Package 'latentFactoR' reference manual

Title:	Data Simulation Based on Latent Factors
Description:	Generates data based on latent factor models. Data can be continuous, polytomous, dichotomous, or mixed. Skews, cross-loadings, wording effects, population errors, and local dependencies can be added. All parameters can be manipulated. Data categorization is based on Garrido, Abad, and Ponsoda (2011) <doi:10.1177/0013164410389489>.
Authors:	Alexander Christensen [aut, cre] , Luis Eduardo Garrido [aut] , Maria Dolores Nieto Canaveras [aut], Hudson Golino [aut] , Marcos Jimenez [aut], Francisco Abad [ctb], Eduardo Garcia-Garzon [ctb], Vithor Franco [aut]
Maintainer:	Alexander Christensen <[email protected]>
License:	GPL (>= 3.0)
Version:	0.0.7
Built:	2024-10-28 05:39:31 UTC
Source:	https://github.com/alexchristensen/latentfactor

latentFactoR–package

Description

Generates data based on latent factor models. Data can be continuous, polytomous, dichotomous, or mixed. Skew, cross-loadings, and population error can be added. All parameters can be manipulated. Data categorization is based on Garrido, Abad, and Ponsoda (2011).

Author(s)

Alexander P. Christensen <[email protected]>, Maria Dolores Nieto Canaveras <[email protected]>, Hudson Golino <[email protected]>, Luis Eduardo Garrido <[email protected]>

References

Christensen, A. P., Garrido, L. E., & Golino, H. (2022).
Unique variable analysis: A network psychometrics method to detect local dependence.
PsyArXiv

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.

Adds (Substantial) Cross-loadings to `simulate_factors` Data

Description

Intended to add substantial cross-loadings to simulated data from simulate_factors. See examples to get started

Usage

add_cross_loadings(
  lf_object,
  proportion_cross_loadings,
  proportion_cross_loadings_range = NULL,
  magnitude_cross_loadings,
  magnitude_cross_loadings_range = NULL,
  leave_cross_loadings = FALSE
)
add_cross_loadings(
  lf_object,
  proportion_cross_loadings,
  proportion_cross_loadings_range = NULL,
  magnitude_cross_loadings,
  magnitude_cross_loadings_range = NULL,
  leave_cross_loadings = FALSE
)

Arguments

`lf_object`	Data object from `simulate_factors`
`proportion_cross_loadings`	Numeric (length = 1 or `factors`). Proportion of variables that should be cross-loaded randomly onto one other factor. Accepts number of variables to cross-load onto one other factor as well
`proportion_cross_loadings_range`	Numeric (length = 2). Range of proportion of variables that should be cross-loaded randomly onto one other factor. Accepts number of variables to cross-load onto one other factor as well
`magnitude_cross_loadings`	Numeric (length = 1, `factors`, or total number of variables to cross-load across all factors). The magnitude or size of the cross-loadings. Must range between `-1` and `1`.
`magnitude_cross_loadings_range`	Numeric (length = 2). The range of the magnitude or size of the cross-loadings. Defaults to `NULL`
`leave_cross_loadings`	Boolean. Should cross-loadings be kept? Defaults to `FALSE`. Convergence problems can arise if cross-loadings are kept, so setting them to zero is the default. Only set to `TRUE` with careful consideration of the structure. Make sure to perform additional checks that the data are adequate

Value

Returns a list containing the same parameters as the original lf_object but with updated data, population_correlation, and parameters (specifically, loadings matrix). Also returns original lf_object in original_results

Author(s)

Alexander P. Christensen <[email protected]>, Hudson Golino <[email protected]>, Luis Eduardo Garrido <[email protected]>

References

Christensen, A. P., Garrido, L. E., & Golino, H. (2022). Unique variable analysis: A network psychometrics method to detect local dependence. PsyArXiv

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
)

# Add substantial cross-loadings
two_factor_CL <- add_cross_loadings(
  lf_object = two_factor,
  proportion_cross_loadings = 0.25,
  magnitude_cross_loadings = 0.35
)

# Randomly vary proportions
two_factor_CL <- add_cross_loadings(
  lf_object = two_factor,
  proportion_cross_loadings_range = c(0, 0.25),
  magnitude_cross_loadings = 0.35
)

# Randomly vary magnitudes
two_factor_CL <- add_cross_loadings(
  lf_object = two_factor,
  proportion_cross_loadings = 0.25,
  magnitude_cross_loadings_range = c(0.35, 0.45)
)

# Set number of cross-loadings per factor (rather than proportion)
two_factor_CL <- add_cross_loadings(
  lf_object = two_factor,
  proportion_cross_loadings = 2,
  magnitude_cross_loadings = 0.35
)

# 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
)

# Add substantial cross-loadings
two_factor_CL <- add_cross_loadings(
  lf_object = two_factor,
  proportion_cross_loadings = 0.25,
  magnitude_cross_loadings = 0.35
)

# Randomly vary proportions
two_factor_CL <- add_cross_loadings(
  lf_object = two_factor,
  proportion_cross_loadings_range = c(0, 0.25),
  magnitude_cross_loadings = 0.35
)

# Randomly vary magnitudes
two_factor_CL <- add_cross_loadings(
  lf_object = two_factor,
  proportion_cross_loadings = 0.25,
  magnitude_cross_loadings_range = c(0.35, 0.45)
)

# Set number of cross-loadings per factor (rather than proportion)
two_factor_CL <- add_cross_loadings(
  lf_object = two_factor,
  proportion_cross_loadings = 2,
  magnitude_cross_loadings = 0.35
)

Adds Local Dependence to `simulate_factors` Data

Description

Adds local dependence to simulated data from simulate_factors. See examples to get started

