Return model implied residuals for linear dependencies between items or at the person level.
If the latent trait density was approximated (e.g., Davidian curves, Empirical histograms, etc)
then passing use_dentype_estimate = TRUE will use the internally saved quadrature and
density components (where applicable).
Usage
# S4 method for class 'SingleGroupClass'
residuals(
object,
type = "LD",
p.adjust = "none",
df.p = FALSE,
approx.z = FALSE,
full.scores = FALSE,
QMC = FALSE,
printvalue = NULL,
tables = FALSE,
verbose = TRUE,
Theta = NULL,
suppress = NA,
theta_lim = c(-6, 6),
quadpts = NULL,
fold = TRUE,
upper = TRUE,
technical = list(),
...
)Arguments
- object
an object of class
SingleGroupClassorMultipleGroupClass. Bifactor models are automatically detected and utilized for better accuracy- type
type of residuals to be displayed. Can be either
'LD'or'LDG2'for a local dependence matrix based on the X2 or G2 statistics (Chen & Thissen, 1997),'Q3'for the statistic proposed by Yen (1984),'JSI'for the jack-knife statistic proposed Edwards et al. (2018),'exp'for the expected values for the frequencies of every response pattern, and'expfull'for the expected values for every theoretically observable response pattern. For the 'LD' and 'LDG2' types, the upper diagonal elements represent the standardized residuals in the form of signed Cramers V coefficients- p.adjust
method to use for adjusting all p-values (see
p.adjustfor available options). Default is'none'- df.p
logical; print the degrees of freedom and p-values?
- approx.z
logical; transform \(\chi^2(df)\) information from LD tests into approximate z-ratios instead using the transformation \(z=\sqrt{2 * \chi^2} - \sqrt{2 * df - 1}\)?
- full.scores
logical; compute relevant statistics for each subject in the original data?
- QMC
logical; use quasi-Monte Carlo integration? If
quadptsis omitted the default number of nodes is 5000- printvalue
a numeric value to be specified when using the
res='exp'option. Only prints patterns that have standardized residuals greater thanabs(printvalue). The default (NULL) prints all response patterns- tables
logical; for LD type, return the observed, expected, and standardized residual tables for each item combination?
- verbose
logical; allow information to be printed to the console?
- Theta
a matrix of factor scores used for statistics that require empirical estimates (i.e., Q3). If supplied, arguments typically passed to
fscores()will be ignored and these values will be used instead- suppress
a numeric value indicating which parameter local dependency combinations to flag as being too high (for LD, LDG2, and Q3 the standardize correlations are used; for JSI, the z-ratios are used). Absolute values for the standardized estimates greater than this value will be returned, while all values less than this value will be set to missing
- theta_lim
range for the integration grid
- quadpts
number of quadrature nodes to use. The default is extracted from model (if available) or generated automatically if not available
- fold
logical; apply the sum 'folding' described by Edwards et al. (2018) for the JSI statistic?
- upper
logical; which portion of the matrix (upper versus lower triangle) should the
suppressargument be applied to?- technical
list of technical arguments when models are re-estimated (see
mirtfor details)- ...
additional arguments to be passed to
fscores()
References
Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29. doi:10.18637/jss.v048.i06
Chen, W. H. & Thissen, D. (1997). Local dependence indices for item pairs using item response theory. Journal of Educational and Behavioral Statistics, 22, 265-289.
Edwards, M. C., Houts, C. R. & Cai, L. (2018). A Diagnostic Procedure to Detect Departures From Local Independence in Item Response Theory Models. Psychological Methods, 23, 138-149.
Yen, W. (1984). Effects of local item dependence on the fit and equating performance of the three parameter logistic model. Applied Psychological Measurement, 8, 125-145.
