This function computes traditional IRT item fit statistics, including the \(\chi^{2}\) fit statistic (e.g., Bock, 1960; Yen, 1981), the log-likelihood ratio \(\chi^{2}\) fit statistic (\(G^{2}\); McKinley & Mills, 1985), and the infit and outfit statistics (Ames et al., 2015). It also returns contingency tables used to compute the \(\chi^{2}\) and \(G^{2}\) statistics.
Usage
irtfit(x, ...)
# Default S3 method
irtfit(
x,
score,
data,
group.method = c("equal.width", "equal.freq"),
n.width = 10,
loc.theta = "average",
range.score = NULL,
D = 1,
alpha = 0.05,
missing = NA,
overSR = 2,
min.collapse = 1,
pcm.loc = NULL,
...
)
# S3 method for class 'est_item'
irtfit(
x,
group.method = c("equal.width", "equal.freq"),
n.width = 10,
loc.theta = "average",
range.score = NULL,
alpha = 0.05,
missing = NA,
overSR = 2,
min.collapse = 1,
pcm.loc = NULL,
...
)
# S3 method for class 'est_irt'
irtfit(
x,
score,
group.method = c("equal.width", "equal.freq"),
n.width = 10,
loc.theta = "average",
range.score = NULL,
alpha = 0.05,
missing = NA,
overSR = 2,
min.collapse = 1,
pcm.loc = NULL,
...
)Arguments
- x
A data frame containing item metadata (e.g., item parameters, number of categories, IRT model types, etc.); or an object of class
est_irtobtained fromest_irt(), orest_itemfromest_item().See
est_irt()orsimdat()for more details about the item metadata. This data frame can be easily created using theshape_df()function.- ...
Further arguments passed to or from other methods.
- score
A numeric vector containing examinees' ability estimates (theta values).
- data
A matrix of examinees' item responses corresponding to the items specified in the
xargument. Rows represent examinees and columns represent items.- group.method
A character string specifying the method used to group examinees along the ability scale when computing the \(\chi^{2}\) and \(G^{2}\) fit statistics. Available options are:
"equal.width": Divides the ability scale into intervals of equal width."equal.freq": Divides the examinees into groups with (approximately) equal numbers of examinees.
Note that
"equal.freq"does not guarantee exactly equal group sizes due to ties in ability estimates. Default is"equal.width". The number of groups and the range of the ability scale are controlled by then.widthandrange.scorearguments, respectively.- n.width
An integer specifying the number of intervals (groups) into which the ability scale is divided for computing the fit statistics. Default is 10.
- loc.theta
A character string indicating the point on the ability scale at which the expected category probabilities are calculated for each group. Available options are:
"average": Uses the average ability estimate of examinees within each group."middle": Uses the midpoint of each group's ability interval.
Default is
"average".- range.score
A numeric vector of length two specifying the lower and upper bounds of the ability scale. Ability estimates below the lower bound or above the upper bound are truncated to the respective bound. If
NULL, the observed minimum and maximum of thescorevector are used. Note that this range restriction is independent of the grouping method specified ingroup.method. Default isNULL.- D
A scaling constant used in IRT models to make the logistic function closely approximate the normal ogive function. A value of 1.7 is commonly used for this purpose. Default is 1.
- alpha
A numeric value specifying the significance level (\(\alpha\)) for the hypothesis tests of the \(\chi^{2}\) and \(G^{2}\) item fit statistics. Default is
0.05.- missing
A value indicating missing responses in the data set. Default is
NA. See Details below.- overSR
A numeric threshold used to identify ability groups (intervals) whose standardized residuals exceed the specified value. This is used to compute the proportion of misfitting groups per item. Default is 2.
- min.collapse
An integer specifying the minimum expected frequency required for a cell in the contingency table. Neighboring groups will be merged if any expected cell frequency falls below this threshold when computing the \(\chi^{2}\) and \(G^{2}\) statistics. Default is 1.
- pcm.loc
A vector of integers indicating the locations (indices) of partial credit model (PCM) items for which slope parameters are fixed.