Usage

add_local_dependence(
  lf_object,
  method = c("correlate_residuals", "minor_factors", "threshold_shifts"),
  proportion_LD,
  proportion_LD_range = NULL,
  add_residuals = NULL,
  add_residuals_range = NULL,
  allow_multiple = FALSE
)
add_local_dependence(
  lf_object,
  method = c("correlate_residuals", "minor_factors", "threshold_shifts"),
  proportion_LD,
  proportion_LD_range = NULL,
  add_residuals = NULL,
  add_residuals_range = NULL,
  allow_multiple = FALSE
)

Arguments

`lf_object`	Data object from `simulate_factors`
`method`	Character (length = 1). Method to generate local dependence between variables. Only `"correlate_residuals"` at the moment. Future developments will include minor factor and threshold-shift methods. Description of methods: `"correlate_residuals"` — Adds residuals directly to the population correlation matrix prior to data generation (uses population correlation matrix from `simulate_factors`) `"minor_factors"` — Coming soon... `"threshold_shifts"` — Coming soon...
`proportion_LD`	Numeric (length = 1 or `factors`). Proportion of variables that should be locally dependent across all or each factor. Accepts number of locally dependent values as well
`proportion_LD_range`	Numeric (length = 2). Range of proportion of variables that are randomly selected from a random uniform distribution. Accepts number of locally dependent values as well. Defaults to `NULL`
`add_residuals`	Numeric (length = 1, `factors`, or total number of locally dependent variables). Amount of residual to add to the population correlation matrix between two variables. Only used when `method = "correlated_residuals"`. Magnitudes are drawn from a random uniform distribution using +/- 0.05 of value input. Can also be specified directly (same length as total number of locally dependent variables). General effect sizes range from small (0.20), moderate (0.30), to large (0.40)
`add_residuals_range`	Numeric (length = 2). Range of the residuals to add to the correlation matrix are randomly selected from a random uniform distribution. Defaults to `NULL`
`allow_multiple`	Boolean. Whether a variable should be allowed to be locally dependent with more than one other variable. Defaults to `FALSE`. Set to `TRUE` for more complex locally dependence patterns

Value

Returns a list containing:

`data`	Simulated data from the specified factor model
`population_correlation`	Population correlation matrix with local dependence added
`original_correlation`	Original population correlation matrix before local dependence was added
`correlated_residuals`	A data frame with the first two columns specifying the variables that are locally dependent and the third column specifying the magnitude of the added residual for each locally dependent pair
`original_results`	Original `lf_object` input into function

Author(s)

Alexander P. Christensen <[email protected]>, Hudson Golino <[email protected]>, Luis Eduardo Garrido <[email protected]>

References

Christensen, A. P., Garrido, L. E., & Golino, H. (2023). Unique variable analysis: A network psychometrics method to detect local dependence. Multivariate Behavioral Research, 1–18.

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
)

# Add local dependence
two_factor_LD <- add_local_dependence(
  lf_object = two_factor,
  proportion_LD = 0.25,
  add_residuals = 0.20,
  allow_multiple = FALSE
)

# Randomly vary proportions
two_factor_LD <- add_local_dependence(
  lf_object = two_factor,
  proportion_LD_range = c(0.10, 0.50),
  add_residuals = 0.20,
  allow_multiple = FALSE
)

# Randomly vary residuals
two_factor_LD <- add_local_dependence(
  lf_object = two_factor,
  proportion_LD = 0.25,
  add_residuals_range = c(0.20, 0.40),
  allow_multiple = FALSE
)

# Randomly vary proportions, residuals, and allow multiple
two_factor_LD <- add_local_dependence(
  lf_object = two_factor,
  proportion_LD_range = c(0.10, 0.50),
  add_residuals_range = c(0.20, 0.40),
  allow_multiple = TRUE
)

# 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
)

# Add local dependence
two_factor_LD <- add_local_dependence(
  lf_object = two_factor,
  proportion_LD = 0.25,
  add_residuals = 0.20,
  allow_multiple = FALSE
)

# Randomly vary proportions
two_factor_LD <- add_local_dependence(
  lf_object = two_factor,
  proportion_LD_range = c(0.10, 0.50),
  add_residuals = 0.20,
  allow_multiple = FALSE
)

# Randomly vary residuals
two_factor_LD <- add_local_dependence(
  lf_object = two_factor,
  proportion_LD = 0.25,
  add_residuals_range = c(0.20, 0.40),
  allow_multiple = FALSE
)

# Randomly vary proportions, residuals, and allow multiple
two_factor_LD <- add_local_dependence(
  lf_object = two_factor,
  proportion_LD_range = c(0.10, 0.50),
  add_residuals_range = c(0.20, 0.40),
  allow_multiple = TRUE
)

Adds Methods Factors to `simulate_factors` Data

Description

Adds methods factors to simulated data from simulate_factors. See examples to get started

Usage

add_method_factors(
  lf_object,
  proportion_negative = 0.5,
  proportion_negative_range = NULL,
  methods_factors,
  methods_loadings,
  methods_loadings_range = 0,
  methods_correlations,
  methods_correlations_range = NULL
)
add_method_factors(
  lf_object,
  proportion_negative = 0.5,
  proportion_negative_range = NULL,
  methods_factors,
  methods_loadings,
  methods_loadings_range = 0,
  methods_correlations,
  methods_correlations_range = NULL
)

Arguments

`lf_object`	Data object from `simulate_factors`. Data must be categorical. If data are not categorical, then there function with throw an error
`proportion_negative`	Numeric (length = 1 or `factors`). Proportion of variables that should have negative (or flipped) dominant loadings across all or each factor. Accepts number of variables as well. The first variables on each factor, up to the corresponding proportion, will be flipped. Set to `0` to not have any loadings flipped. Defaults to `0.50`
`proportion_negative_range`	Numeric (length = 2). Range of proportion of variables that are randomly selected from a uniform distribution. Accepts number of number of variables as well. Defaults to `NULL`
`methods_factors`	Numeric
`methods_loadings`	Numeric
`methods_loadings_range`	Numeric
`methods_correlations`	Numeric
`methods_correlations_range`	Numeric

Value

Returns a list containing:

`data`	Biased data simulated data from the specified factor model
`unbiased_data`	The corresponding unbiased data prior to replacing values to generate the (biased) `data`
`parameters`	Bias-adjusted parameters of the `lf_object` input into function
`original_results`	Original `lf_object` input into function

Author(s)

Alexander P. Christensen <[email protected]>, Luis Eduardo Garrido <[email protected]>

References

Garcia-Pardina, A., Abad, F. J., Christensen, A. P., Golino, H., & Garrido, L. E. (2024). Dimensionality assessment in the presence of wording effects: A network psychometric and factorial approach. Behavior Research Methods.