Examples
# \donttest{
x <- mirt(Science, 1)
residuals(x)
#> LD matrix (lower triangle) and standardized residual correlations (upper triangle)
#>
#> Upper triangle summary:
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> -0.147 -0.136 -0.111 -0.045 0.041 0.152
#>
#> Comfort Work Future Benefit
#> Comfort -0.147 -0.101 0.152
#> Work 25.512 0.088 -0.141
#> Future 12.002 9.208 -0.122
#> Benefit 27.321 23.235 17.461
residuals(x, tables = TRUE)
#> $Comfort_Work
#> $Comfort_Work$Obs
#>
#> 1 2 3 4
#> 1 2 0 1 2
#> 2 2 11 15 4
#> 3 24 71 148 23
#> 4 5 16 42 26
#>
#> $Comfort_Work$Exp
#> [,1] [,2] [,3] [,4]
#> [1,] 1.046123 1.787854 1.922925 0.262908
#> [2,] 5.722535 11.386923 13.625623 1.972172
#> [3,] 23.322258 69.348472 140.029013 31.718143
#> [4,] 3.487224 14.109434 50.763258 21.495135
#>
#> $Comfort_Work$std_res
#>
#> 1 2 3 4
#> 1 0.9326115 -1.3371066 -0.6655567 3.3878247
#> 2 -1.5561252 -0.1146625 0.3723298 1.4439717
#> 3 0.1403392 0.1983204 0.6736015 -1.5479971
#> 4 0.8100928 0.5033119 -1.2299596 0.9716541
#>
#>
#> $Comfort_Future
#> $Comfort_Future$Obs
#>
#> 1 2 3 4
#> 1 2 2 1 0
#> 2 3 11 11 7
#> 3 8 51 155 52
#> 4 1 8 43 37
#>
#> $Comfort_Future$Exp
#> [,1] [,2] [,3] [,4]
#> [1,] 0.7680477 1.812936 2.091572 0.3472546
#> [2,] 3.6749826 11.241583 15.084907 2.7057791
#> [3,] 9.1976778 52.384929 148.579175 54.2561060
#> [4,] 0.7527106 6.828614 42.541147 39.7325783
#>
#> $Comfort_Future$std_res
#>
#> 1 2 3 4
#> 1 1.40572316 0.13893088 -0.75477217 -0.58928310
#> 2 -0.35209910 -0.07205318 -1.05174604 2.61058722
#> 3 -0.39491253 -0.19134814 0.52675890 -0.30629167
#> 4 0.28503062 0.44826372 0.07035076 -0.43351011
#>
#>
#> $Comfort_Benefit
#> $Comfort_Benefit$Obs
#>
#> 1 2 3 4
#> 1 4 0 1 0
#> 2 5 10 13 4
#> 3 11 81 133 41
#> 4 1 9 46 33
#>
#> $Comfort_Benefit$Exp
#> [,1] [,2] [,3] [,4]
#> [1,] 0.6710457 1.95217 1.959779 0.4368153
#> [2,] 3.6241191 12.16983 13.682082 3.2312240
#> [3,] 14.8454892 71.28246 131.343241 46.9466978
#> [4,] 2.3173267 14.55596 44.803655 28.1781067
#>
#> $Comfort_Benefit$std_res
#>
#> 1 2 3 4
#> 1 4.0637950 -1.3972006 -0.6855953 -0.6609200
#> 2 0.7227359 -0.6219892 -0.1844000 0.4276774
#> 3 -0.9980547 1.1509727 0.1445624 -0.8679073
#> 4 -0.8653661 -1.4562597 0.1787310 0.9083677
#>
#>
#> $Work_Future
#> $Work_Future$Obs
#>
#> 1 2 3 4
#> 1 7 10 14 2
#> 2 3 28 57 10
#> 3 3 31 122 50
#> 4 1 3 17 34
#>
#> $Work_Future$Exp
#> [,1] [,2] [,3] [,4]
#> [1,] 4.6004355 12.483087 14.34426 2.150355
#> [2,] 5.8020446 27.786418 52.26417 10.780046
#> [3,] 3.6903551 28.936581 118.01439 55.699488
#> [4,] 0.3005835 3.061977 23.67397 28.411829
#>
#> $Work_Future$std_res
#>
#> 1 2 3 4
#> 1 1.11874979 -0.70279865 -0.09089724 -0.10253275
#> 2 -1.16328067 0.04051800 0.65507895 -0.23757996