Value
This function returns an object of class irtfit, which includes
the following components:
- fit_stat
A data frame containing the results of three IRT item fit statistics— \(\chi^{2}\), \(G^{2}\), infit, and outfit—for all evaluated items. Each row corresponds to one item, and the columns include: the item ID; \(\chi^{2}\) statistic; \(G^{2}\) statistic; degrees of freedom for \(\chi^{2}\) and \(G^{2}\); critical values and p-values for both statistics; outfit and infit values; the number of examinees used to compute these statistics; and the proportion of ability groups (prior to cell collapsing) that have standardized residuals greater than the threshold specified in the
overSRargument.- contingency.fitstat
A list of contingency tables used to compute the \(\chi^{2}\) and \(G^{2}\) fit statistics for all items. Note that the cell-collapsing strategy is applied to these tables to ensure sufficient expected frequencies.
- contingency.plot
A list of contingency tables used to generate raw and standardized residual plots (Hambleton et al., 1991) via the
plot.irtfit(). Note that these tables are based on the original, uncollapsed groupings.- individual.info
A list of data frames containing individual residuals and corresponding variance values. This information is used to compute infit and outfit statistics.
- item_df
A data frame containing the item metadata provided in the argument
x.- ancillary
A list of ancillary information used during the item fit analysis.
Details
To compute the \(\chi^2\) and \(G^2\) item fit statistics, the group.method
argument determines how the ability scale is divided into groups:
"equal.width": Examinees are grouped based on intervals of equal width a long the ability scale."equal.freq": Examinees are grouped such that each group contains (approximately) the same number of individuals.
Note that "equal.freq" does not guarantee exactly equal frequencies across
all groups, since grouping is based on quantiles.
When dividing the ability scale into intervals to compute the \(\chi^2\) and \(G^2\) fit statistics, the intervals should be:
Wide enough to ensure that each group contains a sufficient number of examinees (to avoid unstable estimates),
Narrow enough to ensure that examinees within each group are relatively homogeneous in ability (Hambleton et al., 1991).
If you want to divide the ability scale into a number of groups other than
the default of 10, specify the desired number using the n.width argument.
For reference:
Yen (1981) used 10 fixed-width groups,
Bock (1960) allowed for flexibility in the number of groups.
Regarding degrees of freedom (df):
The \(\chi^2\) statistic is approximately chi-square distributed with degrees of freedom equal to the number of ability groups minus the number of item parameters (Ames et al., 2015).
The \(G^2\) statistic is approximately chi-square distributed with degrees of freedom equal to the number of ability groups (Ames et al., 2015; Muraki & Bock, 2003).
Note that if
"DRM"is specified for an item in the item metadata set, the item is treated as a"3PLM"when computing the degrees of freedom for the \(\chi^{2}\) fit statistic.
Note that infit and outfit statistics should be interpreted with caution when
applied to non-Rasch models. The returned object—particularly the contingency
tables—can be passed to plot.irtfit() to generate raw and standardized
residual plots (Hambleton et al., 1991).
Methods (by class)
irtfit(default): Default method for computing traditional IRT item fit statistics using a data framexthat contains item metadata.irtfit(est_item): An object created by the functionest_item().irtfit(est_irt): An object created by the functionest_irt().
References
Ames, A. J., & Penfield, R. D. (2015). An NCME Instructional Module on Item-Fit Statistics for Item Response Theory Models. Educational Measurement: Issues and Practice, 34(3), 39-48.
Bock, R.D. (1960), Methods and applications of optimal scaling. Chapel Hill, NC: L.L. Thurstone Psychometric Laboratory.
Hambleton, R. K., Swaminathan, H., & Rogers, H. J. (1991).Fundamentals of item response theory. Newbury Park, CA: Sage.
McKinley, R., & Mills, C. (1985). A comparison of several goodness-of-fit statistics. Applied Psychological Measurement, 9, 49-57.
Muraki, E. & Bock, R. D. (2003). PARSCALE 4: IRT item analysis and test scoring for rating scale data (Computer Software). Chicago, IL: Scientific Software International. URL http://www.ssicentral.com
Wells, C. S., & Bolt, D. M. (2008). Investigation of a nonparametric procedure for assessing goodness-of-fit in item response theory. Applied Measurement in Education, 21(1), 22-40.
Yen, W. M. (1981). Using simulation results to choose a latent trait model. Applied Psychological Measurement, 5, 245-262.
