efa_screen: Screen data for exploratory factor analysis

In EFAtools: Fast and Flexible Implementations of Exploratory Factor Analysis Tools

Screen data for exploratory factor analysis

Description

Checks whether your data are suitable for exploratory factor analysis (EFA). From a correlation matrix or raw data, it reports the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy, Bartlett's test of sphericity, the determinant and condition number of the correlation matrix, and each variable's squared multiple correlation (SMC). When you supply raw data, it also reports each variable's variance and percentage of missing values, category counts for categorical variables, tests of multivariate normality, and multivariate outliers.

Usage

efa_screen(
  x,
  N = NA,
  use = c("pairwise.complete.obs", "all.obs", "complete.obs", "everything",
    "na.or.complete"),
  cor_method = c("pearson", "spearman", "kendall", "poly", "tetra"),
  mcd_alpha = 0.5,
  outlier_cutoff = 0.975,
  seed = NULL
)

Arguments

x	data.frame or matrix. Raw data, or a correlation matrix. Needs at least three variables, none of which is a perfect linear combination of the others.
N	numeric. The number of observations. Set this only when you supply a correlation matrix; it is needed for Bartlett's test of sphericity and is taken from the data automatically when you supply raw data. Default is NA.
use	character. How to handle missing values in raw data. For cor_method = "pearson", "spearman", or "kendall" this is passed to stats::cor(). For "poly" or "tetra" the same rule is applied to the raw data before the correlations are estimated; "all.obs" and "everything" then stop with an error on any missing value, instead of returning NA correlations. Default is "pairwise.complete.obs".
cor_method	character. How to compute correlations from raw data: "pearson", "spearman", or "kendall" (via stats::cor()), or "poly" / "tetra" for polychoric / tetrachoric correlations of ordinal or binary data. A Spearman or Kendall correlation matrix is screened on its own scale, not converted to look like a Pearson correlation matrix; Kendall's tau in particular measures something different from a Pearson correlation, not just a rescaled version of it. Default is "pearson".
mcd_alpha	numeric. The proportion of cases used to build the robust outlier estimate, between 0.5 and 1. The default, 0.5, is the most robust choice; a larger value uses more of the data but resists outliers less well. Used only with raw data.
outlier_cutoff	numeric. The probability used to set the cutoff for flagging a multivariate outlier, between 0.5 and 0.9999. Default is 0.975. Used only with raw data.
seed	integer. A seed for the random subsets used by the outlier detection, so the result is reproducible. Does not affect your random-number generator elsewhere. Default is NULL. Used only with raw data.

Details

The diagnostics are computed from the analysis correlation matrix R:

KMO

The Kaiser-Meyer-Olkin measure of sampling adequacy (Kaiser, 1970; Kaiser & Rice, 1974), overall and for each variable; see efa_kmo(). It shows how much common variance your variables share. Higher values are better; a common rule of thumb treats values below .50 as unacceptable.

Bartlett

Bartlett's (1951) test of sphericity: the likelihood-ratio test of whether the correlation matrix is an identity matrix, i.e., whether your variables correlate with each other at all; see efa_bartlett(). A significant result supports doing a factor analysis. The test needs the sample size N; without it, this diagnostic is skipped with a warning and ⁠$bartlett⁠ is NULL. If N is too small relative to the number of variables, the statistic is NA, also with a warning.

Determinant

The determinant of R, reported as a number only. It falls as you add variables even when the variables are not collinear, so a fixed cut-off on it (such as the 0.00001 often quoted from Field, 2018) says more about how many variables you have than about your data. Use the condition number instead.

Condition number

The ratio of the largest to the smallest eigenvalue of R. Its square root, the condition index, is the collinearity diagnostic of Belsley, Kuh & Welsch (1980); it drives the printed report and its recommendation. An index of 10 or less is rarely of interest. An index above 30 flags a near linear dependency: two or more variables that together carry much the same information. An index between the two is not negligible, but it stays below the value that flags a dependency. Belsley (1991) gives 30 as one example value and calls the choice of a cut-off "somewhat of an art form", so the report grades an index above 30 by its position on the scale 1, 3, 10, 30, 100, 300, 1000: moderate (30 to 100), strong (100 to 300), or very strong (above 300). These values come from regression diagnostics on data that are not centred, but a correlation matrix is centred, so use them as a guide and not as a test.

SMC

The squared multiple correlation of each variable with all the others. A low value flags a variable that has little in common with the rest of your set.

Variance and missing data

For raw data: each variable's variance (over its available values) and percentage of missing values, computed from every row you supplied. These missing-value percentages explain why the correlation matrix's sample size (N) can be smaller than the number of rows in your data. Ordered-factor columns are recoded to integer levels first, so variance reflects those codes.

Categories

For raw data: for each variable with fewer than ten distinct values (treated as categorical), the count of responses in each category. A category with fewer than five responses is flagged as sparse, and an unused category between the smallest and largest response is flagged as empty. As a rule of thumb, items with fewer than five response categories are better analysed with cor_method = "poly" or "tetra" than with Pearson correlations (Rhemtulla et al., 2012).

