REM_EFA | R Documentation |

This function uses the robust expectation maximization (REM) algorithm to estimate the parameters of an exploratory factor analysis model as suggested by Nieser & Cochran (2021).

```
REM_EFA(X, k_range, delta = 0.05, rotation = "oblimin", ctrREM = controlREM())
```

`X` |
data to analyze; should be a data frame or matrix |

`k_range` |
vector of the number of factors to consider |

`delta` |
hyperparameter between 0 and 1 that captures the researcherâ€™s tolerance of incorrectly down-weighting data from the model (default = 0.05) |

`rotation` |
factor rotation method (default = 'oblimin'); 'varimax' is the only other available option at this time |

`ctrREM` |
control parameters (default: (steps = 25, tol = 1e-6, maxiter = 1e3, min_weights = 1e-30, max_ueps = 0.3, chk_gamma = 0.9, n = 2e4)) |

REM_EFA returns an object of class "REM". The function `summary()`

is used to obtain estimated parameters from the model. An object of class "REM" in Exploratory Factor Analysis is a list of outputs with four different components for each number of factor: the matched call (call), estimates using traditional expectation maximization (EM_output), estimates using robust expectation maximization (REM_output), and a summary table (summary_table). The list contains the following components:

`call` |
match call |

`model` |
model frame |

`k` |
number of factors |

`constraints` |
p x k matrix of zeros and ones denoting the factors (rows) and observed variables (columns) |

`epsilon` |
hyperparameter on the likelihood scale |

`AIC_rem` |
Akaike information criterion based on REM estimates |

`BIC_rem` |
Bayesian information criterion based on REM estimates |

`mu` |
item intercepts |

`lambda` |
factor loadings |

`psi` |
unique variances of items |

`phi` |
factor covariance matrix |

`gamma` |
average weight |

`weights` |
estimated REM weights |

`ind_lik` |
likelihood value for each individual |

`lik_rem` |
joint log-likelihood evaluated at REM estimates |

`lik` |
joint log-likelihood evaluated at EM estimates |

`mu.se` |
standard errors of items intercepts |

`lambda.se` |
standard errors of factor loadings |

`psi.se` |
standard errors of unique variances of items |

`gamma.se` |
standard error of gamma |

`summary_table` |
summary of EM and REM estimates, SEs, Z statistics, p-values, and 95% confidence intervals |

The summary function can be used to obtain estimated parameters from the optimal model based on the BIC from the EM and REM algorithms.

Bryan Ortiz-Torres (bortiztorres@wisc.edu); Kenneth Nieser (nieser@stanford.edu)

Nieser, K. J., & Cochran, A. L. (2021). Addressing heterogeneous populations in latent variable settings through robust estimation. Psychological Methods.

`summary.REMLA()`

for more detailed summaries, `oblimin()`

and `varimax()`

for details on the rotation

```
# Modeling Exploratory Factor Analysis
library(lavaan)
library(GPArotation)
df <- HolzingerSwineford1939
data = df[,-c(1:6)]
model_EFA = REM_EFA( X = data, k_range = 1:3, delta = 0.05)
summary(model_EFA)
```

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.