Author
Hwanggyu Lim hglim83@gmail.com
Examples
# \donttest{
## Example 1
## Use the simulated CAT data
# Identify items with more than 10,000 responses
over10000 <- which(colSums(simCAT_MX$res.dat, na.rm = TRUE) > 10000)
# Select items with more than 10,000 responses
x <- simCAT_MX$item.prm[over10000, ]
# Extract response data for the selected items
data <- simCAT_MX$res.dat[, over10000]
# Extract examinees' ability estimates
score <- simCAT_MX$score
# Compute item fit statistics
fit1 <- irtfit(
x = x, score = score, data = data, group.method = "equal.width",
n.width = 10, loc.theta = "average", range.score = NULL, D = 1, alpha = 0.05,
missing = NA, overSR = 2
)
# View the fit statistics
fit1$fit_stat
#> id X2 G2 df.X2 df.G2 crit.val.X2 crit.val.G2 p.X2 p.G2 outfit
#> 1 V37 157.239 137.111 7 9 14.07 16.92 0 0 1.129
#> 2 V40 134.853 121.555 8 10 15.51 18.31 0 0 1.087
#> 3 V59 182.470 166.750 8 10 15.51 18.31 0 0 1.087
#> 4 V63 172.870 153.429 7 9 14.07 16.92 0 0 1.091
#> 5 V66 216.148 191.918 8 10 15.51 18.31 0 0 1.196
#> 6 V74 158.851 145.358 8 10 15.51 18.31 0 0 1.105
#> 7 V75 251.708 226.279 8 10 15.51 18.31 0 0 1.161
#> 8 V84 220.177 190.837 8 10 15.51 18.31 0 0 1.099
#> 9 V89 216.934 190.497 8 10 15.51 18.31 0 0 1.151
#> 10 V97 162.835 146.236 8 10 15.51 18.31 0 0 1.086
#> 11 V107 212.665 187.084 8 10 15.51 18.31 0 0 1.112
#> 12 V150 241.878 210.551 8 10 15.51 18.31 0 0 1.112
#> 13 V157 166.947 148.510 8 10 15.51 18.31 0 0 1.139
#> 14 V166 161.125 135.352 8 10 15.51 18.31 0 0 1.087
#> 15 V172 257.947 232.775 8 10 15.51 18.31 0 0 1.109
#> 16 V176 217.621 191.815 8 10 15.51 18.31 0 0 1.112
#> 17 V185 159.682 135.802 7 9 14.07 16.92 0 0 1.184
#> 18 V186 190.901 170.650 8 10 15.51 18.31 0 0 1.118
#> 19 V187 217.861 192.502 8 10 15.51 18.31 0 0 1.090
#> 20 V201 707.671 998.945 26 30 38.89 43.77 0 0 0.776
#> 21 V202 1236.908 1746.382 20 24 31.41 36.42 0 0 0.725
#> 22 V211 935.227 1280.437 23 27 35.17 40.11 0 0 0.769
#> 23 V214 2157.262 2669.312 26 30 38.89 43.77 0 0 0.702
#> 24 V217 1322.558 1758.534 17 21 27.59 32.67 0 0 0.683
#> 25 V220 2091.594 3119.452 26 30 38.89 43.77 0 0 0.693
#> 26 V222 1006.092 1360.961 20 24 31.41 36.42 0 0 0.657
#> 27 V223 1090.650 1372.033 23 27 35.17 40.11 0 0 0.699
#> 28 V226 988.500 1425.971 23 27 35.17 40.11 0 0 0.765
#> infit N overSR.prop
#> 1 1.078 17939 0.500
#> 2 1.058 25834 0.800
#> 3 1.064 21249 0.800
#> 4 1.062 19778 0.700
#> 5 1.092 26369 0.900
#> 6 1.068 25948 0.800
#> 7 1.093 24606 0.700
#> 8 1.066 22926 0.800
#> 9 1.081 25991 0.700
#> 10 1.058 22275 0.800
#> 11 1.072 22510 0.800
#> 12 1.075 21040 0.700
#> 13 1.074 25736 0.800
#> 14 1.057 18980 0.600
#> 15 1.077 23044 0.700
#> 16 1.072 23353 0.800
#> 17 1.095 15965 0.500
#> 18 1.072 24494 0.800
#> 19 1.065 20929 0.800
#> 20 0.807 7384 0.725
#> 21 0.760 13254 0.750
#> 22 0.793 8375 0.850
#> 23 0.728 8348 0.825
#> 24 0.722 11879 0.600
#> 25 0.722 8159 0.825
#> 26 0.725 16423 0.750
#> 27 0.754 17179 0.800
#> 28 0.790 9487 0.650
# View the contingency tables used to compute fit statistics
fit1$contingency.fitstat
#> $V37
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 814 642 172 660.044874 153.9551 0.788697789 0.2113022
#> 2 1537 1001 536 1038.234261 498.7657 0.651268705 0.3487313