#> 3 -0.35936723 0.38358699 0.36688237 -0.76367799
#> 4 1.27571400 -0.03541829 -1.37166696 1.04838334
#>
#>
#> $Work_Benefit
#> $Work_Benefit$Obs
#>
#> 1 2 3 4
#> 1 4 8 12 9
#> 2 6 34 47 11
#> 3 8 52 111 35
#> 4 3 6 23 23
#>
#> $Work_Benefit$Exp
#> [,1] [,2] [,3] [,4]
#> [1,] 4.233251 13.170723 13.31610 2.858063
#> [2,] 7.660483 32.196149 44.96112 11.814929
#> [3,] 8.417022 46.931424 106.55195 44.440425
#> [4,] 1.147224 7.662122 26.95958 19.679427
#>
#> $Work_Benefit$std_res
#>
#> 1 2 3 4
#> 1 -0.1133671 -1.4247756 -0.3606627 3.6330344
#> 2 -0.5999380 0.3179060 0.3040694 -0.2370851
#> 3 -0.1437407 0.7398678 0.4309125 -1.4161278
#> 4 1.7298113 -0.6004660 -0.7625934 0.7485258
#>
#>
#> $Future_Benefit
#> $Future_Benefit$Obs
#>
#> 1 2 3 4
#> 1 5 1 6 2
#> 2 5 32 30 5
#> 3 8 53 118 31
#> 4 3 14 39 40
#>
#> $Future_Benefit$Exp
#> [,1] [,2] [,3] [,4]
#> [1,] 2.960508 6.706374 4.143629 0.5829072
#> [2,] 7.760422 29.142832 29.887302 5.4775063
#> [3,] 9.227453 52.779344 109.948223 36.3417805
#> [4,] 1.509597 11.331867 47.809604 36.3906499
#>
#> $Future_Benefit$std_res
#>
#> 1 2 3 4
#> 1 1.18532911 -2.20351681 0.91195681 1.85608815
#> 2 -0.99090687 0.52926095 0.02061456 -0.20402700
#> 3 -0.40407692 0.03037266 0.76788760 -0.88610042
#> 4 1.21303423 0.79260501 -1.27408623 0.59832081
#>
#>
residuals(x, type = 'exp')
#> Comfort Work Future Benefit freq exp std.res
#> 1 1 1 1 1 2 0.124 5.324
#> 2 1 3 2 1 1 0.067 3.605
#> 3 1 4 2 3 1 0.019 7.046
#> 4 1 4 3 1 1 0.006 12.642
#> 5 2 1 1 1 1 0.460 0.796
#> 6 2 1 2 4 1 0.095 2.930
#> 7 2 2 1 1 1 0.351 1.095
#> 8 2 2 2 2 4 2.147 1.264
#> 9 2 2 2 3 2 1.616 0.302
#> 10 2 2 3 1 1 0.377 1.015
#> 11 2 2 3 2 1 1.716 -0.547
#> 12 2 2 3 3 1 2.228 -0.823
#> 13 2 2 4 3 1 0.251 1.497
#> 14 2 3 1 3 1 0.213 1.707
#> 15 2 3 2 2 2 1.545 0.366
#> 16 2 3 2 3 1 1.489 -0.401
#> 17 2 3 3 2 3 2.248 0.502
#> 18 2 3 3 3 3 3.910 -0.460
#> 19 2 3 3 4 2 1.035 0.948
#> 20 2 3 4 1 1 0.041 4.763
#> 21 2 3 4 3 2 0.866 1.218
#> 22 2 4 2 1 1 0.029 5.690
#> 23 2 4 4 3 2 0.259 3.418
#> 24 2 4 4 4 1 0.184 1.902
#> 25 3 1 1 1 1 0.644 0.444
#> 26 3 1 1 3 2 0.638 1.705
#> 27 3 1 2 2 2 3.923 -0.971
#> 28 3 1 2 3 4 3.077 0.526
#> 29 3 1 3 2 5 3.567 0.759
#> 30 3 1 3 3 5 5.097 -0.043
#> 31 3 1 3 4 3 1.160 1.709
#> 32 3 1 4 3 1 0.764 0.269
#> 33 3 1 4 4 1 0.320 1.203
#> 34 3 2 1 2 1 1.781 -0.585
#> 35 3 2 1 4 1 0.154 2.157
#> 36 3 2 2 1 1 2.250 -0.833
#> 37 3 2 2 2 10 8.471 0.525
#> 38 3 2 2 3 7 8.067 -0.376
#> 39 3 2 3 1 1 2.221 -0.819
#> 40 3 2 3 2 16 11.743 1.242
#> 41 3 2 3 3 22 19.584 0.546
#> 42 3 2 3 4 5 4.950 0.023
#> 43 3 2 4 1 1 0.193 1.835
#> 44 3 2 4 2 1 1.293 -0.258
#> 45 3 2 4 3 3 3.778 -0.400
#> 46 3 2 4 4 2 1.716 0.217
#> 47 3 3 1 3 2 0.971 1.044