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
  variable_categories = 5 # 5-point Likert scale
)

# Add methods factors
two_factor_methods_effect <- add_method_factors(
  lf_object = two_factor,
  proportion_negative = 0.50,
  methods_loadings = 0.20,
  methods_loadings_range = 0.10
)

# 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
  variable_categories = 5 # 5-point Likert scale
)

# Add methods factors
two_factor_methods_effect <- add_method_factors(
  lf_object = two_factor,
  proportion_negative = 0.50,
  methods_loadings = 0.20,
  methods_loadings_range = 0.10
)

Adds Population Error to `simulate_factors` Data

Description

Adds population error to simulated data from simulate_factors. See examples to get started

Usage

add_population_error(
  lf_object,
  cfa_method = c("minres", "ml"),
  fit = c("cfi", "rmsea", "rmsr", "raw"),
  misfit = c("close", "acceptable"),
  error_method = c("cudeck", "yuan"),
  tolerance = 0.01,
  convergence_iterations = 10,
  leave_cross_loadings = FALSE
)
add_population_error(
  lf_object,
  cfa_method = c("minres", "ml"),
  fit = c("cfi", "rmsea", "rmsr", "raw"),
  misfit = c("close", "acceptable"),
  error_method = c("cudeck", "yuan"),
  tolerance = 0.01,
  convergence_iterations = 10,
  leave_cross_loadings = FALSE
)

Arguments

`lf_object`	Data object from `simulate_factors`
`cfa_method`	Character (length = 1). Method to generate population error. Defaults to `"ml"`. Available options: `"minres"` — Minimum residual `"ml"` — Maximum likelihood
`fit`	Character (length = 1). Fit index to control population error. Defaults to `"rmsr"`. Available options: `"cfi"` — Comparative fit index `"rmsea"` — Root mean square error of approximation `"rmsr"` — Root mean square residuals `"raw"` — Direct application of error
`misfit`	Character or numeric (length = 1). Magnitude of error to add. Defaults to `"close"`. Available options: `"close"` — Slight deviations from original population correlation matrix `"acceptable"` — Moderate deviations from original population correlation matrix While numbers can be used, they are not recommended. They can be used to specify misfit but the level of misfit will vary depending on the factor structure
`error_method`	Character (length = 1). Method to control population error. Defaults to `"cudeck"`. Description of methods: `"cudeck"` — Description coming soon... see Cudeck & Browne, 1992 for more details `"yuan"` — Description coming soon...
`tolerance`	Numeric (length = 1). Tolerance of SRMR difference between population error correlation matrix and the original population correlation matrix. Ensures that appropriate population error was added. Similarly, verifies that the MAE of the loadings are not greater than the specified amount, ensuring proper convergence. Defaults to `0.01`
`convergence_iterations`	Numeric (length = 1). Number of iterations to reach parameter convergence within the specified 'tolerance'. Defaults to `10`
`leave_cross_loadings`	Boolean. Should cross-loadings be kept? Defaults to `FALSE`. Convergence problems can arise if cross-loadings are kept, so setting them to zero is the default. Only set to `TRUE` with careful consideration of the structure. Make sure to perform additional checks that the data are adequate

Value

Returns a list containing:

`data`	Simulated data from the specified factor model
`population_correlation`	Population correlation matrix with local dependence added
`population_error`	A list containing the parameters used to generate population error: `error_correlation` — Correlation matrix with population error added (same as `population_correlation`) `fit` — Fit measure used to control population error `delta` — Minimum of the objective function corresponding to the misfit value `misfit` — Specified misfit value `loadings` — Estiamted CFA loadings after error has been added
`original_results`	Original `lf_object` input into function

Author(s)

bifactor authors
Marcos Jimenez, Francisco J. Abad, Eduardo Garcia-Garzon, Vithor R. Franco, Luis Eduardo Garrido <[email protected]>

latentFactoR authors
Alexander P. Christensen <[email protected]>, Hudson Golino <[email protected]>, Luis Eduardo Garrido <[email protected]>, Marcos Jimenez, Francisco J. Abad, Eduardo Garcia-Garzon, Vithor R. Franco

References

Cudeck, R., & Browne, M.W. (1992). Constructing a covariance matrix that yields a specified minimizer and a specified minimum discrepancy function value. Psychometrika, 57, 357–369.

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
)

# Add small population error using Cudeck method
two_factor_Cudeck <- add_population_error(
  lf_object = two_factor,
  cfa_method = "minres",
  fit = "rmsr", misfit = "close",
  error_method = "cudeck"
)

# Add small population error using Yuan method
two_factor_Yuan <- add_population_error(
  lf_object = two_factor,
  cfa_method = "minres",
  fit = "rmsr", misfit = "close",
  error_method = "yuan"
)

# 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
)

# Add small population error using Cudeck method
two_factor_Cudeck <- add_population_error(
  lf_object = two_factor,
  cfa_method = "minres",
  fit = "rmsr", misfit = "close",
  error_method = "cudeck"
)

# Add small population error using Yuan method
two_factor_Yuan <- add_population_error(
  lf_object = two_factor,
  cfa_method = "minres",
  fit = "rmsr", misfit = "close",
  error_method = "yuan"
)