#> 3 2630 1388 1242 1400.800535 1229.1995 0.527756654 0.4722433
#> 4 4386 1667 2719 1663.315681 2722.6843 0.380072959 0.6199270
#> 5 3834 1081 2753 943.666706 2890.3333 0.281950965 0.7180490
#> 6 3107 616 2491 470.658865 2636.3411 0.198261989 0.8017380
#> 7 1147 145 1002 97.867617 1049.1324 0.126416739 0.8735833
#> 8 381 47 334 18.705807 362.2942 0.123359580 0.8766404
#> 9 103 1 102 2.614117 100.3859 0.009708738 0.9902913
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.81086594 0.1891341 -0.0221681499 0.0221681499
#> 2 0.67549399 0.3245060 -0.0242252840 0.0242252840
#> 3 0.53262378 0.4673762 -0.0048671235 0.0048671235
#> 4 0.37923294 0.6207671 0.0008400179 -0.0008400179
#> 5 0.24613112 0.7538689 0.0358198473 -0.0358198473
#> 6 0.15148338 0.8485166 0.0467786079 -0.0467786079
#> 7 0.08532486 0.9146751 0.0410918769 -0.0410918769
#> 8 0.04909661 0.9509034 0.0742629740 -0.0742629740
#> 9 0.02537977 0.9746202 -0.0156710371 0.0156710371
#>
#> $V40
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 269 225 44 249.56106 19.43894 0.83643123 0.1635688
#> 2 1097 906 191 952.18873 144.81127 0.82588879 0.1741112
#> 3 2264 1693 571 1785.98317 478.01683 0.74779152 0.2522085
#> 4 4469 2929 1540 3033.53507 1435.46493 0.65540389 0.3445961
#> 5 5123 2632 2491 2706.50075 2416.49925 0.51376147 0.4862385
#> 6 4778 1881 2897 1823.57709 2954.42291 0.39367936 0.6063206
#> 7 3957 1098 2859 999.18951 2957.81049 0.27748294 0.7225171
#> 8 2654 484 2170 414.03275 2239.96725 0.18236624 0.8176338
#> 9 768 98 670 66.98114 701.01886 0.12760417 0.8723958
#> 10 455 26 429 23.89007 431.10993 0.05714286 0.9428571
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.92773626 0.07226374 -0.091305037 0.091305037
#> 2 0.86799337 0.13200663 -0.042104586 0.042104586
#> 3 0.78886182 0.21113818 -0.041070305 0.041070305
#> 4 0.67879505 0.32120495 -0.023391154 0.023391154
#> 5 0.52830388 0.47169612 -0.014542407 0.014542407
#> 6 0.38166117 0.61833883 0.012018190 -0.012018190
#> 7 0.25251188 0.74748812 0.024971062 -0.024971062
#> 8 0.15600330 0.84399670 0.026362944 -0.026362944
#> 9 0.08721503 0.91278497 0.040389136 -0.040389136
#> 10 0.05250564 0.94749436 0.004637215 -0.004637215
#>
#> $V59
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 110 88 22 100.54210 9.457899 0.8000000 0.2000000
#> 2 494 389 105 424.47426 69.525740 0.7874494 0.2125506
#> 3 1645 1215 430 1299.36185 345.638149 0.7386018 0.2613982
#> 4 3933 2605 1328 2718.12089 1214.879109 0.6623443 0.3376557
#> 5 4239 2416 1823 2431.36905 1807.630949 0.5699457 0.4300543
#> 6 4744 2183 2561 2136.01650 2607.983504 0.4601602 0.5398398
#> 7 3568 1325 2243 1171.24358 2396.756418 0.3713565 0.6286435
#> 8 1969 566 1403 450.92230 1518.077696 0.2874556 0.7125444
#> 9 438 100 338 66.23718 371.762820 0.2283105 0.7716895
#> 10 109 20 89 9.88696 99.113040 0.1834862 0.8165138
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.91401910 0.0859809 -0.114019098 0.114019098
#> 2 0.85925964 0.1407404 -0.071810243 0.071810243
#> 3 0.78988562 0.2101144 -0.051283800 0.051283800
#> 4 0.69110625 0.3088937 -0.028761986 0.028761986
#> 5 0.57357137 0.4264286 -0.003625631 0.003625631
#> 6 0.45025643 0.5497436 0.009903774 -0.009903774