#> 48 3 3 2 1 1 1.764 -0.575
#> 49 3 3 2 2 13 7.852 1.837
#> 50 3 3 2 3 10 9.780 0.070
#> 51 3 3 2 4 2 1.975 0.018
#> 52 3 3 3 1 5 3.363 0.893
#> 53 3 3 3 2 23 20.447 0.565
#> 54 3 3 3 3 52 45.243 1.005
#> 55 3 3 3 4 8 14.757 -1.759
#> 56 3 3 4 2 7 4.389 1.246
#> 57 3 3 4 3 13 16.979 -0.966
#> 58 3 3 4 4 12 10.323 0.522
#> 59 3 4 1 3 1 0.090 3.030
#> 60 3 4 2 3 1 1.098 -0.093
#> 61 3 4 3 2 2 3.043 -0.598
#> 62 3 4 3 3 4 8.562 -1.559
#> 63 3 4 3 4 4 3.637 0.191
#> 64 3 4 4 1 1 0.160 2.100
#> 65 3 4 4 2 1 1.287 -0.253
#> 66 3 4 4 3 6 6.466 -0.183
#> 67 3 4 4 4 3 5.659 -1.118
#> 68 4 1 1 4 1 0.006 12.587
#> 69 4 1 2 2 1 0.325 1.183
#> 70 4 1 2 4 2 0.057 8.158
#> 71 4 1 3 4 1 0.300 1.278
#> 72 4 2 2 1 1 0.193 1.836
#> 73 4 2 2 3 3 1.017 1.967
#> 74 4 2 3 3 8 4.462 1.675
#> 75 4 2 3 4 2 1.448 0.459
#> 76 4 2 4 2 1 0.433 0.862
#> 77 4 2 4 4 1 1.080 -0.077
#> 78 4 3 2 3 1 1.665 -0.516
#> 79 4 3 3 2 2 4.874 -1.302
#> 80 4 3 3 3 21 14.002 1.870
#> 81 4 3 3 4 3 5.965 -1.214
#> 82 4 3 4 2 2 2.097 -0.067
#> 83 4 3 4 3 5 10.419 -1.679
#> 84 4 3 4 4 8 8.830 -0.279
#> 85 4 4 3 2 1 0.966 0.034
#> 86 4 4 3 3 2 3.571 -0.831
#> 87 4 4 3 4 3 2.063 0.652
#> 88 4 4 4 2 2 0.906 1.149
#> 89 4 4 4 3 6 5.780 0.092
#> 90 4 4 4 4 12 7.470 1.657
residuals(x, suppress = .15)
#> LD matrix (lower triangle) and standardized residual correlations (upper triangle)
#>
#> Upper triangle summary:
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> -0.147 -0.136 -0.111 -0.045 0.041 0.152
#>
#> Comfort Work Future Benefit
#> Comfort 0.152
#> Work
#> Future
#> Benefit 27.321
residuals(x, df.p = TRUE)
#> Degrees of freedom (lower triangle) and p-values:
#>
#> Comfort Work Future Benefit
#> Comfort 0.002 0.213 0.001
#> Work 9 0.418 0.006
#> Future 9 9.000 0.042
#> Benefit 9 9.000 9.000
#>
#> LD matrix (lower triangle) and standardized residual correlations (upper triangle)
#>
#> Upper triangle summary:
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> -0.147 -0.136 -0.111 -0.045 0.041 0.152
#>
#> Comfort Work Future Benefit
#> Comfort -0.147 -0.101 0.152
#> Work 25.512 0.088 -0.141
#> Future 12.002 9.208 -0.122
#> Benefit 27.321 23.235 17.461
residuals(x, df.p = TRUE, p.adjust = 'fdr') # apply FWE control
#> Degrees of freedom (lower triangle) and p-values:
#>
#> Comfort Work Future Benefit
#> Comfort 0.007 0.256 0.007
#> Work 9 0.418 0.011
#> Future 9 9.000 0.063
#> Benefit 9 9.000 9.000
#>
#> LD matrix (lower triangle) and standardized residual correlations (upper triangle)
#>
#> Upper triangle summary:
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> -0.147 -0.136 -0.111 -0.045 0.041 0.152
#>
#> Comfort Work Future Benefit
#> Comfort -0.147 -0.101 0.152
#> Work 25.512 0.088 -0.141
#> Future 12.002 9.208 -0.122