Adds Wording Effects to `simulate_factors` Data

Description

Adds wording effects to simulated data from simulate_factors. See examples to get started

Usage

add_wording_effects(
  lf_object,
  method = c("acquiescence", "difficulty", "random_careless", "straight_line", "mixed"),
  proportion_negative = 0.5,
  proportion_negative_range = NULL,
  proportion_biased_cases = 0.1,
  proportion_biased_variables = 1,
  proportion_biased_variables_range = NULL,
  proportion_biased_person = 1,
  proportion_biased_person_range = NULL
)
add_wording_effects(
  lf_object,
  method = c("acquiescence", "difficulty", "random_careless", "straight_line", "mixed"),
  proportion_negative = 0.5,
  proportion_negative_range = NULL,
  proportion_biased_cases = 0.1,
  proportion_biased_variables = 1,
  proportion_biased_variables_range = NULL,
  proportion_biased_person = 1,
  proportion_biased_person_range = NULL
)

Arguments

`lf_object`	Data object from `simulate_factors`. Data must be categorical. If data are not categorical, then there function with throw an error
`method`	Character (length = 1). Method to generate wording effect to add to the data. Description of methods: `"acquiescence"` —Generates new data with flipped dominant loadings (based on `proportion_negative`) and ensures a bias such that variables have a restricted range of responding (e.g., only 4s and 5s on a 5-point Likert scale) `"difficulty"` — Generates new data with flipped dominant loadings (based on `proportion_negative`) and uses this data as the data without wording effects. Then, the signs of the dominant loadings are obtained and the dominant loadings are made to be absolute. Finally, the skews are multiplied by the signs of the original dominant loadings when generating the data with the wording effects `"random_careless"` — Number of cases up to `proportion_biased_cases` are sampled and replaced by values from a random uniform distribution ranging between the lowest and highest response category for each variable. These values then replace the values in the original data `"straight_line"` — Coming soon...
`proportion_negative`	Numeric (length = 1 or `factors`). Proportion of variables that should have negative (or flipped) dominant loadings across all or each factor. Accepts number of variables as well. The first variables on each factor, up to the corresponding proportion, will be flipped. Set to `0` to not have any loadings flipped. Defaults to `0.50`
`proportion_negative_range`	Numeric (length = 2). Range of proportion of variables that are randomly selected from a uniform distribution. Accepts number of number of variables as well. Defaults to `NULL`
`proportion_biased_cases`	Numeric (length = 1). Proportion of cases that should be biased with wording effects. Also accepts number of cases to be biased. The first n number of cases, up to the corresponding proportion, will be biased. Defaults to `0.10` or 10 percent of cases.
`proportion_biased_variables`	Numeric (length = 1 or `factors`). Proportion of variables that should be biased with wording effects. For `method = "difficulty"`, proportion of biased variables will only count for the negative variables. For `method = "acquiescence"`, proportion of biased variables will only count for variables below the mid-point of the `variable_categories`. Defaults to `1` or all possible variables
`proportion_biased_variables_range`	Numeric (length = 2). Range of proportion of variables that should be biased with wording effects. Values are drawn randomly from a uniform distribution. Defaults to `NULL`
`proportion_biased_person`	Numeric (length = 1 or `proportion_biased_cases` x `sample_size`). Person-specific parameter of how many much bias the `proportion_biased_cases` will have over the possible biased variables. This parameter interacts with `proportion_biased_variables`. Parameter specifies the proportion of variables that should have bias per person. If one value is provided, then all biased cases will have the same proportion of variables biased. Individual values are possible by providing values for each biased case (`round(nrow(lf_object$data) * proportion_biased_cases)`). Setting individual values for each biased case is not recommended (use `proportion_biased_person_range` instead). Defaults to `1` or all possible biased variables for all biased cases
`proportion_biased_person_range`	Numeric (length = 2). Range to randomly draw bias from a uniform distribution. Allows for random person-specific bias to be obtained. Defaults to `NULL`

Value

Returns a list containing:

`data`	Biased data simulated data from the specified factor model
`unbiased_data`	The corresponding unbiased data prior to replacing values to generate the (biased) `data`
`biased_sample_size`	The number of cases that have biased data
`adjusted_results`	Bias-adjusted `lf_object` input into function
`original_results`	Original `lf_object` input into function

Author(s)

Alexander P. Christensen <[email protected]>, Luis Eduardo Garrido <[email protected]>

References

Garcia-Pardina, A., Abad, F. J., Christensen, A. P., Golino, H., & Garrido, L. E. (2022). Dimensionality assessment in the presence of wording effects: A network psychometric and factorial approach. PsyArXiv.

Garrido, L. E., Golino, H., Christensen, A. P., Martinez-Molina, A., Arias, V. B., Guerra-Pena, K., ... & Abad, F. J. (2022). A systematic evaluation of wording effects modeling under the exploratory structural equation modeling framework. PsyArXiv.

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
  variable_categories = 5 # 5-point Likert scale
)

# Add wording effects using acquiescence method
two_factor_acquiescence <- add_wording_effects(
  lf_object = two_factor,
  proportion_negative = 0.50,
  proportion_biased_cases = 0.10,
  method = "acquiescence"
)

# Add wording effects using difficulty method
two_factor_difficulty <- add_wording_effects(
  lf_object = two_factor,
  proportion_negative = 0.50,
  proportion_biased_cases = 0.10,
  method = "difficulty"
)

# Add wording effects using random careless method
two_factor_random_careless <- add_wording_effects(
  lf_object = two_factor,
  proportion_negative = 0.50,
  proportion_biased_cases = 0.10,
  method = "random_careless"
)

# Add wording effects using straight line method
two_factor_random_careless <- add_wording_effects(
  lf_object = two_factor,
  proportion_negative = 0.50,
  proportion_biased_cases = 0.10,
  method = "straight_line"
)

