C_H
Reputation: 191
mixedCor: Misidentification of categorical data for PCA?
I am running a series of principal components analyses using the psych package in R. I have a mix of continuous (read discrete), binary, and ordinal variables. See below for a subset of the data comprising 10 continuous (read discrete) variables (c1 to c10) and one dichotomous variable (d):
dput(s)
structure(c(21, 0, 0, 6, 3, 18, 15, 0, 18, 0, 12, 13, 3, 3, 0,
21, 6, 0, 0, 12, 12, 11, 0, 0, 12, 0, 0, 0, 21, 10, 0, 0, 0,
0, 4, 0, 3, 30, 8, 12, 0, 0, 0, 0, 0, 0, 9, 0, 7, 15, 0, 11,
0, 0, 24, 0, 22, 0, 21, 0, 15, 12, 0, 0, 0, 0, 0, 18, 17, 4,
0, 26, 13, 0, 0, 12, 17, 0, 0, 0, 0, 22, 0, 0, 0, 0, 3, 0, 0,
21, 11, 8, 30, 22, 11, 18, 0, 5, 6, 0, 6, 0, 0, 15, 0, 18, 0,
24, 6, 18, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0, 9, 5, 15, 3, 15, 19,
20, 15, 27, 12, 0, 0, 0, 22, 0, 0, 12, 18, 22, 0, 15, 8, 18,
5, 11, 0, 9, 0, 0, 0, 5, 0, 6, 0, 21, 19, 11, 12, 24, 5, 6, 0,
0, 4, 0, 0, 0, 3, 3, 0, 0, 4, 5, 0, 29, 3, 21, 5, 5, 8, 18, 0,
0, 0, 0, 0, 6, 27, 24, 0, 3, 12, 3, 0, 3, 0, 0, 8, 0, 0, 5, 3,
0, 0, 10, 3, 5, 4, 4, 0, 4, 9, 12, 6, 0, 5, 3, 4, 3, 8, 25, 3,
0, 0, 10, 13, 3, 4, 21, 6, 0, 0, 6, 0, 23, 0, 5, 6, 9, 9, 0,
6, 0, 4, 3, 7, 7, 29, 8, 0, 21, 9, 0, 5, 5, 0, 9, 0, 11, 11,
3, 7, 0, 11, 14, 3, 4, 6, 10, 4, 0, 17, 11, 3, 0, 3, 3, 0, 7,
3, 0, 4, 5, 4, 0, 0, 6, 3, 0, 15, 13, 17, 3, 21, 0, 15, 0, 11,
10, 3, 4, 0, 3, 5, 0, 0, 0, 5, 3, 4, 0, 3, 0, 9, 3, 9, 0, 5,
8, 0, 12, 4, 13, 3, 8, 5, 11, 11, 9, 5, 7, 3, 10, 22, 4, 3, 5,
5, 25, 0, 31, 8, 4, 4, 5, 10, 0, 3, 0, 0, 0, 0, 8, 0, 6, 9, 4,
8, 11, 5, 3, 0, 3, 15, 0, 0, 0, 0, 3, 0, 0, 10, 11, 5, 23, 5,
10, 18, 0, 6, 3, 0, 0, 4, 5, 0, 3, 25, 3, 0, 4, 8, 7, 5, 3, 0,
0, 3, 7, 0, 0, 0, 0, 0, 0, 33, 0, 0, 0, 0, 8, 9, 0, 6, 0, 8,
0, 0, 0, 28, 31, 10, 0, 0, 35, 0, 0, 0, 5, 3, 0, 0, 0, 0, 0,
0, 0, 9, 0, NA, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 0, 8, 0, 0, 4,
0, 22, 0, NA, 0, 27, NA, 0, 0, 3, 0, 0, 24, 17, 12, 0, 15, 6,
0, 0, 11, 34, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 32, 7, 7,
33, 17, 0, 24, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 7, 16, 0,
0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 10, 6, 3, 0, 16, 15, 11, 9, 11,
0, 0, 0, 22, 0, 3, 0, 8, 6, 0, 0, 3, 12, 0, 5, 0, 9, 0, 0, 0,
3, 0, 4, 0, 12, 12, 11, 0, 24, 0, 14, 0, 0, 3, 0, 0, 0, 0, 0,
0, 0, 3, 14, 0, 0, 0, 6, 7, 0, 0, 0, 0, 0, 0, 3, 0, 3, 3, 24,
0, 6, 16, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, NA, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, NA, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0,
3, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 6, 6, 3, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, NA, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0,
0, 0, 0, NA, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 6, 6, 6, 0, 10, 0, 0,
0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 6, 3, 6,
0, 0, 3, 3, 3, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 13, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 3, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, NA, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0,
0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, NA, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
5, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0,
0, 0, 0, 0, NA, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 6, 0, 9, 0, 0,
0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0,
0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 3, 0, 0, 0,
0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0,
9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 9, 31, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
6, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, NA, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1), .Dim = c(200L,
11L), .Dimnames = list(c("1", "2", "3", "4", "5", "6", "7", "8",
"9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19",
"20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30",
"31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41",
"42", "43", "44", "45", "46", "47", "48", "49", "50", "51", "52",
"53", "54", "55", "56", "57", "58", "59", "60", "61", "62", "63",
"64", "65", "66", "67", "68", "69", "70", "71", "72", "73", "74",
"75", "76", "77", "78", "79", "80", "81", "82", "83", "84", "85",
"86", "87", "88", "89", "90", "91", "92", "93", "94", "95", "96",
"97", "98", "99", "100", "101", "102", "103", "104", "105", "106",
"107", "108", "109", "110", "111", "112", "113", "114", "115",
"116", "117", "118", "119", "120", "121", "122", "123", "124",
"125", "126", "127", "128", "129", "130", "131", "132", "133",
"134", "135", "136", "137", "138", "139", "140", "141", "142",
"143", "144", "145", "146", "147", "148", "149", "150", "151",
"152", "153", "154", "155", "156", "157", "158", "159", "160",
"161", "162", "163", "164", "165", "166", "167", "168", "169",
"170", "171", "172", "173", "174", "175", "176", "177", "178",
"179", "180", "181", "182", "183", "184", "185", "186", "187",
"188", "189", "190", "191", "192", "193", "194", "195", "196",
"197", "198", "199", "200"), c("c1", "c2", "c3", "c4", "c5",
"c6", "c7", "c8", "c9", "c10", "d")))
Running:
pca <- principal(s, nfactors = 11, rotate = "none", cor = "mixed"
should compute a heterogeneous correlation matrix; however, the code throws an error, in which it seems to be misidentifying the dichotomous variable (d) as a polytomous variable:
Some polytomous variables have fewer categories than they should. Please check your data.
Potential bad items are
Error in mixedCor(r, use = use, correct = correct) :
I am stopping because of the problem with polytomous data
Why is the variable being misidentified and how do I rectify the issue?
Upvotes: 2
Views: 701
Answers (1)
Chuck P
Reputation: 3923
I'm worried you're missing too much data across the correlation matrix, but if you're sure it's misidentification try this...
library(psych)
# Make variable types explicit...
new_s <- mixedCor(s, c=c("c1", "c2", "c3", "c4", "c5", "c6", "c7", "c8", "c9", "c10"), d = "d")
#> Warning in biserialc(x[, j], y[, i], j, i): For x = 7 y = 1 x seems to be
#> dichotomous, not continuous
#> Warning in biserialc(x[, j], y[, i], j, i): For x = 9 y = 1 x seems to be
#> dichotomous, not continuous
#> Warning in biserialc(x[, j], y[, i], j, i): For x = 10 y = 1 x seems to be
#> dichotomous, not continuous
# Feed this new matrix to PCA
principal(new_s$rho, nfactors = 11, rotate = "none", cor = "mixed")
#> Warning in cor.smooth(model): Matrix was not positive definite, smoothing was
