| residuals-method {mirt} | R Documentation |
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).
## S4 method for signature '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(),
...
)
object |
an object of class |
type |
type of residuals to be displayed.
Can be either |
p.adjust |
method to use for adjusting all p-values (see |
df.p |
logical; print the degrees of freedom and p-values? |
approx.z |
logical; transform |
full.scores |
logical; compute relevant statistics for each subject in the original data? |
QMC |
logical; use quasi-Monte Carlo integration? If |
printvalue |
a numeric value to be specified when using the |
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 |
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 |
technical |
list of technical arguments when models are re-estimated (see |
... |
additional arguments to be passed to |
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.
## No test:
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.
## -0.765 -0.314 0.042 -0.001 0.290 0.720
##
## Item_1 Item_2 Item_3 Item_4 Item_5 Item_6 Item_7 Item_8 Item_9 Item_10
## Item_1 -0.195 0.290 0.270 0.095 -0.379 0.327 0.077 -0.261 -0.352
## Item_2 -0.195 -0.420 0.294 0.105 0.499 -0.193 -0.426 0.521 -0.108
## Item_3 0.290 -0.420 -0.511 -0.765 -0.741 0.240 0.256 0.720 0.331
## Item_4 0.270 0.294 -0.511 -0.199 0.688 -0.003 0.083 -0.314 -0.385
## Item_5 0.095 0.105 -0.765 -0.199 0.144 0.339 0.178 -0.122 0.698
## Item_6 -0.379 0.499 -0.741 0.688 0.144 -0.036 0.381 0.042 -0.435
## Item_7 0.327 -0.193 0.240 -0.003 0.339 -0.036 0.123 -0.193 -0.350
## Item_8 0.077 -0.426 0.256 0.083 0.178 0.381 0.123 -0.629 -0.065
## Item_9 -0.261 0.521 0.720 -0.314 -0.122 0.042 -0.193 -0.629 0.339
## Item_10 -0.352 -0.108 0.331 -0.385 0.698 -0.435 -0.350 -0.065 0.339
residuals(mod, type = 'JSI', fold=FALSE) # unfolded
## JSI summary statistics:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.440 -0.151 0.021 0.000 0.148 0.389
##
## Item_1 Item_2 Item_3 Item_4 Item_5 Item_6 Item_7 Item_8 Item_9 Item_10
## Item_1 -0.085 0.100 0.124 0.051 -0.161 0.184 0.048 -0.104 -0.151
## Item_2 -0.110 -0.195 0.145 0.054 0.263 -0.112 -0.206 0.250 -0.038
## Item_3 0.190 -0.225 -0.233 -0.440 -0.407 0.166 0.157 0.354 0.149
## Item_4 0.146 0.149 -0.278 -0.100 0.389 -0.001 0.045 -0.149 -0.167
## Item_5 0.044 0.052 -0.325 -0.099 0.070 0.186 0.079 -0.046 0.344
## Item_6 -0.218 0.236 -0.334 0.299 0.074 -0.030 0.161 0.023 -0.185
## Item_7 0.143 -0.081 0.075 -0.002 0.153 -0.006 0.049 -0.070 -0.134
## Item_8 0.030 -0.220 0.098 0.038 0.099 0.220 0.074 -0.307 -0.025
## Item_9 -0.156 0.270 0.366 -0.165 -0.076 0.019 -0.123 -0.322 0.186
## Item_10 -0.200 -0.070 0.182 -0.218 0.354 -0.249 -0.216 -0.041 0.153
# 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.
## -1.032 -0.333 0.069 0.036 0.302 2.703
##
## Item_1 Item_2 Item_3 Item_4 Item_5 Item_6 Item_7 Item_8 Item_9 Item_10
## Item_1 2.703 -0.992 -1.032 -0.550 0.136 -0.333 -0.248 0.338 -0.360
## Item_2 2.703 -0.454 -0.860 -0.456 -0.238 -0.114 -0.525 0.302 -0.508
## Item_3 -0.992 -0.454 1.035 0.375 0.265 0.250 0.377 -0.626 0.445
## Item_4 -1.032 -0.860 1.035 0.797 0.263 0.000 0.076 0.085 0.468
## Item_5 -0.550 -0.456 0.375 0.797 -0.191 0.423 -0.153 0.218 0.306
## Item_6 0.136 -0.238 0.265 0.263 -0.191 0.069 -0.100 0.056 0.219
## Item_7 -0.333 -0.114 0.250 0.000 0.423 0.069 -0.091 0.274 -0.263
## Item_8 -0.248 -0.525 0.377 0.076 -0.153 -0.100 -0.091 0.177 0.824
## Item_9 0.338 0.302 -0.626 0.085 0.218 0.056 0.274 0.177 -0.756
## Item_10 -0.360 -0.508 0.445 0.468 0.306 0.219 -0.263 0.824 -0.756
## End(No test)