#> Benefit 27.321 23.235 17.461
# Pearson's X2 estimate for goodness-of-fit
full_table <- residuals(x, type = 'expfull')
head(full_table)
#> Comfort Work Future Benefit freq exp res
#> 1 1 1 1 1 2 0.124 5.324
#> 2 1 1 1 2 0 0.160 -0.400
#> 3 1 1 1 3 0 0.054 -0.233
#> 4 1 1 1 4 0 0.005 -0.073
#> 5 1 1 2 1 0 0.092 -0.303
#> 6 1 1 2 2 0 0.219 -0.468
X2 <- with(full_table, sum((freq - exp)^2 / exp))
df <- nrow(full_table) - extract.mirt(x, 'nest') - 1
p <- pchisq(X2, df = df, lower.tail=FALSE)
data.frame(X2, df, p, row.names='Pearson-X2')
#> X2 df p
#> Pearson-X2 689.3347 239 2.942933e-45
# above FOG test as a function
PearsonX2 <- function(x){
full_table <- residuals(x, type = 'expfull')
X2 <- with(full_table, sum((freq - exp)^2 / exp))
df <- nrow(full_table) - extract.mirt(x, 'nest') - 1
p <- pchisq(X2, df = df, lower.tail=FALSE)
data.frame(X2, df, p, row.names='Pearson-X2')
}
PearsonX2(x)
#> X2 df p
#> Pearson-X2 689.3347 239 2.942933e-45
# extract results manually
out <- residuals(x, df.p = TRUE, verbose=FALSE)
str(out)
#> List of 2
#> $ df.p: 'mirt_matrix' num [1:4, 1:4] NA 9 9 9 0.00245 ...
#> ..- attr(*, "dimnames")=List of 2
#> .. ..$ : chr [1:4] "Comfort" "Work" "Future" "Benefit"
#> .. ..$ : chr [1:4] "Comfort" "Work" "Future" "Benefit"
#> $ LD : 'mirt_matrix' num [1:4, 1:4] NA 25.512 12.002 27.321 -0.147 ...
#> ..- attr(*, "dimnames")=List of 2
#> .. ..$ : chr [1:4] "Comfort" "Work" "Future" "Benefit"
#> .. ..$ : chr [1:4] "Comfort" "Work" "Future" "Benefit"
out$df.p[1,2]
#> [1] 0.002454207
# with and without supplied factor scores
Theta <- fscores(x)
residuals(x, type = 'Q3', Theta=Theta)
#> Q3 summary statistics:
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> -0.320 -0.249 -0.225 -0.190 -0.205 0.085
#>
#> Comfort Work Future Benefit
#> Comfort 1.000 -0.203 -0.252 0.085
#> Work -0.203 1.000 -0.208 -0.242
#> Future -0.252 -0.208 1.000 -0.320
#> Benefit 0.085 -0.242 -0.320 1.000
residuals(x, type = 'Q3', method = 'ML')
#> Q3 summary statistics:
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> -0.514 -0.426 -0.357 -0.311 -0.270 0.053
#>
#> Comfort Work Future Benefit
#> Comfort 1.000 -0.262 -0.419 0.053
#> Work -0.262 1.000 -0.428 -0.295
#> Future -0.419 -0.428 1.000 -0.514
#> Benefit 0.053 -0.295 -0.514 1.000
# Edwards et al. (2018) JSI statistic
N <- 250
a <- rnorm(10, 1.7, 0.3)
d <- rnorm(10)
dat <- simdata(a, d, N=250, itemtype = '2PL')
mod <- mirt(dat, 1)
residuals(mod, type = 'JSI')
#> JSI summary statistics:
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> -1.046 -0.175 0.011 0.012 0.219 1.356
#>
#> Item_1 Item_2 Item_3 Item_4 Item_5 Item_6 Item_7 Item_8 Item_9 Item_10
#> Item_1 -0.161 0.054 0.229 0.332 -0.330 0.307 -0.619 0.176 -0.028