#> done
#> Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
#> Warning in log(det(m.inv.r)): NaNs produced
#> Principal Components Analysis
#> Call: principal(r = new_s$rho, nfactors = 11, rotate = "none", cor = "mixed")
#> Standardized loadings (pattern matrix) based upon correlation matrix
#> PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11 h2
#> c1 0.45 0.39 0.64 -0.05 0.30 -0.09 -0.10 -0.33 0.12 0.06 0 1.0
#> c2 0.46 0.47 0.23 0.62 -0.11 -0.12 -0.24 0.20 -0.06 0.00 0 1.0
#> c3 0.55 0.31 0.52 -0.48 -0.04 0.03 0.07 0.27 -0.12 -0.08 0 1.0
#> c4 0.33 0.68 -0.38 0.01 0.22 0.44 0.17 0.02 -0.05 0.16 0 1.0
#> c5 0.56 0.29 -0.07 -0.10 -0.73 0.01 0.08 -0.12 0.16 0.04 0 1.0
#> c6 0.73 0.27 -0.44 0.00 0.23 -0.13 0.08 0.04 0.22 -0.29 0 1.0
#> c7 0.85 -0.19 -0.14 0.06 -0.09 0.24 -0.18 -0.23 -0.27 -0.15 0 1.0
#> c8 0.71 0.06 -0.39 -0.09 0.07 -0.52 0.12 -0.03 -0.17 0.17 0 1.0
#> c9 0.65 -0.44 0.29 0.34 0.04 0.13 0.46 0.04 0.08 0.04 0 1.0
#> c10 0.77 -0.36 -0.17 -0.13 0.09 0.14 -0.39 0.14 0.20 0.16 0 1.0
#> d 1.01 -0.46 0.14 -0.05 0.04 0.00 0.03 0.03 -0.05 0.01 0 1.3
#> u2 com
#> c1 -2.9e-04 4.0
#> c2 -1.2e-03 4.0
#> c3 -1.5e-02 4.3
#> c4 -9.2e-03 3.5
#> c5 -8.2e-04 2.5
#> c6 -5.1e-05 3.0
#> c7 -2.9e-02 2.0
#> c8 -1.3e-02 2.9
#> c9 -4.9e-02 4.0
#> c10 -3.1e-02 2.7
#> d -2.6e-01 1.5
#>
#> PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11
#> SS loadings 4.91 1.67 1.38 0.78 0.77 0.60 0.52 0.31 0.26 0.20 0.00
#> Proportion Var 0.45 0.15 0.13 0.07 0.07 0.05 0.05 0.03 0.02 0.02 0.00
#> Cumulative Var 0.45 0.60 0.72 0.80 0.86 0.92 0.97 0.99 1.02 1.04 1.04
#> Proportion Explained 0.43 0.15 0.12 0.07 0.07 0.05 0.05 0.03 0.02 0.02 0.00
#> Cumulative Proportion 0.43 0.58 0.70 0.77 0.83 0.89 0.93 0.96 0.98 1.00 1.00
#>
#> Mean item complexity = 3.1
#> Test of the hypothesis that 11 components are sufficient.
#>
#> The root mean square of the residuals (RMSR) is 0.03
#>
#> Fit based upon off diagonal values = 1
You can only also run a PCA on this data if you move to pairwise which means you can't also have mixed
library(psych)
s <-
cor(s)
#> c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 d
#> c1 1.0000000 0.4346003 NA NA NA 0.2240019 NA NA 0.2394707 0.1374522 NA
#> c2 0.4346003 1.0000000 NA NA NA 0.3264929 NA NA 0.2507157 0.1502570 NA
#> c3 NA NA 1 NA NA NA NA NA NA NA NA
#> c4 NA NA NA 1 NA NA NA NA NA NA NA
#> c5 NA NA NA NA 1 NA NA NA NA NA NA
#> c6 0.2240019 0.3264929 NA NA NA 1.0000000 NA NA 0.2630730 0.5129754 NA
#> c7 NA NA NA NA NA NA 1 NA NA NA NA
#> c8 NA NA NA NA NA NA NA 1 NA NA NA
#> c9 0.2394707 0.2507157 NA NA NA 0.2630730 NA NA 1.0000000 0.3958641 NA
#> c10 0.1374522 0.1502570 NA NA NA 0.5129754 NA NA 0.3958641 1.0000000 NA
#> d NA NA NA NA NA NA NA NA NA NA 1
cor(s, use = "pairwise")
#> c1 c2 c3 c4 c5 c6 c7
#> c1 1.0000000 0.43460033 0.5944554 0.17820073 0.1585417 0.2240019 0.2133379
#> c2 0.4346003 1.00000000 0.2721470 0.27657740 0.3458928 0.3264929 0.3064696
#> c3 0.5944554 0.27214700 1.0000000 0.22051983 0.3980126 0.2540505 0.2620851
#> c4 0.1782007 0.27657740 0.2205198 1.00000000 0.2582113 0.5332303 0.2655366
#> c5 0.1585417 0.34589275 0.3980126 0.25821130 1.0000000 0.3704633 0.4592527
#> c6 0.2240019 0.32649293 0.2540505 0.53323028 0.3704633 1.0000000 0.5407480