# Add wording effects using mixed method
two_factor_mixed <- add_wording_effects(
  lf_object = two_factor,
  proportion_negative = 0.50,
  proportion_biased_cases = 0.10,
  method = "mixed"
)

# Add wording effects using acquiescence and straight line method
two_factor_multiple <- add_wording_effects(
  lf_object = two_factor,
  proportion_negative = 0.50,
  proportion_biased_cases = 0.10,
  method = c("acquiescence", "straight_line")
)

# 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
  variable_categories = 5 # 5-point Likert scale
)

# Add wording effects using acquiescence method
two_factor_acquiescence <- add_wording_effects(
  lf_object = two_factor,
  proportion_negative = 0.50,
  proportion_biased_cases = 0.10,
  method = "acquiescence"
)

# Add wording effects using difficulty method
two_factor_difficulty <- add_wording_effects(
  lf_object = two_factor,
  proportion_negative = 0.50,
  proportion_biased_cases = 0.10,
  method = "difficulty"
)

# Add wording effects using random careless method
two_factor_random_careless <- add_wording_effects(
  lf_object = two_factor,
  proportion_negative = 0.50,
  proportion_biased_cases = 0.10,
  method = "random_careless"
)

# Add wording effects using straight line method
two_factor_random_careless <- add_wording_effects(
  lf_object = two_factor,
  proportion_negative = 0.50,
  proportion_biased_cases = 0.10,
  method = "straight_line"
)

# Add wording effects using mixed method
two_factor_mixed <- add_wording_effects(
  lf_object = two_factor,
  proportion_negative = 0.50,
  proportion_biased_cases = 0.10,
  method = "mixed"
)

# Add wording effects using acquiescence and straight line method
two_factor_multiple <- add_wording_effects(
  lf_object = two_factor,
  proportion_negative = 0.50,
  proportion_biased_cases = 0.10,
  method = c("acquiescence", "straight_line")
)

Categorize Continuous Data

Description

Categorizes continuous data based on Garrido, Abad and Ponsoda (2011; see references). Categorical data with 2 to 6 categories can include skew between -2 to 2 in increments of 0.05

Usage

categorize(data, categories, skew_value = 0)
categorize(data, categories, skew_value = 0)

Arguments

`data`	Numeric (length = n). A vector of continuous data with n values. For matrices, use `apply`
`categories`	Numeric (length = 1). Number of categories to create. Between 2 and 6 categories can be used with skew
`skew_value`	Numeric (length = 1). Value of skew. Ranges between -2 to 2 in increments of 0.05. Skews not in this sequence will be converted to the nearest value in this sequence. Defaults to `0` or no skew

Value

Returns a numeric vector of the categorize data

Author(s)

Maria Dolores Nieto Canaveras <[email protected]>, Luis Eduardo Garrido <[email protected]>, Hudson Golino <[email protected]>, Alexander P. Christensen <[email protected]>

References

Examples

# Dichotomous data (no skew)
dichotomous <- categorize(
  data = rnorm(1000),
  categories = 2
)

# Dichotomous data (with positive skew)
dichotomous_skew <- categorize(
  data = rnorm(1000),
  categories = 2,
  skew_value = 1.25
)

# 5-point Likert scale (no skew)
five_likert <- categorize(
  data = rnorm(1000),
  categories = 5 
)

# 5-point Likert scale (negative skew)
five_likert <- categorize(
  data = rnorm(1000),
  categories = 5,
  skew_value = -0.45
)

# Dichotomous data (no skew)
dichotomous <- categorize(
  data = rnorm(1000),
  categories = 2
)

# Dichotomous data (with positive skew)
dichotomous_skew <- categorize(
  data = rnorm(1000),
  categories = 2,
  skew_value = 1.25
)

# 5-point Likert scale (no skew)
five_likert <- categorize(
  data = rnorm(1000),
  categories = 5 
)

# 5-point Likert scale (negative skew)
five_likert <- categorize(
  data = rnorm(1000),
  categories = 5,
  skew_value = -0.45
)

Transforms `simulate_factors` Data to Zipf's Distribution

Description

Zipf's distribution is commonly found for text data. Closely related to the Pareto and power-law distributions, the Zipf's distribution produces highly skewed data. This transformation is intended to mirror the data generating process of Zipf's law seen in semantic network and topic modeling data.

Usage

data_to_zipfs(lf_object, beta = 2.7, alpha = 1, dichotomous = FALSE)
data_to_zipfs(lf_object, beta = 2.7, alpha = 1, dichotomous = FALSE)

Arguments

`lf_object`	Data object from `simulate_factors`
`beta`	Numeric (length = 1). Sets the shift in rank. Defaults to `2.7`
`alpha`	Numeric (length = 1). Sets the power of the rank. Defaults to `1`
`dichotomous`	Boolean (length = 1). Whether data should be dichotomized rather than frequencies (e.g., semantic network analysis). Defaults to `FALSE`

Details

The formula used to transform data is (Piantadosi, 2014):

f(r) proportional to 1 / (r + beta)^alpha

where f(r) is the rth most frequency, r is the rank-order of the data, beta is a shift in the rank (following Mandelbrot, 1953, 1962), and alpha is the power of the rank with greater values suggesting greater differences between the largest frequency to the next, and so forth.

The function will transform continuous data output from simulate_factors. See examples to get started

Value

Returns a list containing:

`data`	Simulated data that has been transform to follow Zipf's distribution
`RMSE`	A vector of root mean square errors for transformed data and data assumed to follow theoretical Zipf's distribution and Spearman's correlation matrix of the transformed data compared to the original population correlation matrix
`spearman_correlation`	Spearman's correlation matrix of the transformed data
`original_correlation`	Original population correlation matrix before the data were transformed
`original_results`	Original `lf_object` input into function

Author(s)

Alexander P. Christensen <[email protected]>, Hudson Golino <[email protected]>, Luis Eduardo Garrido <[email protected]>

References

Mandelbrot, B. (1953). An informational theory of the statistical structure of language. Communication Theory, 84, 486–502.

