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Exploratory Factor Analysis Optimization with AI Assistance

optimal_efa_with_ai.Rd

Automatically refines an Exploratory Factor Analysis (EFA) solution by combining model-fit criteria (scaled RMSEA) and item-loading quality, and-when requested- integrates AI-generated conceptual analyses and factor naming. At each iteration it:

  1. Estimates the specified EFA model on the current set of items.

  2. Computes the scaled RMSEA and checks whether it is <= threshold_rmsea and every factor retains at least min_items_per_factor items.

  3. If fit or structure criteria are not met, identifies and removes the item whose exclusion yields the greatest RMSEA improvement or that exhibits structural issues (cross-loading or no loading).

  4. Repeats steps 1-3 until both fit and structure criteria are satisfied or max_steps iterations are reached.

Optionally, when analyze_removed = TRUE and item_definitions are provided, it calls the OpenAI API to generate concise justifications for both exclusion and retention of each item, using the provided definitions and the final loading structure as context. If generate_factor_names = TRUE, it also prompts the AI to propose brief (1-2 word) tentative names for each factor, taking into account the specified domain_name, scale_title, and construct_definition.

Usage

optimal_efa_with_ai(
  data,
  items                    = NULL,
  n_factors                = 5,
  n_items                  = NULL,
  name_items               = "PPTQ",
  estimator                = "WLSMV",
  rotation                 = "oblimin",
  threshold_rmsea          = 0.08,
  threshold_loading        = 0.30,
  min_items_per_factor     = 2,
  apply_threshold          = TRUE,
  max_steps                = NULL,
  verbose                  = TRUE,
  exclude_items            = character(0),
  analyze_removed          = FALSE,
  api_key                  = NULL,
  item_definitions         = NULL,
  domain_name              = "Dominio por Defecto",
  scale_title              = "Título de la Escala por Defecto",
  construct_definition     = "",
  model_name               = "Modelo EFA",
  gpt_model                = "gpt-3.5-turbo",
  generate_factor_names    = FALSE,
  ...
)

Arguments

data

A data.frame containing the observed variables for the EFA.

items

Character vector of item names to include; if NULL, names are generated using name_items and n_items.

n_factors

Integer. Number of factors to extract (default 5).

n_items

Integer. Number of items per factor when items is NULL.

name_items

Character. Prefix for item names (default "PPTQ").

estimator

Character. Estimator to use (e.g., "WLSMV").

rotation

Character. Rotation method (e.g., "oblimin").

threshold_rmsea

Numeric. Maximum allowable scaled RMSEA to stop refinement (default 0.08).

threshold_loading

Numeric. Minimum absolute loading to consider an item well-loaded (default 0.30).

min_items_per_factor

Integer. Minimum items required per factor (default 2).

apply_threshold

Logical. If TRUE, zeros out loadings below threshold_loading in the final solution.

max_steps

Integer or NULL. Maximum number of iterations; if NULL, set to length(items) - 1.

verbose

Logical. If TRUE, prints progress and removal decisions.

exclude_items

Character vector of items to exclude from the start.

analyze_removed

Logical. If TRUE, performs conceptual analysis for each removed and conserved item via the OpenAI API.

api_key

String. OpenAI API key (required if analyze_removed = TRUE or generate_factor_names = TRUE).

item_definitions

Named list mapping each item to its text definition for AI prompts.

domain_name

Character. Domain or factor context used in AI prompts.

scale_title

Character. Scale title used in AI prompts.

construct_definition

Character. Brief definition of the construct used in AI prompts.

model_name

Character. Label for the EFA model in AI prompts.

gpt_model

Character. Name of the ChatGPT model to use (e.g., "gpt-3.5-turbo").

generate_factor_names

Logical. If TRUE, triggers factor naming via AI.

...

Additional arguments passed to the package's internal EFA engine.

Details

The function proceeds as follows:

  1. Fits the exploratory models with the package's internal EFA engine.

  2. Determines the initial set of items from items or from name_items and n_items.

  3. Enters an iterative loop:

    1. Estimates the EFA model with the current items.

    2. Computes the scaled RMSEA.

    3. Evaluates the factor-loading structure for cross-loadings or lack of loadings.

    4. If RMSEA <= threshold_rmsea and each factor has >= min_items_per_factor, stops.

    5. Otherwise, removes the item whose exclusion most improves RMSEA or that has the worst structural issue.

  4. If analyze_removed = TRUE, for each excluded and conserved item, generates via OpenAI concise justifications based on the final structure.

