EFAsim.data: Simulate Data that Conforms to the theory of Exploratory...
In EFAfactors: Determining the Number of Factors in Exploratory Factor Analysis
EFAsim.data R Documentation
Simulate Data that Conforms to the theory of Exploratory Factor Analysis.
Description
This function is used to simulate data that conforms to the theory of exploratory factor analysis,
with a high degree of customization for the variables involved.
Usage
EFAsim.data(
nfact,
vpf,
N = 500,
distri = "normal",
fc = "R",
pl = "R",
cl = "R",
low.vpf = 5,
up.vpf = 15,
a = NULL,
b = NULL,
vis = TRUE,
seed = NULL
)
Arguments
nfact
A numeric value specifying the number of factors to simulate.
vpf
A numeric or character value specifying the number of items under each factor.
If a numeric value is provided, the numeric must be larger than 2,
and the number of items under each factor will be fixed
to this value. If a character value is provided, it must be one of 'S', 'M', 'L', or 'R'.
These represent random selection of items under each factor from U(5, 10), U(5, 15),
U(5, 20), or U(low.vpf up.vpf), respectively.
N
A numeric value specifying the number of examinees to simulate.
distri
A character, either 'normal' or 'beta', indicating whether the simulated data
will follow a standard multivariate normal distribution or a multivariate beta distribution.
fc
A numeric or character value specifying the degree of correlation between factors.
If a numeric value is provided, it must be within the range of 0 to 0.75, and the correlation
between all factors will be fixed at this value. If a character value is provided, it must be 'R',
and the correlations between factors will be randomly selected from U(0.0, 0.5).
pl
A numeric or character value specifying the size of the primary factor loadings.
If a numeric value is provided, it must be within the range of 0 to 1, and all primary factor
loadings in the loading matrix will be fixed at this value. If a character value is provided,
it must be one of 'L', 'M', 'H', or 'R', representing pl~U(0.35, 0.50), pl~U(0.50, 0.65),
pl~U(0.65, 0.80), or pl~U(0.35, 0.80), respectively, consistent with the settings in Goretzko & Buhner (2020).
cl
A numeric or character value specifying the size of cross-loadings.
If a numeric value is provided, it must be within the range of 0 to 0.5, and all cross-loadings
in the loading matrix will be fixed at this value. If a character value is provided, it must be
one of 'L', 'H', 'None', or 'R', representing cl~U(-0.1, 0.1), cl~U(-0.2, -0.1) \cup U(0.1, 0.2),
cl = 0, or cl~U(-0.2, 0.2), respectively, consistent with the settings in Auerswald & Moshagen (2019).
low.vpf
A numeric value specifying the minimum number of items per factor, must be larger than 2, effective only when vpf is 'R'. (default = 5)
up.vpf
A numeric value specifying the maximum number of items per factor, effective only when vpf is 'R'. (default = 15)
a
A numeric or NULL specifying the 'a' parameter of the beta distribution, effective only when distri = 'beta'.
If a numeric value is provided, it will be used as the 'a' parameter of the beta distribution.
If NULL, a random integer between 1 and 10 will be used. (default = NULL)
b
A numeric or NULL specifying the 'b' parameter of the beta distribution, effective only when distri = 'beta'.
If a numeric value is provided, it will be used as the 'b' parameter of the beta distribution.
If NULL, a random integer between 1 and 10 will be used. (default = NULL)
vis
A logical value indicating whether to print process information. (default = TRUE)
seed
A numeric or NULL specifying the random seed. If a numeric value is provided, it will be used as the seed.
If NULL, the current timestamp will be used. (default = NULL)
Details
A population correlation matrix was created for each data set based on the following decomposition:
\mathbf{\Sigma} = \mathbf{\Lambda} \mathbf{\Phi} \mathbf{\Lambda}^T + \mathbf{\Delta}
where \mathbf{\Lambda} is the loading matrix, \mathbf{\Phi} is the factor correlation
matrix, and \mathbf{\Delta} is a diagonal matrix,
with \mathbf{\Delta} = 1 - \text{diag}(\mathbf{\Lambda} \mathbf{\Phi} \mathbf{\Lambda}^T).
The purpose of \mathbf{\Delta} is to ensure that the diagonal elements of \mathbf{\Sigma} are 1.
The response data for each subject was simulated using the following formula:
X_i = L_i + \epsilon_i, \quad 1 \leq i \leq I
where L_i follows a a standard normal distribution (distri = 'normal') or a beta
distribution (distri = 'beta'), representing the contribution of latent factors.
And \epsilon_i is the residual term following a standard normal distribution
(distri = 'normal') or a beta distribution (distri = 'beta') . L_i and \epsilon_i
are uncorrelated, and \epsilon_i and \epsilon_j are also uncorrelated.
Value
An object of class EFAdata is a list containing the following components:
loadings
A simulated loading matrix.
items
A list containing all factors and the item indices under each factor.
cor.factors
A simulated factor correlation matrix.
cor.items
A simulated item correlation matrix.
response
A simulated response data matrix.
References
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. https://doi.org/10.1037/met0000262.
