable 'cluster' in 'data'
multilevel.cfa(Demo.twolevel[, c("y1", "y2", "y3", "y4", "cluster")], cluster = "cluster")

# Example 1c: Alternative specification with cluster variable 'cluster' not in 'data'
multilevel.cfa(Demo.twolevel[, c("y1", "y2", "y3", "y4")], cluster = Demo.twolevel$cluster)

#——————————————————————————————————————
## Type of Construct

# Example 2a: Within-cluster constructs
multilevel.cfa(Demo.twolevel, y1:y4, cluster = "cluster", const = "within")

# Example 2b: Shared cluster-level construct
multilevel.cfa(Demo.twolevel, y1:y4, cluster = "cluster", const = "shared")

# Example 2c: Individual and configural cluster construct (default)
multilevel.cfa(Demo.twolevel, y1:y4, cluster = "cluster", const = "config")

# Example 2d: Simultaneous shared and configural cluster construct
multilevel.cfa(Demo.twolevel, y1:y4, cluster = "cluster", const = "shareconf")

#——————————————————————————————————————
## Residual Covariances at the Within Level

# Example 3a: Residual covariance between 'y1' and 'y3'
multilevel.cfa(Demo.twolevel, y1:y4, cluster = "cluster", rescov = c("y1", "y3"))

# Example 3b: Residual covariance between 'y1' and 'y3', and 'y2' and 'y4'
multilevel.cfa(Demo.twolevel, y1:y4, cluster = "cluster",
               rescov = list(c("y1", "y3"), c("y2", "y4")))

#——————————————————————————————————————
## Residual Variances at the Between Level fixed at 0

# Example 4a: All residual variances fixed at 0
# i.e., strong factorial invariance across clusters
multilevel.cfa(Demo.twolevel, y1:y4, cluster = "cluster", fix.resid = "all")

# Example 4b: Residual variances of 'y1', 'y2', and 'y4' fixed at 0
# i.e., partial strong factorial invariance across clusters
multilevel.cfa(Demo.twolevel, y1:y4, cluster = "cluster", fix.resid = c("y1", "y2"))

#——————————————————————————————————————
## Arguments 'print', 'mod.minval', 'resid.minval', and 'opdyke.minmax'

# Example 5a: Request all results
item.cfa(Demo.twolevel, y1:y6, cluster = "cluster", print = "all")

# Example 5b: Request modification indices with value equal or higher than 2
item.cfa(Demo.twolevel, y1:y6, cluster = "cluster", print = "modind", mod.minval = 2)

# Example 5c: Highlight absolute residual correlation equal or higher than 0.05
item.cfa(Demo.twolevel, y1:y6, cluster = "cluster", print = "resid", resid.minval = 0.05,
         color = "b.blue")

# Example 5d: Highlight Opdyke distribution percentiles outside 0.45 and 0.55
item.cfa(Demo.twolevel, y1:y6, cluster = "cluster", print = "opdyke", opdyke.minmax = c(0.45, 0.55),
         color = "black", style = "bold")

#————————————————————————————————————————————————————————————————————————————
# Model Specification using 'model' for One or Multiple-Factor Model
#
# Same factor structure at the Within and Between Level

# Example 6a: One-factor model
multilevel.cfa(Demo.twolevel, cluster = "cluster", model = c("y1", "y2", "y3", "y4"))

# Example 6b: Two-factor model
multilevel.cfa(Demo.twolevel, cluster = "cluster",
               model = list(c("y1", "y2", "y3"), c("y4", "y5", "y6")))

# Example 6c: Two-factor model with user-specified labels for the factors
multilevel.cfa(Demo.twolevel, cluster = "cluster",
               model = list(factor1 = c("y1", "y2", "y3"), factor2 = c("y4", "y5", "y6")))

#——————————————————————————————————————
# Type of Construct

# Example 7a: Within-cluster constructs
multilevel.cfa(Demo.twolevel, cluster = "cluster", const = "within",
               model = list(c("y1", "y2", "y3"), c("y4", "y5", "y6")))

# Example 7b: Shared cluster-level construct
multilevel.cfa(Demo.twolevel, cluster = "cluster", const = "shared",
               model = list(c("y1", "y2", "y3"), c("y4", "y5", "y6")))

# Example 7c: Individual and configural cluster construct (default)
multilevel.cfa(Demo.twolevel, cluster = "cluster", const = "config",
               model = list(c("y1", "y2", "y3"), c("y4", "y5", "y6")))

# Example 7d: Simultaneous shared and configural cluster construct
multilevel.cfa(Demo.twolevel, cluster = "cluster", const = "shareconf",
               model = list(c("y1", "y2", "y3"), c("y4", "y5", "y6")))

#——————————————————————————————————————
## Residual Covariances at the Within Level

# Example 8a: Residual covariance between 'y1' and 'y4' at the Within level
multilevel.cfa(Demo.twolevel, cluster = "cluster",
               model = list(c("y1", "y2", "y3"), c("y4", "y5", "y6")),
               rescov = c("y1", "y4"))

# Example 8b: Fix all residual variances at 0
# i.e., strong factorial invariance across clusters
multilevel.cfa(Demo.twolevel, cluster = "cluster",
               model = list(c("y1", "y2", "y3"), c("y4", "y5", "y6")),
               fix.resid = "all")

#————————————————————————————————————————————————————————————————————————————
# Model Specification Using 'model.w' and 'model.b' for One or Multiple_Factor Model
#
# Different factor structure at the Within and Between Level

# Example 9a: Simultaneous and level-specific fit indices
multilevel.cfa(Demo.twolevel, cluster = "cluster",
               model.w = c("y1", "y2", "y3", "y4", "y5", "y6"),
               model.b = c("y1", "y2", "y3", "y4", "y5", "y6"), ls.fit = TRUE)

# Example 9b: Two-factor model at the Within level and one-factor model at the Between level
multilevel.cfa(Demo.twolevel, cluster = "cluster",
               model.w = list(c("y1", "y2", "y3"), c("y4", "y5", "y6")),
               model.b = c("y1", "y2", "y3", "y4", "y5", "y6"))

# Example 9c: Residual covariance between 'y1' and 'y4' at the Within level
# Residual covariance between 'y5' and 'y6' at the Between level
multilevel.cfa(Demo.twolevel, cluster = "cluster",
               model.w = list(c("y1", "y2", "y3"), c("y4", "y5", "y6")),
               model.b = c("y1", "y2", "y3", "y4", "y5", "y6"),
               rescov.w = c("y1", "y4"),
               rescov.b = c("y5", "y6"))

#————————————————————————————————————————————————————————————————————————————
# lavaan Model and Summary of the Estimated Model

# Example 10
mod <- multilevel.cfa(Demo.twolevel, y1:y4, cluster = "cluster", output = FALSE)

# lavaan model syntax
cat(mod$model)

# Fitted lavaan object
lavaan::summary(mod$model.fit, standardized = TRUE, fit.measures = TRUE)

#————————————————————————————————————————————————————————————————————————————
# Write Results

# Example 11a: Write results into a text file
multilevel.cfa(Demo.twolevel, y1:y4, cluster = "cluster", print = "all",
                      write = "Multilevel_CFA.txt", output = FALSE)

# Example 11b: Write results into an Excel file
multilevel.cfa(Demo.twolevel, y1:y4, cluster = "cluster", print = "all",
               write = "Multilevel_CFA.xlsx", output = FALSE)

## End(Not run)

misty documentation built on Aug. 2, 2026, 9:06 a.m.