#> 7 0.32826334 0.6717367 0.043093167 -0.043093167
#> 8 0.22901082 0.7709892 0.058444741 -0.058444741
#> 9 0.15122644 0.8487736 0.077084063 -0.077084063
#> 10 0.09070605 0.9092939 0.092780185 -0.092780185
#>
#> $V63
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 748 623 125 647.359334 100.64067 0.8328877 0.1671123
#> 2 1331 1008 323 1035.496631 295.50337 0.7573253 0.2426747
#> 3 2540 1663 877 1721.385605 818.61440 0.6547244 0.3452756
#> 4 4481 2439 2042 2438.934149 2042.06585 0.5442981 0.4557019
#> 5 4133 1759 2374 1687.815345 2445.18466 0.4255988 0.5744012
#> 6 3855 1228 2627 1120.874746 2734.12525 0.3185473 0.6814527
#> 7 1956 513 1443 377.938553 1578.06145 0.2622699 0.7377301
#> 8 633 146 487 78.386234 554.61377 0.2306477 0.7693523
#> 9 101 16 85 7.415968 93.58403 0.1584158 0.8415842
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.86545366 0.1345463 -3.256595e-02 3.256595e-02
#> 2 0.77798395 0.2220161 -2.065863e-02 2.065863e-02
#> 3 0.67771087 0.3222891 -2.298646e-02 2.298646e-02
#> 4 0.54428345 0.4557165 1.469553e-05 -1.469553e-05
#> 5 0.40837536 0.5916246 1.722348e-02 -1.722348e-02
#> 6 0.29075869 0.7092413 2.778865e-02 -2.778865e-02
#> 7 0.19322012 0.8067799 6.904982e-02 -6.904982e-02
#> 8 0.12383291 0.8761671 1.068148e-01 -1.068148e-01
#> 9 0.07342543 0.9265746 8.499042e-02 -8.499042e-02
#>
#> $V66
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 714 660 54 684.298856 29.70114 0.92436975 0.07563025
#> 2 1602 1387 215 1441.152929 160.84707 0.86579276 0.13420724
#> 3 2560 1979 581 2060.105629 499.89437 0.77304688 0.22695313
#> 4 4577 2877 1700 2993.539060 1583.46094 0.62857767 0.37142233
#> 5 5127 2269 2858 2270.443275 2856.55673 0.44255900 0.55744100
#> 6 4753 1372 3381 1241.490009 3511.50999 0.28865979 0.71134021
#> 7 3828 666 3162 515.668506 3312.33149 0.17398119 0.82601881
#> 8 2353 234 2119 152.320754 2200.67925 0.09944751 0.90055249
#> 9 585 34 551 15.905649 569.09435 0.05811966 0.94188034
#> 10 270 9 261 3.552967 266.44703 0.03333333 0.96666667
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.95840176 0.04159824 -0.0340320110 0.0340320110
#> 2 0.89959609 0.10040391 -0.0338033267 0.0338033267
#> 3 0.80472876 0.19527124 -0.0316818862 0.0316818862
#> 4 0.65403956 0.34596044 -0.0254618876 0.0254618876
#> 5 0.44284051 0.55715949 -0.0002815047 0.0002815047
#> 6 0.26120135 0.73879865 0.0274584453 -0.0274584453
#> 7 0.13470964 0.86529036 0.0392715502 -0.0392715502
#> 8 0.06473470 0.93526530 0.0347128116 -0.0347128116
#> 9 0.02718914 0.97281086 0.0309305142 -0.0309305142
#> 10 0.01315914 0.98684086 0.0201741951 -0.0201741951
#>
#> $V74
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 262 236 26 250.67682 11.32318 0.90076336 0.09923664
#> 2 838 733 105 763.54729 74.45271 0.87470167 0.12529833
#> 3 1969 1575 394 1667.13159 301.86841 0.79989843 0.20010157
#> 4 4220 3029 1191 3154.21550 1065.78450 0.71777251 0.28222749
#> 5 5095 2952 2143 3043.63129 2051.36871 0.57939156 0.42060844
#> 6 4869 2178 2691 2122.31567 2746.68433 0.44731978 0.55268022
#> 7 4334 1318 3016 1232.88261 3101.11739 0.30410706 0.69589294
#> 8 3071 655 2416 525.77970 2545.22030 0.21328557 0.78671443
#> 9 887 117 770 82.12432 804.87568 0.13190530 0.86809470