Multivariate normality

For raw data, using only complete cases: two tests of multivariate normality, Mardia's (1970) test of skewness and kurtosis and the Henze-Zirkler (1990) test. A small p-value on either test suggests your data depart from a multivariate normal distribution, a reason to prefer a robust or ordinal method over normal-theory maximum likelihood. In a very small sample the kurtosis statistic is NA. The Henze-Zirkler p-value is not available with more than about 50 to 60 variables; its test statistic is still reported.

Outliers

For raw data, using only complete cases: multivariate outliers, found from a robust estimate of each case's distance from the centre of your data (the minimum covariance determinant method; Rousseeuw & Van Driessen, 1999). A flagged case is unusually far from the rest of your sample. When there are too few complete cases, the variables are too collinear, or too many cases share identical answers, a plain (non-robust) distance is used instead, with a warning explaining why.

Value

An object of class efa_screen, a list containing:

kmo	A list with the overall KMO (KMO) and the per-variable KMO (KMO_i).
bartlett	A list with Bartlett's chi-square statistic (chisq), its p_value, and its degrees of freedom (df); chisq and p_value are NA when N was too small for the correction. NULL when N is unavailable.
determinant	The determinant of the correlation matrix.
condition	The condition number of the correlation matrix (largest eigenvalue over smallest).
smc	The per-variable squared multiple correlations.
per_item	A data frame with one row per variable (row names are the variable names): variance, missing (percentage), smc, kmo_i, and flags (any sparse/empty-category issues). NULL when a correlation matrix is supplied instead of raw data.
normality	A list with mardia (skewness skewness, skewness_df, skewness_p, kurtosis kurtosis and kurtosis_p, and the underlying b1p/b2p), hz (the Henze-Zirkler statistic and its p_value), and n_complete (the number of complete cases used). NULL without raw data, or a note explaining why when the complete-case data cannot support the tests.
outliers	A list with distances (each complete case's robust distance, named by its row number), cutoff (the flagging threshold, on the same scale as distances), flagged (the row numbers exceeding cutoff), center and cov (the robust location and scatter), method ("mcd" or the "classical" fallback), fallback_reason (why the robust estimate was unavailable, when method is "classical"), and n_complete. NULL without raw data, or a note explaining why when no covariance can be formed.
categories	A named list with the response-category counts for each categorical variable (in category order); NA for a variable treated as continuous. NULL without raw data.
note	Explains why the raw-data diagnostics (per_item, normality, outliers, categories) are missing, when a correlation matrix is supplied instead of raw data. NULL when raw data are supplied.
settings	The settings used: N, n_obs (rows in the raw data supplied, NA for a correlation-matrix input), use, cor_method, mcd_alpha, outlier_cutoff, and seed.

Source

Bartlett, M. S. (1951). The effect of standardization on a Chi-square approximation in factor analysis. Biometrika, 38, 337-344.

Belsley, D. A. (1991). A guide to using the collinearity diagnostics. Computer Science in Economics and Management, 4, 33-50.

Belsley, D. A., Kuh, E. & Welsch, R. E. (1980). Regression diagnostics: Identifying influential data and sources of collinearity. Wiley.

Cochran, W. G. (1954). Some methods for strengthening the common \chi^2 tests. Biometrics, 10, 417-451.

Croux, C. & Haesbroeck, G. (1999). Influence function and efficiency of the minimum covariance determinant scatter matrix estimator. Journal of Multivariate Analysis, 71, 161-190.

Field, A. (2018). Discovering statistics using IBM SPSS statistics (5th ed.). Sage.

Henze, N. & Zirkler, B. (1990). A class of invariant consistent tests for multivariate normality. Communications in Statistics - Theory and Methods, 19, 3595-3617.

Kaiser, H. F. (1970). A second generation little jiffy. Psychometrika, 35, 401-415.

Kaiser, H. F. & Rice, J. (1974). Little jiffy, mark IV. Educational and Psychological Measurement, 34, 111-117.

Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57, 519-530.

Mardia, K. V. (1974). Applications of some measures of multivariate skewness and kurtosis in testing normality and robustness studies. Sankhya B, 36, 115-128.

Pison, G., Van Aelst, S. & Willems, G. (2002). Small sample corrections for LTS and MCD. Metrika, 55, 111-123.

Rhemtulla, M., Brosseau-Liard, P. E. & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17, 354-373.

Rousseeuw, P. J. & Van Driessen, K. (1999). A fast algorithm for the minimum covariance determinant estimator. Technometrics, 41, 212-223.

See Also

efa_kmo() and efa_bartlett() for the individual suitability measures, and efa_retain() for factor retention criteria.

Other factor analysis suitability: efa_bartlett(), efa_kmo(), print.efa_screen()

Examples

# From a correlation matrix (supply N for Bartlett's test of sphericity)
efa_screen(test_models$baseline$cormat, N = 500)

# From raw data (N is taken from the data; the seed makes the outlier
# diagnostics reproducible)
efa_screen(GRiPS_raw, seed = 1)

EFAtools documentation built on Aug. 21, 2026, 5:16 p.m.