如何从 R class 载荷中提取百分比方差信息

Question

I used varimax() to rotate a matrix and the result is of class loadings like this:

Loadings:
      [,1]   [,2]   [,3]   [,4]   [,5]  
 [1,] -0.517  0.824 -0.207              
 [2,] -0.495  0.855 -0.110              
 [3,] -0.434  0.868 -0.175              
 [4,] -0.471  0.873                     
 [5,] -0.447  0.853        -0.208       
 [6,] -0.544  0.833                     
 [7,] -0.532  0.835                     
 [8,] -0.653  0.746                     
 [9,] -0.470  0.877                     
[10,] -0.658  0.737                     
[11,] -0.543  0.835                     
[12,] -0.581  0.802                     
[13,] -0.573  0.812                     
[14,] -0.613  0.774 -0.113              
[15,] -0.607  0.782 -0.110              
[16,] -0.626  0.754 -0.154              
[17,] -0.552  0.820                     
[18,] -0.571  0.808                     
[19,] -0.382  0.911         0.101       
[20,] -0.671  0.719 -0.128              
[21,] -0.507  0.806 -0.228         0.134
[22,] -0.611  0.748 -0.212              
[23,] -0.679  0.692 -0.190              
[24,] -0.539  0.792 -0.163         0.142
[25,] -0.709  0.677 -0.131              
[26,] -0.683  0.684 -0.179         0.120
[27,] -0.466  0.866                0.110
[28,] -0.621  0.741 -0.175 -0.106  0.113
[29,] -0.504  0.835                0.171
[30,] -0.559  0.757 -0.246         0.213
[31,] -0.555  0.774 -0.243         0.146
[32,] -0.609  0.713 -0.288         0.158
[33,] -0.244        -0.961              
[34,] -0.795  0.470 -0.357              
[35,] -0.852  0.470 -0.196              
[36,] -0.866  0.417 -0.230 -0.109       
[37,] -0.748  0.621 -0.159              
[38,] -0.798  0.567 -0.127 -0.127       
[39,] -0.847  0.486 -0.177              
[40,] -0.809  0.572 -0.106              
[41,] -0.733  0.647 -0.170              
[42,] -0.794  0.586 -0.130              
[43,] -0.834  0.526 -0.131              
[44,] -0.771  0.628                     
[45,] -0.739  0.661                     
[46,] -0.819  0.563                     
[47,] -0.774  0.615                     
[48,] -0.840  0.504 -0.171              
[49,] -0.813  0.567                     
[50,] -0.833  0.536                     
[51,] -0.845  0.498 -0.156              
[52,] -0.809  0.577                     
[53,] -0.837  0.514 -0.165              
[54,] -0.887  0.406 -0.171  0.103       
[55,] -0.866  0.476                     
[56,] -0.763  0.638                     
[57,] -0.882  0.450 -0.100              
[58,] -0.845  0.518 -0.111              
[59,] -0.799  0.596                     
[60,] -0.747  0.653                     
[61,] -0.782  0.617                     

                 [,1]   [,2]  [,3]  [,4]  [,5]
SS loadings    28.861 28.871 2.125 0.259 0.282
Proportion Var  0.473  0.473 0.035 0.004 0.005
Cumulative Var  0.473  0.946 0.981 0.985 0.990

I can get the loadings easily but how could I get the summary information underneath like Proportion var . I tried str() and it returned

'loadings' num [1:61, 1:5] -0.517 -0.495 -0.434 -0.471 -0.447 ...

I tried summary it simply gave the summary on the loadings matrix. and dim() also just returned the loadings matrix size. I just don't understand where the summary information is stored.

Answer 1

The reason you can't find them is because they're not stored but are calculated as part of the print method for the loadings object.

You can see how they're calculated by examing the print function:

getS3method("print", "loadings")

function (x, digits = 3L, cutoff = 0.1, sort = FALSE, ...) 
{
    Lambda <- unclass(x)
    p <- nrow(Lambda)
    factors <- ncol(Lambda)
    if (sort) {
        mx <- max.col(abs(Lambda))
        ind <- cbind(1L:p, mx)
        mx[abs(Lambda[ind]) < 0.5] <- factors + 1
        Lambda <- Lambda[order(mx, 1L:p), ]
    }
    cat("\nLoadings:\n")
    fx <- setNames(format(round(Lambda, digits)), NULL)
    nc <- nchar(fx[1L], type = "c")
    fx[abs(Lambda) < cutoff] <- strrep(" ", nc)
    print(fx, quote = FALSE, ...)
    vx <- colSums(x^2)
    varex <- rbind(`SS loadings` = vx)
    if (is.null(attr(x, "covariance"))) {
        varex <- rbind(varex, `Proportion Var` = vx/p)
        if (factors > 1) 
            varex <- rbind(varex, `Cumulative Var` = cumsum(vx/p))
    }
    cat("\n")
    print(round(varex, digits))
    invisible(x)
}

So they can be calculated by:

set.seed(5)
mat <- replicate(10, trunc(runif(50, 0, 10)))
f1 <- factanal(mat, factors = 3)

x <- loadings(f1)
vx <- colSums(x^2)

rbind(`SS loadings` = vx,
      `Proportion Var` = vx/nrow(x),
      `Cumulative Var` = cumsum(vx/nrow(x)))

                 Factor1   Factor2   Factor3
SS loadings    1.1858135 1.1654288 1.0721485
Proportion Var 0.1185813 0.1165429 0.1072149
Cumulative Var 0.1185813 0.2351242 0.3423391