#> c7 0.2133379 0.30646960 0.2620851 0.26553664 0.4592527 0.5407480 1.0000000
#> c8 0.1518731 0.24817433 0.2186919 0.27508923 0.3883494 0.7126438 0.4923743
#> c9 0.2394707 0.25071568 0.2046642 -0.03278746 0.2041263 0.2630730 0.4815600
#> c10 0.1374522 0.15025695 0.2323497 0.11446032 0.2827706 0.5129754 0.6897342
#> d 0.1410538 0.08626762 0.2042181 -0.02416854 0.1309677 0.2039654 0.4720930
#> c8 c9 c10 d
#> c1 0.1518731 0.23947075 0.1374522 0.14105375
#> c2 0.2481743 0.25071568 0.1502570 0.08626762
#> c3 0.2186919 0.20466424 0.2323497 0.20421810
#> c4 0.2750892 -0.03278746 0.1144603 -0.02416854
#> c5 0.3883494 0.20412633 0.2827706 0.13096770
#> c6 0.7126438 0.26307300 0.5129754 0.20396537
#> c7 0.4923743 0.48155995 0.6897342 0.47209296
#> c8 1.0000000 0.24786725 0.4538082 0.24682472
#> c9 0.2478672 1.00000000 0.3958641 0.48647659
#> c10 0.4538082 0.39586413 1.0000000 0.47158572
#> d 0.2468247 0.48647659 0.4715857 1.00000000
pca <- principal(s, nfactors = 11, rotate = "none", use = "pairwise")
pca
#> Principal Components Analysis
#> Call: principal(r = s, nfactors = 11, rotate = "none", use = "pairwise")
#> Standardized loadings (pattern matrix) based upon correlation matrix
#> PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11 h2
#> c1 0.47 0.44 0.59 0.22 0.19 -0.17 -0.09 -0.05 -0.30 0.15 0.04 1
#> c2 0.52 0.41 0.20 0.24 -0.59 -0.04 -0.19 0.22 0.17 -0.05 0.00 1
#> c3 0.54 0.39 0.46 -0.29 0.39 0.01 0.07 -0.02 0.26 -0.18 -0.05 1
#> c4 0.44 0.50 -0.42 0.26 0.14 0.50 0.11 -0.05 0.00 -0.01 0.15 1
#> c5 0.60 0.21 -0.08 -0.67 -0.28 0.11 0.09 0.02 -0.10 0.18 0.02 1
#> c6 0.77 0.11 -0.44 0.19 0.11 -0.15 0.08 -0.05 0.07 0.16 -0.30 1
#> c7 0.81 -0.28 -0.08 -0.06 -0.07 0.15 -0.23 -0.12 -0.25 -0.29 -0.11 1
#> c8 0.70 -0.03 -0.39 -0.01 0.07 -0.47 0.21 0.16 -0.06 -0.14 0.19 1
#> c9 0.56 -0.41 0.37 0.17 -0.27 0.03 0.37 -0.37 0.07 0.02 0.05 1
#> c10 0.71 -0.43 -0.09 -0.03 0.16 -0.03 -0.43 -0.12 0.18 0.16 0.15 1
#> d 0.51 -0.56 0.29 0.09 0.14 0.25 0.14 0.47 -0.03 0.07 -0.03 1
#> u2 com
#> c1 -1.1e-15 4.6
#> c2 -4.4e-15 4.3
#> c3 -3.6e-15 5.3
#> c4 3.4e-15 5.0
#> c5 6.0e-15 3.0
#> c6 2.4e-15 2.5
#> c7 1.9e-15 2.2
#> c8 1.3e-15 3.1
#> c9 -4.4e-16 5.3
#> c10 1.0e-15 3.1
#> d 2.3e-15 4.4
#>
#> PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11
#> SS loadings 4.15 1.58 1.36 0.78 0.77 0.63 0.52 0.47 0.31 0.25 0.19
#> Proportion Var 0.38 0.14 0.12 0.07 0.07 0.06 0.05 0.04 0.03 0.02 0.02
#> Cumulative Var 0.38 0.52 0.64 0.71 0.79 0.84 0.89 0.93 0.96 0.98 1.00
#> Proportion Explained 0.38 0.14 0.12 0.07 0.07 0.06 0.05 0.04 0.03 0.02 0.02
#> Cumulative Proportion 0.38 0.52 0.64 0.71 0.79 0.84 0.89 0.93 0.96 0.98 1.00
#>
#> Mean item complexity = 3.9
#> Test of the hypothesis that 11 components are sufficient.
#>
#> The root mean square of the residuals (RMSR) is 0
#> with the empirical chi square 0 with prob < NA
#>
#> Fit based upon off diagonal values = 1
principal(s, nfactors = 11, rotate = "none", use = "pairwise", cor = "mixed")
#>
#> Some polytomous variables have fewer categories than they should. Please check your data.
#> Potential bad items are
#> Error in mixedCor(r, use = use, correct = correct):
#> I am stopping because of the problem with polytomous data
Upvotes: 2
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