  5. If generate_factor_names = TRUE and api_key provided, proposes tentative names for each factor via AI, considering the specified domain_name, scale_title, and construct_definition.

Value

A list with components:

final_structure

A data.frame of final item loadings and factor assignments.

removed_items

Character vector of items removed during refinement.

steps_log

A data.frame recording each step: step, removed_item, reason, and rmsea.

iterations

Integer. Total number of iterations performed.

final_rmsea

Numeric. Final scaled RMSEA after the last iteration.

bondades_original

Original fit indices and other model information from the package's internal EFA engine.

specifications

Model specifications returned by the package's internal EFA engine.

conceptual_analysis

A list with elements removed and kept, each a named list of AI-generated texts per item, or NULL if analyze_removed = FALSE.

factor_names

Named character vector or list of AI-proposed factor names, or NULL if generate_factor_names = FALSE.

Examples

# \donttest{
data(Data_Expectativas)
# Run the optimized EFA without AI
res_efa <- optimal_efa_with_ai(
  data       = Data_Expectativas,
  items      = paste0("EAF", 1:10),
  name_items = "EAF",
  n_factors  = 2,
  verbose    = FALSE
)
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -1.201524e-16) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -4.163431e-18) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -8.897683e-17) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -1.666993e-17) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -6.845765e-17) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -2.288591e-17) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -1.891747e-17) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= 5.362139e-17) 
#>    is close to zero. This may be a symptom that the model is not identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -6.055497e-17) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -2.146405e-17) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -3.276730e-17) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= 1.634545e-18) 
#>    is close to zero. This may be a symptom that the model is not identified.
#> Warning: lavaan->lav_object_post_check():  
#>    some estimated ov variances are negative
#> Warning: lavaan->lav_object_post_check():  
#>    some estimated ov variances are negative
#> Warning: lavaan->lav_object_post_check():  
#>    some estimated ov variances are negative
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -7.082614e-17) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= 3.576738e-17) 
#>    is close to zero. This may be a symptom that the model is not identified.
#> Warning: lavaan->lav_object_post_check():  
#>    some estimated ov variances are negative
#> Warning: lavaan->lav_object_post_check():  
#>    some estimated ov variances are negative
#> Warning: lavaan->lav_object_post_check():  
#>    some estimated ov variances are negative
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -1.889844e-17) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -1.162264e-17) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -6.271269e-17) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -3.696436e-17) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -4.266688e-17) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= 2.160986e-18) 
#>    is close to zero. This may be a symptom that the model is not identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -6.877305e-17) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= 2.612719e-17) 
#>    is close to zero. This may be a symptom that the model is not identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -8.897683e-17) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -1.666993e-17) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -2.039337e-17) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= 3.648523e-18) 
#>    is close to zero. This may be a symptom that the model is not identified.
res_efa$removed_items
#> [1] "EAF1" "EAF7"
res_efa$final_structure
#>   Items        f1        f2
#> 1  EAF6 0.8488669 0.0000000
#> 2  EAF3 0.7337076 0.0000000
#> 3  EAF5 0.6924926 0.0000000
#> 4  EAF9 0.0000000 0.9562023
#> 5  EAF8 0.0000000 0.9091483
#> 6 EAF10 0.0000000 0.8093829
#> 7  EAF4 0.0000000 0.6706350
#> 8  EAF2 0.0000000 0.6649148
# }
if (FALSE) { # \dontrun{
# With AI-assisted conceptual analysis (requires an OpenAI-compatible API key)
construct_def <- paste("Positive consequences of completing a degree, such as",
                       "prestige, income and self-evaluation.")
item_defs <- as.list(stats::setNames(
  paste("Content of item", 1:10), paste0("EAF", 1:10)))
res_efa_ai <- optimal_efa_with_ai(
  data                  = Data_Expectativas,
  items                 = paste0("EAF", 1:10),
  name_items            = "EAF",
  n_factors             = 2,
  analyze_removed       = TRUE,
  api_key               = Sys.getenv("OPENAI_API_KEY"),
  item_definitions      = item_defs,
  construct_definition  = construct_def,
  scale_title           = "EAF Scale",
  model_name            = "EFA Multidimensional",
  generate_factor_names = TRUE,
  domain_name           = "Academic outcome expectations"
)
res_efa_ai$conceptual_analysis
res_efa_ai$factor_names
} # }