The Comparison Data Forest (CDF; Goretzko & Ruscio, 2019) approach is a combination of Random Forest with the comparison data (CD) approach.
CDF(
response,
num.trees = 500,
mtry = "sqrt",
nfact.max = 10,
N.pop = 10000,
N.Samples = 500,
cor.type = "pearson",
use = "pairwise.complete.obs",
vis = TRUE,
plot = TRUE
)An object of class CDF is a list containing the following components:
The number of factors to be retained.
the trained Random Forest model
A matrix containing the probabilities for factor numbers ranging from 1 to nfact.max (1xnfact.max), where the number in the f-th column represents the probability that the number of factors for the response is f.
A matrix (1×181) containing all the features for determining the number of factors. @seealso extractor.feature.FF
A required N × I matrix or data.frame consisting of the responses of N individuals
to × I items.
the number of trees in the Random Forest. (default = 500) See details.
the maximum depth for each tree, can be a number or a character ("sqrt").
When mtry = "sqrt", it means that the maximum depth of each tree will be determined by the square root of
the number of available features (converted to an integer by round).default = "sqrt". See details.
The maximum number of factors discussed by CD approach. (default = 10)
Size of finite populations of simulating.. (default = 10,000)
Number of samples drawn from each population. (default = 500)
A character string indicating which correlation coefficient (or covariance) is to be computed. One of "pearson" (default), "kendall", or "spearman". @seealso cor.
an optional character string giving a method for computing covariances in the presence of missing values. This must be one of the strings "everything", "all.obs", "complete.obs", "na.or.complete", or "pairwise.complete.obs" (default). @seealso cor.
A Boolean variable that will print the factor retention results when set to TRUE, and will not print when set to FALSE. (default = TRUE)
A Boolean variable that will print the CDF plot when set to TRUE, and will not print it when set to FALSE. @seealso plot.CDF. (Default = TRUE)
Haijiang Qin <Haijiang133@outlook.com>
The Comparison Data Forest (CDF; Goretzko & Ruscio, 2019) Approach is a combination of random forest with the comparison data (CD) approach. Its basic steps involve using the method of Ruscio & Roche (2012) to simulate data with different factor counts, then extracting features from this data to train a random forest model. Once the model is trained, it can be used to predict the number of factors in empirical data. The algorithm consists of the following steps:
1. **Simulation Data:**
For each value of \(nfact\) in the range from 1 to \(nfact_{max}\), generate a population data using the GenData function.
Each population is based on \(nfact\) factors and consists of \(N_{pop}\) observations.
For each generated population, repeat the following for \(N_{rep}\) times, For the \(j\)-th in \(N_{rep}\): a. Draw a sample \(N_{sam}\) from the population that matches the size of the empirical data; b. Compute a feature set \(\mathbf{fea}_{nfact,j}\) from each \(N_{sam}\).
Combine all the generated feature sets \(\mathbf{fea}_{nfact,j}\) into a data frame as \(\mathbf{data}_{train, nfact}\).
Combine all \(\mathbf{data}_{train, nfact}\) into a final data frame as the training dataset \(\mathbf{data}_{train}\).
2. **Training RF:**
Train a Random Forest model \(RF\) using the combined \(\mathbf{data}_{train}\).
3. **Prediction the Empirical Data:**
Calculate the feature set \(\mathbf{fea}_{emp}\)for the empirical data.
Use the trained Random Forest model \(RF\) to predict the number of factors \(nfact_{emp}\) for the empirical data: $$nfact_{emp} = RF(\mathbf{fea}_{emp})$$
According to Goretzko & Ruscio (2024) and Breiman (2001), the number of
trees in the Random Forest num.trees is recommended to be 500.
The Random Forest in CDF performs a classification task, so the recommended maximum
depth for each tree mtry is \(\sqrt{q}\) (where \(q\) is the number of features),
which results in \(m_{try}=\sqrt{181}=13\).
Since the CDF approach requires extensive data simulation and computation, which is much more time consuming than the CD Approach, C++ code is used to speed up the process.
Breiman, L. (2001). Random Forests. Machine Learning, 45(1), 5-32. https://doi.org/10.1023/A:1010933404324
Goretzko, D., & Ruscio, J. (2024). The comparison data forest: A new comparison data approach to determine the number of factors in exploratory factor analysis. Behavior Research Methods, 56(3), 1838-1851. https://doi.org/10.3758/s13428-023-02122-4
Ruscio, J., & Roche, B. (2012). Determining the number of factors to retain in an exploratory factor analysis using comparison data of known factorial structure. Psychological Assessment, 24, 282–292. http://dx.doi.org/10.1037/a0025697.
GenData