Auerswald, M., & Moshagen, M. (2019). How to determine the number of factors to retain in exploratory factor analysis: A comparison of extraction methods under realistic conditions. Psychological methods, 24(4), 468-491. https://doi.org/https://doi.org/10.1037/met0000200
Examples
library(EFAfactors)
## Run EFAsim.data function with default parameters.
data.obj <- EFAsim.data(nfact = 3, vpf = 5, N=500, distri="normal", fc="R", pl="R", cl="R",
low.vpf = 5, up.vpf = 15, a = NULL, b = NULL, vis = TRUE, seed = NULL)
head(data.obj$loadings)
EFAfactors documentation built on Sept. 30, 2024, 1:06 a.m.
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| EFAsim.data | R Documentation |
Simulate Data that Conforms to the theory of Exploratory Factor Analysis.
Description
This function is used to simulate data that conforms to the theory of exploratory factor analysis, with a high degree of customization for the variables involved.
Usage
EFAsim.data(
nfact,
vpf,
N = 500,
distri = "normal",
fc = "R",
pl = "R",
cl = "R",
low.vpf = 5,
up.vpf = 15,
a = NULL,
b = NULL,
vis = TRUE,
seed = NULL
)
Arguments
nfact |
A numeric value specifying the number of factors to simulate. |
vpf |
A numeric or character value specifying the number of items under each factor.
If a numeric value is provided, the numeric must be larger than 2,
and the number of items under each factor will be fixed
to this value. If a character value is provided, it must be one of 'S', 'M', 'L', or 'R'.
These represent random selection of items under each factor from |
N |
A numeric value specifying the number of examinees to simulate. |
distri |
A character, either 'normal' or 'beta', indicating whether the simulated data will follow a standard multivariate normal distribution or a multivariate beta distribution. |
fc |
A numeric or character value specifying the degree of correlation between factors.
If a numeric value is provided, it must be within the range of 0 to 0.75, and the correlation
between all factors will be fixed at this value. If a character value is provided, it must be 'R',
and the correlations between factors will be randomly selected from |
pl |
A numeric or character value specifying the size of the primary factor loadings.
If a numeric value is provided, it must be within the range of 0 to 1, and all primary factor
loadings in the loading matrix will be fixed at this value. If a character value is provided,
it must be one of 'L', 'M', 'H', or 'R', representing |
cl |
A numeric or character value specifying the size of cross-loadings.
If a numeric value is provided, it must be within the range of 0 to 0.5, and all cross-loadings
in the loading matrix will be fixed at this value. If a character value is provided, it must be
one of 'L', 'H', 'None', or 'R', representing |
low.vpf |
A numeric value specifying the minimum number of items per factor, must be larger than 2, effective only when |
up.vpf |
A numeric value specifying the maximum number of items per factor, effective only when |
a |
A numeric or NULL specifying the 'a' parameter of the beta distribution, effective only when |
b |
A numeric or NULL specifying the 'b' parameter of the beta distribution, effective only when |
vis |
A logical value indicating whether to print process information. (default = TRUE) |
seed |
A numeric or NULL specifying the random seed. If a numeric value is provided, it will be used as the seed. If NULL, the current timestamp will be used. (default = NULL) |
Details
A population correlation matrix was created for each data set based on the following decomposition:
\mathbf{\Sigma} = \mathbf{\Lambda} \mathbf{\Phi} \mathbf{\Lambda}^T + \mathbf{\Delta}
where \mathbf{\Lambda} is the loading matrix, \mathbf{\Phi} is the factor correlation
matrix, and \mathbf{\Delta} is a diagonal matrix,
with \mathbf{\Delta} = 1 - \text{diag}(\mathbf{\Lambda} \mathbf{\Phi} \mathbf{\Lambda}^T).
The purpose of \mathbf{\Delta} is to ensure that the diagonal elements of \mathbf{\Sigma} are 1.
The response data for each subject was simulated using the following formula:
X_i = L_i + \epsilon_i, \quad 1 \leq i \leq I
where L_i follows a a standard normal distribution (distri = 'normal') or a beta
distribution (distri = 'beta'), representing the contribution of latent factors.
And \epsilon_i is the residual term following a standard normal distribution
(distri = 'normal') or a beta distribution (distri = 'beta') . L_i and \epsilon_i
are uncorrelated, and \epsilon_i and \epsilon_j are also uncorrelated.
Value
An object of class EFAdata is a list containing the following components:
loadings |
A simulated loading matrix. |
items |
A |
cor.factors |
A simulated factor correlation matrix. |
cor.items |
A simulated item correlation matrix. |
response |
A simulated response data matrix. |
References
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. https://doi.org/10.1037/met0000262.
Auerswald, M., & Moshagen, M. (2019). How to determine the number of factors to retain in exploratory factor analysis: A comparison of extraction methods under realistic conditions. Psychological methods, 24(4), 468-491. https://doi.org/https://doi.org/10.1037/met0000200
Examples
library(EFAfactors)
## Run EFAsim.data function with default parameters.
data.obj <- EFAsim.data(nfact = 3, vpf = 5, N=500, distri="normal", fc="R", pl="R", cl="R",
low.vpf = 5, up.vpf = 15, a = NULL, b = NULL, vis = TRUE, seed = NULL)
head(data.obj$loadings)
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