#> 10 403 21 382 21.71724 381.28276 0.05210918 0.94789082
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.95678174 0.04321826 -0.05601838 0.05601838
#> 2 0.91115429 0.08884571 -0.03645262 0.03645262
#> 3 0.84668948 0.15331052 -0.04679106 0.04679106
#> 4 0.74744443 0.25255557 -0.02967192 0.02967192
#> 5 0.59737611 0.40262389 -0.01798455 0.01798455
#> 6 0.43588328 0.56411672 0.01143650 -0.01143650
#> 7 0.28446761 0.71553239 0.01963945 -0.01963945
#> 8 0.17120798 0.82879202 0.04207760 -0.04207760
#> 9 0.09258660 0.90741340 0.03931870 -0.03931870
#> 10 0.05388892 0.94611108 -0.00177974 0.00177974
#>
#> $V75
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 198 197 1 194.90459 3.095412 0.9949495 0.005050505
#> 2 556 518 38 536.13800 19.861999 0.9316547 0.068345324
#> 3 1254 1108 146 1164.94404 89.055955 0.8835726 0.116427432
#> 4 3346 2744 602 2902.30143 443.698567 0.8200837 0.179916318
#> 5 4800 3439 1361 3604.96323 1195.036774 0.7164583 0.283541667
#> 6 4828 2830 1998 2860.76808 1967.231922 0.5861640 0.413835957
#> 7 4440 1822 2618 1807.42060 2632.579401 0.4103604 0.589639640
#> 8 3457 994 2463 849.94075 2607.059249 0.2875325 0.712467457
#> 9 1109 210 899 143.92794 965.072058 0.1893598 0.810640216
#> 10 618 80 538 44.78631 573.213694 0.1294498 0.870550162
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.98436660 0.01563340 0.010582891 -0.010582891
#> 2 0.96427698 0.03572302 -0.032622304 0.032622304
#> 3 0.92898249 0.07101751 -0.045409924 0.045409924
#> 4 0.86739433 0.13260567 -0.047310650 0.047310650
#> 5 0.75103401 0.24896599 -0.034575672 0.034575672
#> 6 0.59253688 0.40746312 -0.006372841 0.006372841
#> 7 0.40707671 0.59292329 0.003283649 -0.003283649
#> 8 0.24586079 0.75413921 0.041671753 -0.041671753
#> 9 0.12978173 0.87021827 0.059578051 -0.059578051
#> 10 0.07246975 0.92753025 0.056980087 -0.056980087
#>
#> $V84
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 148 126 22 137.42177 10.57823 0.8513514 0.1486486
#> 2 667 534 133 583.41002 83.58998 0.8005997 0.1994003
#> 3 1945 1468 477 1564.90287 380.09713 0.7547558 0.2452442
#> 4 4143 2815 1328 2923.28176 1219.71824 0.6794593 0.3205407
#> 5 4394 2524 1870 2550.49492 1843.50508 0.5744197 0.4255803
#> 6 5181 2275 2906 2302.80495 2878.19505 0.4391044 0.5608956
#> 7 3748 1281 2467 1160.49271 2587.50729 0.3417823 0.6582177
#> 8 1929 518 1411 410.15413 1518.84587 0.2685329 0.7314671
#> 9 601 126 475 85.18522 515.81478 0.2096506 0.7903494
#> 10 170 40 130 14.22200 155.77800 0.2352941 0.7647059
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.92852544 0.07147456 -0.077174091 0.077174091
#> 2 0.87467769 0.12532231 -0.074077987 0.074077987
#> 3 0.80457731 0.19542269 -0.049821526 0.049821526
#> 4 0.70559540 0.29440460 -0.026136074 0.026136074
#> 5 0.58044946 0.41955054 -0.006029794 0.006029794
#> 6 0.44447113 0.55552887 -0.005366714 0.005366714
#> 7 0.30962986 0.69037014 0.032152425 -0.032152425
#> 8 0.21262526 0.78737474 0.055907657 -0.055907657
#> 9 0.14173913 0.85826087 0.067911454 -0.067911454
#> 10 0.08365885 0.91634115 0.151635272 -0.151635272
#>
#> $V89
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 376 358 18 362.432617 13.56738 0.95212766 0.04787234
#> 2 1091 954 137 1002.634148 88.36585 0.87442713 0.12557287
