Running EFA from a correlation matrix

[profandyfield]

The problem

There are many times you might want to run factor analysis from a correlation matrix rather than raw data. For example, secondary analysis of other's work. This is possible in psych::fa() e.g

raq_items <- discovr::raq |>  dplyr::select(-id)
raq_poly <- correlation::correlation(raq_items, method = "polychoric")
raq_poly_mtx <- as.matrix(raq_poly) # store correlation matrix

raq_fa <- psych::fa(r = raq_poly_mtx, n.obs = 2571, nfactors = 4)
#> Loading required namespace: GPArotation

^{Created on 2025-06-26 with reprex v2.1.1}

However, this doesn't work with factor_analysis() sdespite it being a wrapper for psych:fa(). Things I have tried:

1. Pass the matrix direct to r so it filters through to fa()

raq_items <- discovr::raq |>  dplyr::select(-id)
raq_poly <- correlation::correlation(raq_items, method = "polychoric")
raq_poly_mtx <- as.matrix(raq_poly) # store correlation matrix

raq_fa <- parameters::factor_analysis(x = raq_items,
                    n = 4,
                    rotation = "oblimin",
                    r = raq_poly_mtx,
                    standardize = FALSE)
#> Error in is.na(n.obs) && (n.iter > 1): 'length = 59133' in coercion to 'logical(1)'

^{Created on 2025-06-26 with reprex v2.1.1}

2. Assign the matrix to the cor argument

raq_items <- discovr::raq |>  dplyr::select(-id)
raq_poly <- correlation::correlation(raq_items, method = "polychoric")
raq_poly_mtx <- as.matrix(raq_poly) # store correlation matrix

raq_fa <- parameters::factor_analysis(x = raq_items,
                    n = 4,
                    rotation = "oblimin",
                    cor = raq_poly_mtx,
                    standardize = FALSE)
#> Error in switch(cor, cor = {: EXPR must be a length 1 vector

^{Created on 2025-06-26 with reprex v2.1.1}

3. Assign it directluy to x

raq_fa <- parameters::factor_analysis(x = raq_poly_mtx,
                    n = 4,
                    rotation = "oblimin",
                    standardize = FALSE)
#> Error: object 'raq_poly_mtx' not found

^{Created on 2025-06-26 with reprex v2.1.1}

Solution

Make it work 😉

[DominiqueMakowski]

Solution: explicitly expose an argument to input correlations?

[DominiqueMakowski]

Or detect if input is correlation matrix (i.e., detect if IsMatrix and is square), and treat it as such (but will require to know nrows)

[profandyfield]

psych:fa() has n.obs for the number of observations (either an integer if n is the same for all correlations, otherwise a matrix of ns) and although using this would be a bit inconsistent with what you do for n_factors(), I feel pretty strongly that it's a much better option than forcing users to supply raw data because for secondary analysis you will rarely have the raw data but you will usually have a matrix of ns to match the correlation matrix.

[profandyfield]

PS I'd argue you should remove the need to supply raw data to n_factors() while you're at it and add an n.obs style argument 😜

[DominiqueMakowski]

I think the best option is indeed to allow for the first arg to be a cor matrix (we just need to catch it and dispatch it acccordingly), and if we detect so we need to make sure that the user passed an arg (nobs? n_observation? whichever is the most easystatsy) if not we error

[profandyfield]

Small correction ot earlier post, psych::fa() has two arguments:

• n.obs: the sample size on which all correlations are based (n.obs = 2571)
• np.obs: a matrix containing the sample size of the corresponding cell of the correlation matrix.

[strengejacke]

Is this the desired output?

raq_items <- discovr::raq |>  dplyr::select(-id)
raq_poly <- correlation::correlation(raq_items, method = "polychoric")
raq_poly_mtx <- as.matrix(raq_poly) # store correlation matrix

parameters::factor_analysis(
  raq_poly_mtx,
  n = 4,
  rotation = "oblimin",
  standardize = FALSE,
  n.obs = 2571
)
#> Loading required namespace: GPArotation
#> # Rotated loadings from Factor Analysis (oblimin-rotation)
#> 
#> Variable |       MR1 |       MR2 |       MR4 |       MR3 | Complexity | Uniqueness
#> ----------------------------------------------------------------------------------
#> raq_01   |     -0.03 |      0.01 |      0.39 |      0.06 |       1.06 |       0.83
#> raq_02   |      0.25 |      0.48 |      0.02 |     -0.03 |       1.54 |       0.62
#> raq_03   |  2.82e-03 |      0.01 |     -0.43 |     -0.03 |       1.01 |       0.80
#> raq_04   |      0.03 |     -0.02 |      0.56 |  3.89e-03 |       1.01 |       0.67
#> raq_05   |      0.45 | -5.86e-03 |      0.39 |      0.02 |       1.97 |       0.46
#> raq_06   |      0.84 |  3.44e-03 | -6.46e-03 |      0.03 |       1.00 |       0.27
#> raq_07   |      0.56 |      0.04 | -1.24e-03 |      0.04 |       1.02 |       0.65
#> raq_08   | -1.16e-04 |     -0.01 |     -0.01 |      0.88 |       1.00 |       0.25
#> raq_09   |     -0.07 |      0.81 | -1.51e-04 |      0.03 |       1.02 |       0.38
#> raq_10   |      0.49 |     -0.05 |      0.09 |     -0.02 |       1.08 |       0.74
#> raq_11   | -8.69e-03 |      0.01 |      0.03 |      0.72 |       1.00 |       0.45
#> raq_12   |     -0.01 |  8.91e-03 |      0.37 |     -0.07 |       1.07 |       0.89
#> raq_13   |      0.57 |      0.03 |      0.04 |     -0.03 |       1.02 |       0.66
#> raq_14   |      0.42 |      0.04 |  8.46e-03 |      0.06 |       1.06 |       0.78
#> raq_15   |      0.48 |      0.03 |      0.03 |      0.05 |       1.04 |       0.71
#> raq_16   |     -0.05 |      0.02 |      0.51 |     -0.01 |       1.02 |       0.77
#> raq_17   |      0.03 |      0.02 |  2.28e-03 |      0.68 |       1.00 |       0.51
#> raq_18   |      0.63 |  7.02e-03 |     -0.02 |      0.07 |       1.03 |       0.57
#> raq_19   |      0.26 |      0.56 |  4.90e-03 | -7.05e-03 |       1.41 |       0.50
#> raq_20   | -6.18e-04 |  7.48e-03 |      0.54 |      0.05 |       1.02 |       0.68
#> raq_21   |     -0.02 |      0.05 |      0.59 |      0.06 |       1.04 |       0.60
#> raq_22   |      0.19 |      0.52 |      0.03 |      0.05 |       1.29 |       0.59
#> raq_23   |     -0.08 |      0.79 |      0.02 | -7.34e-03 |       1.02 |       0.41
#> 
#> The 4 latent factors (oblimin rotation) accounted for 40.12% of the total variance of the original data (MR1 = 13.23%, MR2 = 9.76%, MR4 = 8.83%, MR3 = 8.29%).

^{Created on 2025-06-26 with reprex v2.1.1}

[strengejacke]

If not, how would the call to psych::fa() look like? Do you pass both data frame and matrix, or just a matrix?

[profandyfield]

only difference is you need to pass the r matrix onto psych::fa() and add arguments that map to n.obs and np.obs within psych::fa() ... the Output should be identical to if you run from the raw data.

[strengejacke]

Do you have an example that uses a matrix in fa()?

[profandyfield]

Yes - in my original post!

[profandyfield]

Or do you mean a matrix of n?