Mandelbrot, B. (1962). On the theory of word frequencies and on related Markovian models of discourse. Structure of Language and its Mathematical Aspects, 190–219.

Piantadosi, S. T. (2014). Zipf’s word frequency law in natural language: A critical review and future directions. Psychonomic Bulletin & Review, 21(5), 1112-1130.

Zipf, G. (1936). The psychobiology of language. London, UK: Routledge.

Zipf, G. (1949). Human behavior and the principle of least effort. New York, NY: Addison-Wesley.

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
)

# Transform data to Mandelbrot's Zipf's
two_factor_zipfs <- data_to_zipfs(
  lf_object = two_factor,
  beta = 2.7,
  alpha = 1
)

# Transform data to Mandelbrot's Zipf's (dichotomous)
two_factor_zipfs_binary <- data_to_zipfs(
  lf_object = two_factor,
  beta = 2.7,
  alpha = 1,
  dichotomous = TRUE
)

# 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
)

# Transform data to Mandelbrot's Zipf's
two_factor_zipfs <- data_to_zipfs(
  lf_object = two_factor,
  beta = 2.7,
  alpha = 1
)

# Transform data to Mandelbrot's Zipf's (dichotomous)
two_factor_zipfs_binary <- data_to_zipfs(
  lf_object = two_factor,
  beta = 2.7,
  alpha = 1,
  dichotomous = TRUE
)

Estimate Number of Dimensions using Empirical Kaiser Criterion

Description

Estimates the number of dimensions in data using Empirical Kaiser Criterion (Braeken & Van Assen, 2017). See examples to get started

Usage

EKC(data, sample_size)
EKC(data, sample_size)

Arguments

`data`	Matrix or data frame. Either a dataset with all numeric values (rows = cases, columns = variables) or a symmetric correlation matrix
`sample_size`	Numeric (length = 1). If input into `data` is a correlation matrix, then specifying the sample size is required

Value

Returns a list containing:

`dimensions`	Number of dimensions identified
`eigenvalues`	Eigenvalues
`reference`	Reference values compared against eigenvalues

Author(s)

Alexander P. Christensen <[email protected]>, Hudson Golino <[email protected]>, Luis Eduardo Garrido <[email protected]>

References

Braeken, J., & Van Assen, M. A. (2017). An empirical Kaiser criterion. Psychological Methods, 22(3), 450–466.

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
)

# Perform Empirical Kaiser Criterion
EKC(two_factor$data)

# 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
)

# Perform Empirical Kaiser Criterion
EKC(two_factor$data)

Estimates Exploratory Structural Equation Model

Description

A general function to estimate an Exploratory Structural Equation Model (ESEM) using the lavaan package. With latentFactoR objects, the function requires fewer inputs

Usage

ESEM(
  data,
  factors,
  variables,
  estimator = c("MLR", "WLSMV"),
  fit_measures = NULL,
  variable_polarity = NULL,
  wording_factor = c("none", "CTCM1", "CTCM1_each", "RI", "RI_each"),
  CTCM1_polarity = c("negative", "positive"),
  ...
)
ESEM(
  data,
  factors,
  variables,
  estimator = c("MLR", "WLSMV"),
  fit_measures = NULL,
  variable_polarity = NULL,
  wording_factor = c("none", "CTCM1", "CTCM1_each", "RI", "RI_each"),
  CTCM1_polarity = c("negative", "positive"),
  ...
)

Arguments

`data`	Numeric matrix, data frame, or `latentFactoR` object
`factors`	Numeric (length = 1). Number of ESEM factors to estimate
`variables`	Numeric (length = 1 or `factors`). Number of variables per factor. A vector the length of the number of factors can be specified to allow varying number of variables on each factor (necessary for some `wording_factor` arguments)
`estimator`	Character. Estimator to be used in `cfa`. Default options are `"MLR"` for continuous data and `"WLSMV"` for categorical data
`fit_measures`	Character. Fit measures to be computed using `fitMeasures`. Defaults to: `"chisq"`, `"df"`, `"pvalue"`, `"cfi"`, `"tli"`, `"rmsea"`, `"rmsea.ci.lower"`, `"rmsea.ci.upper"`, `"rmsea.pvalue"`, and `"srmr"`. Other measures can be added but these measures will always be produced. If scaled values are available (not `NA`), then scaled fit measures will be used.
`variable_polarity`	Numeric/character (length = 1 or total variables). Whether all (length = 1) or each variable (length = total variables) are positive (`1`, `"p"`, `"pos"`, `"positive"`) or negative (`-1`, `"n"`, `"neg"`, `"negative"`) polarity on the factor
`wording_factor`	Character (length = 1). Whether wording factor(s) should be estimated. Defaults to `"none"`. Options include: `"CTCM1"` — Description coming soon... `"CTCM1_each"` — Description coming soon... `"RI"` — Description coming soon... `"RI_each"` — Description coming soon...
`CTCM1_polarity`	Character. Polarity of the CTCM1 wording factor(s). Defaults to `"negative"` for negative polarity variables
`...`	Additional arguments to be passed on to `cfa`

Value

Returns a list containing:

`model`	Estimated ESEM model
`fit`	Fit measures of estimated ESEM model

Author(s)

Alexander P. Christensen <[email protected]>, Luis Eduardo Garrido <[email protected]>

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
  variable_categories = 5 # 5-point Likert scale
)

## Not run: 
# Estimate ESEM model with no wording effects
esem_no_wording_effects <- ESEM(
  data = two_factor,
  estimator = "WLSMV"
)

# Add wording effects using acquiescence method
two_factor_acquiescence <- add_wording_effects(
  lf_object = two_factor,
  proportion_negative = 0.50,
  proportion_biased_cases = 0.10,
  method = "acquiescence"
)

# Estimate ESEM model with wording effects
esem_wording_effects <- ESEM(
  data = two_factor_acquiescence,
  estimator = "WLSMV",
  wording_factor = "RI"
)
## End(Not run)