#> 3 2171 1737 434 1844.427583 326.57242 0.80009212 0.19990788
#> 4 4349 3068 1281 3206.237171 1142.76283 0.70544953 0.29455047
#> 5 5102 2850 2252 2873.633453 2228.36655 0.55860447 0.44139553
#> 6 4852 1918 2934 1858.613969 2993.38603 0.39530091 0.60469909
#> 7 4193 1047 3146 955.855905 3237.14410 0.24970188 0.75029812
#> 8 2796 457 2339 348.234296 2447.76570 0.16344778 0.83655222
#> 9 767 96 671 45.798485 721.20152 0.12516297 0.87483703
#> 10 294 19 275 9.465732 284.53427 0.06462585 0.93537415
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.96391654 0.03608346 -0.011788876 0.011788876
#> 2 0.91900472 0.08099528 -0.044577588 0.044577588
#> 3 0.84957512 0.15042488 -0.049482996 0.049482996
#> 4 0.73723550 0.26276450 -0.031785967 0.031785967
#> 5 0.56323666 0.43676334 -0.004632194 0.004632194
#> 6 0.38306141 0.61693859 0.012239495 -0.012239495
#> 7 0.22796468 0.77203532 0.021737204 -0.021737204
#> 8 0.12454732 0.87545268 0.038900466 -0.038900466
#> 9 0.05971119 0.94028881 0.065451780 -0.065451780
#> 10 0.03219637 0.96780363 0.032429482 -0.032429482
#>
#> $V97
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 572 485 87 511.987531 60.01247 0.8479021 0.1520979
#> 2 1239 986 253 1022.768395 216.23161 0.7958031 0.2041969
#> 3 2483 1762 721 1838.311851 644.68815 0.7096255 0.2903745
#> 4 4495 2757 1738 2782.912757 1712.08724 0.6133482 0.3866518
#> 5 4298 2083 2215 2083.695592 2214.30441 0.4846440 0.5153560
#> 6 4535 1707 2828 1622.134751 2912.86525 0.3764057 0.6235943
#> 7 3008 891 2117 735.214020 2272.78598 0.2962101 0.7037899
#> 8 1357 301 1056 218.740833 1138.25917 0.2218128 0.7781872
#> 9 249 53 196 25.020167 223.97983 0.2128514 0.7871486
#> 10 39 6 33 2.254606 36.74539 0.1538462 0.8461538
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.89508310 0.1049169 -0.0471809980 0.0471809980
#> 2 0.82547893 0.1745211 -0.0296758636 0.0296758636
#> 3 0.74035918 0.2596408 -0.0307337296 0.0307337296
#> 4 0.61911296 0.3808870 -0.0057647958 0.0057647958
#> 5 0.48480586 0.5151941 -0.0001618408 0.0001618408
#> 6 0.35769234 0.6423077 0.0187133956 -0.0187133956
#> 7 0.24441955 0.7555804 0.0517905519 -0.0517905519
#> 8 0.16119442 0.8388056 0.0606183988 -0.0606183988
#> 9 0.10048260 0.8995174 0.1123688056 -0.1123688056
#> 10 0.05781041 0.9421896 0.0960357451 -0.0960357451
#>
#> $V107
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 147 119 28 135.452087 11.54791 0.8095238 0.1904762
#> 2 620 508 112 534.542775 85.45723 0.8193548 0.1806452
#> 3 1808 1353 455 1415.191511 392.80849 0.7483407 0.2516593
#> 4 4094 2605 1489 2722.474468 1371.52553 0.6362970 0.3637030
#> 5 4277 2210 2067 2247.527136 2029.47286 0.5167173 0.4832827
#> 6 4820 1913 2907 1857.437044 2962.56296 0.3968880 0.6031120
#> 7 3783 1141 2642 973.927861 2809.07214 0.3016125 0.6983875
#> 8 2267 495 1772 371.722870 1895.27713 0.2183502 0.7816498
#> 9 559 98 461 54.746938 504.25306 0.1753131 0.8246869
#> 10 135 19 116 7.180443 127.81956 0.1407407 0.8592593
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.92144277 0.07855723 -0.111918960 0.111918960
#> 2 0.86216577 0.13783423 -0.042810927 0.042810927
#> 3 0.78273867 0.21726133 -0.034397959 0.034397959
#> 4 0.66499132 0.33500868 -0.028694301 0.028694301
