simulate_factors {latentFactoR}

Simulates Latent Factor Data

Description

Simulates data from a latent factor model based on many manipulable parameters. Parameters do not have default values and must each be set. See examples to get started

Usage

simulate_factors(
  factors,
  variables,
  variables_range = NULL,
  loadings,
  loadings_range = NULL,
  cross_loadings,
  cross_loadings_range = NULL,
  correlations,
  correlations_range = NULL,
  sample_size,
  variable_categories = Inf,
  categorical_limit = 7,
  skew = 0,
  skew_range = NULL
)

Arguments

factors

Numeric (length = 1). Number of factors

variables

Numeric (length = 1 or factors). Number of variables per factor. Can be a single value or as many values as there are factors. Minimum three variables per factor

variables_range

Numeric (length = 2). Range of variables to randomly select from a random uniform distribution. Minimum three variables per factor

loadings

Numeric or matrix (length = 1, factors, total number of variables (factors x variables), or factors x total number of variables. Loadings drawn from a random uniform distribution using +/- 0.10 of value input. Can be a single value or as many values as there are factors (corresponding to the factors). Can also be a loading matrix. Columns must match factors and rows must match total variables (factors x variables) General effect sizes range from small (0.40), moderate (0.55), to large (0.70)

loadings_range

Numeric (length = 2). Range of loadings to randomly select from a random uniform distribution. General effect sizes range from small (0.40), moderate (0.55), to large (0.70)

cross_loadings

Numeric or matrix(length = 1, factors, or factors x total number of variables. Cross-loadings drawn from a random normal distribution with a mean of 0 and standard deviation of value input. Can be a single value or as many values as there are factors (corresponding to the factors). Can also be a loading matrix. Columns must match factors and rows must match total variables (factors x variables)

cross_loadings_range

Numeric (length = 2). Range of cross-loadings to randomly select from a random uniform distribution

correlations

Numeric (length = 1 or factors x factors). Can be a single value that will be used for all correlations between factors. Can also be a square matrix (factors x factors). General effect sizes range from orthogonal (0.00), small (0.30), moderate (0.50), to large (0.70)

correlations_range

Numeric (length = 2). Range of correlations to randomly select from a random uniform distribution. General effect sizes range from orthogonal (0.00), small (0.30), moderate (0.50), to large (0.70)

sample_size

Numeric (length = 1). Number of cases to generate from a random multivariate normal distribution using rmvnorm

variable_categories

Numeric (length = 1 or total variables (factors x variables)). Number of categories for each variable. Inf is used for continuous variables; otherwise, values reflect number of categories

categorical_limit

Numeric (length = 1). Values greater than input value are considered continuous. Defaults to 7 meaning that 8 or more categories are considered continuous (i.e., variables are not categorized from continuous to categorical)

skew

Numeric (length = 1 or categorical variables). Skew to be included in categorical variables. It is randomly sampled from provided values. Can be a single value or as many values as there are (total) variables. Current skew implementation is between -2 and 2 in increments of 0.05. Skews that are not in this sequence will be converted to their nearest value in the sequence. Not recommended to use with variables_range. Future versions will incorporate finer skews

skew_range

Numeric (length = 2). Randomly selects skews within in the range. Somewhat redundant with skew but more flexible. Compatible with variables_range

Value

Returns a list containing:

data

Simulated data from the specified factor model

population_correlation

Population correlation matrix

parameters

A list containing the parameters used to generate the data:

• factors — Number of factors

• variables — Variables on each factor

• loadings — Loading matrix

• factor_correlations — Correlations between factors

• categories — Categories for each variable

• skew — Skew for each variable

Author(s)

Maria Dolores Nieto Canaveras <[e-mail]>, Alexander P. Christensen <[e-mail]>, Hudson Golino <[e-mail]>, Luis Eduardo Garrido <[e-mail]>

References

Garrido, L. E., Abad, F. J., & Ponsoda, V. (2011).
Performance of Velicer’s minimum average partial factor retention method with categorical variables.
Educational and Psychological Measurement, 71(3), 551-570.

Golino, H., Shi, D., Christensen, A. P., Garrido, L. E., Nieto, M. D., Sadana, R., ... & Martinez-Molina, A. (2020). Investigating the performance of exploratory graph analysis and traditional techniques to identify the number of latent factors: A simulation and tutorial. Psychological Methods, 25(3), 292-320.

Examples

# Generate factor data
two_factor <- simulate_factors(
  factors = 2, # factors = 2
  variables = 6, # variables per factor = 6
  loadings = 0.55, # loadings between = 0.45 to 0.65
  cross_loadings = 0.05, # cross-loadings N(0, 0.05)
  correlations = 0.30, # correlation between factors = 0.30
  sample_size = 1000 # number of cases = 1000
)

# Randomly vary loadings
two_factor_loadings <- simulate_factors(
  factors = 2, # factors = 2
  variables = 6, # variables per factor = 6
  loadings_range = c(0.30, 0.80), # loadings between = 0.30 to 0.80
  cross_loadings = 0.05, # cross-loadings N(0, 0.05)
  correlations = 0.30, # correlation between factors = 0.30
  sample_size = 1000 # number of cases = 1000
)

# Generate dichotomous data
two_factor_dichotomous <- simulate_factors(
  factors = 2, # factors = 2
  variables = 6, # variables per factor = 6
  loadings = 0.55, # loadings between = 0.45 to 0.65
  cross_loadings = 0.05, # cross-loadings N(0, 0.05)
  correlations = 0.30, # correlation between factors = 0.30
  sample_size = 1000, # number of cases = 1000
  variable_categories = 2 # dichotomous data
)

# Generate dichotomous data with skew
two_factor_dichotomous_skew <- simulate_factors(
  factors = 2, # factors = 2
  variables = 6, # variables per factor = 6
  loadings = 0.55, # loadings between = 0.45 to 0.65
  cross_loadings = 0.05, # cross-loadings N(0, 0.05)
  correlations = 0.30, # correlation between factors = 0.30
  sample_size = 1000, # number of cases = 1000
  variable_categories = 2, # dichotomous data
  skew = 1 # all variables with have a skew of 1
)

# Generate dichotomous data with variable skew
two_factor_dichotomous_skew <- simulate_factors(
  factors = 2, # factors = 2
  variables = 6, # variables per factor = 6
  loadings = 0.55, # loadings between = 0.45 to 0.65
  cross_loadings = 0.05, # cross-loadings N(0, 0.05)
  correlations = 0.30, # correlation between factors = 0.30
  sample_size = 1000, # number of cases = 1000
  variable_categories = 2, # dichotomous data
  skew_range = c(-2, 2) # skew = -2 to 2 (increments of 0.05)
)