#> Item_2 -0.161 -0.471 -0.160 0.319 0.317 -0.180 -0.016 0.412 0.018
#> Item_3 0.054 -0.471 -0.256 -0.506 0.056 -0.178 1.356 0.104 -0.079
#> Item_4 0.229 -0.160 -0.256 0.362 -0.175 -0.142 0.512 0.044 -0.377
#> Item_5 0.332 0.319 -0.506 0.362 0.135 -0.066 -1.046 -0.516 0.866
#> Item_6 -0.330 0.317 0.056 -0.175 0.135 0.047 0.219 -0.007 0.011
#> Item_7 0.307 -0.180 -0.178 -0.142 -0.066 0.047 0.020 0.139 -0.081
#> Item_8 -0.619 -0.016 1.356 0.512 -1.046 0.219 0.020 0.333 -0.051
#> Item_9 0.176 0.412 0.104 0.044 -0.516 -0.007 0.139 0.333 -0.393
#> Item_10 -0.028 0.018 -0.079 -0.377 0.866 0.011 -0.081 -0.051 -0.393
residuals(mod, type = 'JSI', fold=FALSE) # unfolded
#> JSI summary statistics:
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> -0.551 -0.089 -0.003 0.006 0.105 0.690
#>
#> Item_1 Item_2 Item_3 Item_4 Item_5 Item_6 Item_7 Item_8 Item_9 Item_10
#> Item_1 -0.102 0.108 0.147 0.128 -0.152 0.223 -0.339 0.079 -0.016
#> Item_2 -0.059 -0.184 -0.084 0.151 0.166 -0.091 -0.010 0.200 0.003
#> Item_3 -0.054 -0.288 -0.089 -0.276 -0.002 -0.147 0.690 0.067 -0.013
#> Item_4 0.082 -0.076 -0.167 0.161 -0.102 -0.100 0.273 0.039 -0.187
#> Item_5 0.203 0.169 -0.230 0.201 0.072 -0.017 -0.551 -0.278 0.491
#> Item_6 -0.178 0.151 0.058 -0.073 0.062 0.026 0.108 -0.004 0.011
#> Item_7 0.084 -0.088 -0.030 -0.042 -0.049 0.022 0.004 0.041 -0.041
#> Item_8 -0.279 -0.007 0.666 0.239 -0.495 0.111 0.017 0.183 -0.045
#> Item_9 0.097 0.212 0.037 0.004 -0.238 -0.003 0.098 0.150 -0.213
#> Item_10 -0.012 0.015 -0.066 -0.190 0.374 0.000 -0.040 -0.006 -0.180
# LD between items 1-2
aLD <- numeric(10)
aLD[1:2] <- rnorm(2, 2.55, 0.15)
a2 <- cbind(a, aLD)
dat <- simdata(a2, d, N=250, itemtype = '2PL')
mod <- mirt(dat, 1)
# JSI executed in parallel over multiple cores
if(interactive()) mirtCluster()
residuals(mod, type = 'JSI')
#> JSI summary statistics:
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> -1.676 -0.550 -0.006 0.019 0.489 4.804
#>
#> Item_1 Item_2 Item_3 Item_4 Item_5 Item_6 Item_7 Item_8 Item_9 Item_10
#> Item_1 4.804 -1.676 -0.731 -0.550 -0.546 -1.542 -1.020 -0.100 -0.514
#> Item_2 4.804 -1.289 -0.629 -1.082 -1.025 -0.948 -0.326 -0.427 -0.610
#> Item_3 -1.676 -1.289 0.802 -0.117 0.837 0.820 1.140 0.734 0.039
#> Item_4 -0.731 -0.629 0.802 0.847 -0.006 0.226 0.367 0.470 -0.317
#> Item_5 -0.550 -1.082 -0.117 0.847 0.195 0.467 0.201 -0.055 0.680
#> Item_6 -0.546 -1.025 0.837 -0.006 0.195 0.306 -0.420 0.489 0.978
#> Item_7 -1.542 -0.948 0.820 0.226 0.467 0.306 0.514 0.211 0.086
#> Item_8 -1.020 -0.326 1.140 0.367 0.201 -0.420 0.514 -0.475 0.672
#> Item_9 -0.100 -0.427 0.734 0.470 -0.055 0.489 0.211 -0.475 -0.629
#> Item_10 -0.514 -0.610 0.039 -0.317 0.680 0.978 0.086 0.672 -0.629
# }