# 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
  variable_categories = 5 # 5-point Likert scale
)

## Not run: 
# Estimate ESEM model with no wording effects
esem_no_wording_effects <- ESEM(
  data = two_factor,
  estimator = "WLSMV"
)

# Add wording effects using acquiescence method
two_factor_acquiescence <- add_wording_effects(
  lf_object = two_factor,
  proportion_negative = 0.50,
  proportion_biased_cases = 0.10,
  method = "acquiescence"
)

# Estimate ESEM model with wording effects
esem_wording_effects <- ESEM(
  data = two_factor_acquiescence,
  estimator = "WLSMV",
  wording_factor = "RI"
)
## End(Not run)

Estimates Dimensions using Several State-of-the-art Methods

Description

Estimates dimensions using Exploratory Graph Analysis (EGA), Empirical Kaiser Criterion (EKC), Factor Forest (factor_forest), Exploratory Factor Analysis with out-of-sample prediction (fspe), Next Eigenvalue Sufficiency Test (NEST), and parallel analysis (fa.parallel)

Usage

estimate_dimensions(
  data,
  sample_size,
  EGA_args = list(corr = "auto", uni.method = "louvain", model = "glasso",
    consensus.method = "most_common", plot.EGA = FALSE),
  FF_args = list(maximum_factors = 8, PA_correlation = "cor"),
  FSPE_args = list(maxK = 8, rep = 1, method = "PE", pbar = FALSE),
  NEST_args = list(iterations = 1000, maximum_iterations = 500, alpha = 0.05, convergence
    = 0.00001),
  PA_args = list(fm = "minres", fa = "both", cor = "cor", n.iter = 20, sim = FALSE, plot
    = FALSE)
)
estimate_dimensions(
  data,
  sample_size,
  EGA_args = list(corr = "auto", uni.method = "louvain", model = "glasso",
    consensus.method = "most_common", plot.EGA = FALSE),
  FF_args = list(maximum_factors = 8, PA_correlation = "cor"),
  FSPE_args = list(maxK = 8, rep = 1, method = "PE", pbar = FALSE),
  NEST_args = list(iterations = 1000, maximum_iterations = 500, alpha = 0.05, convergence
    = 0.00001),
  PA_args = list(fm = "minres", fa = "both", cor = "cor", n.iter = 20, sim = FALSE, plot
    = FALSE)
)

Arguments

`data`	Matrix or data frame. Either a dataset with all numeric values (rows = cases, columns = variables) or a symmetric correlation matrix
`sample_size`	Numeric (length = 1). If input into `data` is a correlation matrix, then specifying the sample size is required
`EGA_args`	List. List of arguments to be passed along to `EGA`. Defaults are listed
`FF_args`	List. List of arguments to be passed along to `factor_forest`. Defaults are listed
`FSPE_args`	List. List of arguments to be passed along to `fspe`. Defaults are listed
`NEST_args`	List. List of arguments to be passed along to `NEST`. Defaults are listed
`PA_args`	List. List of arguments to be passed along to `fa.parallel`. Defaults are listed

Value

Returns a list containing:

dimensions

Dimensions estimated from each method

A list of each methods output (see their respective functions for their outputs)

Author(s)

Maria Dolores Nieto Canaveras <[email protected]>, Alexander P. Christensen <[email protected]>, Hudson Golino <[email protected]>, Luis Eduardo Garrido <[email protected]>

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
)

## Not run: 
# Estimate dimensions
estimate_dimensions(two_factor$data)
## End(Not run)

# 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
)

## Not run: 
# Estimate dimensions
estimate_dimensions(two_factor$data)
## End(Not run)

Estimate Number of Dimensions using Factor Forest

Description

Estimates the number of dimensions in data using the pre-trained Random Forest model from Goretzko and Buhner (2020, 2022). See examples to get started

Usage

factor_forest(
  data,
  sample_size,
  maximum_factors = 8,
  PA_correlation = c("cor", "poly", "tet")
)
factor_forest(
  data,
  sample_size,
  maximum_factors = 8,
  PA_correlation = c("cor", "poly", "tet")
)

Arguments

`data`	Matrix or data frame. Either a dataset with all numeric values (rows = cases, columns = variables) or a symmetric correlation matrix
`sample_size`	Numeric (length = 1). If input into `data` is a correlation matrix, then specifying the sample size is required
`maximum_factors`	Numeric (length = 1). Maximum number of factors to search over. Defaults to `8`
`PA_correlation`	Character (length = 1). Type of correlation used in `fa.parallel`. Must be set: `"cor"` — Pearson's correlation `"poly"` — Polychoric correlation `"tet"` — Tetrachoric correlation

Value

Returns a list containing:

`dimensions`	Number of dimensions identified
`probabilities`	Probability that the number of dimensions is most likely

Author(s)

# Authors of Factor Forest
David Goretzko and Markus Buhner

# Authors of {latentFactoR}
Alexander P. Christensen <[email protected]>, Hudson Golino <[email protected]>, Luis Eduardo Garrido <[email protected]>

References

Goretzko, D., & Buhner, M. (2022). Factor retention using machine learning with ordinal data. Applied Psychological Measurement, 01466216221089345.

Goretzko, D., & Buhner, M. (2020). One model to rule them all? Using machine learning algorithms to determine the number of factors in exploratory factor analysis. Psychological Methods, 25(6), 776-786.

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
)

## Not run: 
# Perform Factor Forest
factor_forest(two_factor$data)
## End(Not run)

# 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
)

## Not run: 
# Perform Factor Forest
factor_forest(two_factor$data)
## End(Not run)

Estimate Number of Dimensions using Next Eigenvalue Sufficiency Test

Description

Estimates the number of dimensions in data using NEST (Achim, 2017). See examples to get started

Usage

NEST(
  data,
  sample_size,
  iterations = 1000,
  maximum_iterations = 500,
  alpha = 0.05,
  convergence = 0.00001
)
NEST(
  data,
  sample_size,
  iterations = 1000,
  maximum_iterations = 500,
  alpha = 0.05,
  convergence = 0.00001
)

Arguments

`data`	Matrix or data frame. Either a dataset with all numeric values (rows = cases, columns = variables) or a symmetric correlation matrix
`sample_size`	Numeric (length = 1). If input into `data` is a correlation matrix, then specifying the sample size is required
`iterations`	Numeric (length = 1). Number of iterations to estimate rank. Defaults to `1000`
`maximum_iterations`	Numeric (length = 1). Maximum umber of iterations to obtain convergence of eigenvalues. Defaults to `500`
`alpha`	Numeric (length = 1). Significance level for determine sufficient eigenvalues. Defaults to `0.05`
`convergence`	Numeric (length = 1). Value necessary to be less than or equal to when establishing convergence of eigenvalues

Value

Returns a list containing:

`dimensions`	Number of dimensions identified
`loadings`	Loading matrix
`converged`	Whether estimation converged. If `FALSE`, then results are reported from last convergence point. Interpret results with caution.

Author(s)

Alexander P. Christensen <[email protected]>, Hudson Golino <[email protected]>, Luis Eduardo Garrido <[email protected]>

References

Achim, A. (2017). Testing the number of required dimensions in exploratory factor analysis. The Quantitative Methods for Psychology, 13(1), 64–74.

Brandenburg, N., & Papenberg, M. (2022). Reassessment of innovative methods to determine the number of factors: A simulation-Based comparison of Exploratory Graph Analysis and Next Eigenvalue Sufficiency Test. Psychological Methods.

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
)

## Not run: 
# Perform NEST
NEST(two_factor$data)
## End(Not run)

# 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
)

## Not run: 
# Perform NEST
NEST(two_factor$data)
## End(Not run)

Obtain Zipf's Distribution Parameters from Data

Description

Zipf's distribution is commonly found for text data. Closely related to the Pareto and power-law distributions, the Zipf's distribution produces highly skewed data. This function obtains the best fitting parameters to Zipf's distribution

Usage

obtain_zipfs_parameters(data)
obtain_zipfs_parameters(data)

Arguments

data

Numeric vector, matrix, or data frame. Numeric data to determine Zipf's distribution parameters

Details

The best parameters are optimized by minimizing the aboslute difference between the original frequencies and the frequencies obtained by the beta and alpha parameters in the following formula (Piantadosi, 2014):

f(r) proportional to 1 / (r + beta)^alpha

Value

Returns a vector containing the estimated beta and alpha parameters. Also contains zipfs_sse which corresponds to the sum of square error between frequencies based on the parameter values estimated and the original data frequencies

Author(s)

Alexander P. Christensen <[email protected]>, Hudson Golino <[email protected]>, Luis Eduardo Garrido <[email protected]>

References

Mandelbrot, B. (1953). An informational theory of the statistical structure of language. Communication Theory, 84, 486–502.

Mandelbrot, B. (1962). On the theory of word frequencies and on related Markovian models of discourse. Structure of Language and its Mathematical Aspects, 190–219.

Piantadosi, S. T. (2014). Zipf’s word frequency law in natural language: A critical review and future directions. Psychonomic Bulletin & Review, 21(5), 1112-1130.

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
)

# Transform data to Mandelbrot's Zipf's
two_factor_zipfs <- data_to_zipfs(
  lf_object = two_factor,
  beta = 2.7,
  alpha = 1
)

# Obtain Zipf's distribution parameters
obtain_zipfs_parameters(two_factor_zipfs$data)

# 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
)

# Transform data to Mandelbrot's Zipf's
two_factor_zipfs <- data_to_zipfs(
  lf_object = two_factor,
  beta = 2.7,
  alpha = 1
)

# Obtain Zipf's distribution parameters
obtain_zipfs_parameters(two_factor_zipfs$data)

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
)
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 <[email protected]>, Alexander P. Christensen <[email protected]>, Hudson Golino <[email protected]>, Luis Eduardo Garrido <[email protected]>

References

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)
)

# 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)
)

Skew Tables

Description

Tables for skew based on the number of categories (2, 3, 4, 5, or 6) in the data

Usage

data(skew_tables)
data(skew_tables)

Format

A list (length = 5)

Examples

data("skew_tables")

data("skew_tables")

Package 'latentFactoR'

Help Index

latentFactoR–package

Description

Author(s)

References

Adds (Substantial) Cross-loadings to simulate_factors Data

Description

Usage

Arguments

Value

Author(s)

References

Examples

Adds Local Dependence to simulate_factors Data

Description

Usage

Arguments

Value

Author(s)

References

Examples

Adds Methods Factors to simulate_factors Data

Description

Usage

Arguments

Value

Author(s)

References

Examples

Adds Population Error to simulate_factors Data

Description

Usage

Arguments

Value

Author(s)

References

Examples

Adds Wording Effects to simulate_factors Data

Description

Usage

Arguments

Value

Author(s)

References

Examples

Categorize Continuous Data

Description

Usage

Arguments

Value

Author(s)

References

Examples

Transforms simulate_factors Data to Zipf's Distribution

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Estimate Number of Dimensions using Empirical Kaiser Criterion

Description

Usage

Arguments

Value

Author(s)

References

Examples

Estimates Exploratory Structural Equation Model

Description

Usage

Arguments

Value

Author(s)

Examples

Estimates Dimensions using Several State-of-the-art Methods

Description

Adds (Substantial) Cross-loadings to `simulate_factors` Data

Adds Local Dependence to `simulate_factors` Data

Adds Methods Factors to `simulate_factors` Data

Adds Population Error to `simulate_factors` Data

Adds Wording Effects to `simulate_factors` Data

Transforms `simulate_factors` Data to Zipf's Distribution