#> 5 0.52549150 0.47450850 -0.008774173 0.008774173
#> 6 0.38536038 0.61463962 0.011527584 -0.011527584
#> 7 0.25744855 0.74255145 0.044163928 -0.044163928
#> 8 0.16397127 0.83602873 0.054378972 -0.054378972
#> 9 0.09793728 0.90206272 0.077375782 -0.077375782
#> 10 0.05318847 0.94681153 0.087552276 -0.087552276
#>
#> $V150
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 280 225 55 252.09604 27.90396 0.80357143 0.1964286
#> 2 877 686 191 727.72118 149.27882 0.78221209 0.2177879
#> 3 2167 1524 643 1602.51519 564.48481 0.70327642 0.2967236
#> 4 4349 2601 1748 2654.70473 1694.29527 0.59806852 0.4019315
#> 5 4286 2049 2237 2002.84093 2283.15907 0.47806813 0.5219319
#> 6 4520 1606 2914 1509.46067 3010.53933 0.35530973 0.6446903
#> 7 2977 816 2161 653.46383 2323.53617 0.27410144 0.7258986
#> 8 1313 287 1026 181.86735 1131.13265 0.21858340 0.7814166
#> 9 232 48 184 19.20296 212.79704 0.20689655 0.7931034
#> 10 39 1 38 1.77352 37.22648 0.02564103 0.9743590
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.90034302 0.09965698 -0.09677159 0.09677159
#> 2 0.82978469 0.17021531 -0.04757261 0.04757261
#> 3 0.73950863 0.26049137 -0.03623221 0.03623221
#> 4 0.61041728 0.38958272 -0.01234875 0.01234875
#> 5 0.46729840 0.53270160 0.01076973 -0.01076973
#> 6 0.33395148 0.66604852 0.02135826 -0.02135826
#> 7 0.21950414 0.78049586 0.05459730 -0.05459730
#> 8 0.13851283 0.86148717 0.08007057 -0.08007057
#> 9 0.08277137 0.91722863 0.12412518 -0.12412518
#> 10 0.04547487 0.95452513 -0.01983384 0.01983384
#>
#> $V157
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 573 510 63 539.603559 33.39644 0.89005236 0.1099476
#> 2 1507 1265 242 1319.518800 187.48120 0.83941606 0.1605839
#> 3 2532 1906 626 1974.430854 557.56915 0.75276461 0.2472354
#> 4 4573 2851 1722 2923.395659 1649.60434 0.62344194 0.3765581
#> 5 5126 2342 2784 2309.368158 2816.63184 0.45688646 0.5431135
#> 6 4731 1482 3249 1349.075807 3381.92419 0.31325301 0.6867470
#> 7 3701 708 2993 599.373605 3101.62640 0.19129965 0.8087004
#> 8 2189 265 1924 187.280219 2001.71978 0.12105984 0.8789402
#> 9 537 45 492 21.449704 515.55030 0.08379888 0.9162011
#> 10 267 7 260 5.562012 261.43799 0.02621723 0.9737828
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.94171651 0.05828349 -0.051664152 0.051664152
#> 2 0.87559310 0.12440690 -0.036177041 0.036177041
#> 3 0.77979102 0.22020898 -0.027026404 0.027026404
#> 4 0.63927305 0.36072695 -0.015831108 0.015831108
#> 5 0.45052051 0.54947949 0.006365947 -0.006365947
#> 6 0.28515659 0.71484341 0.028096426 -0.028096426
#> 7 0.16194910 0.83805090 0.029350553 -0.029350553
#> 8 0.08555515 0.91444485 0.035504697 -0.035504697
#> 9 0.03994358 0.96005642 0.043855300 -0.043855300
#> 10 0.02083151 0.97916849 0.005385721 -0.005385721
#>
#> $V166
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 779 658 121 669.116761 109.88324 0.8446727 0.1553273
#> 2 863 646 217 675.691289 187.30871 0.7485516 0.2514484
#> 3 2396 1603 793 1644.067798 751.93220 0.6690317 0.3309683
#> 4 3797 2068 1729 2085.249368 1711.75063 0.5446405 0.4553595
#> 5 3700 1597 2103 1579.414109 2120.58589 0.4316216 0.5683784
#> 6 3979 1333 2646 1221.380479 2757.61952 0.3350088 0.6649912
#> 7 2277 591 1686 478.965498 1798.03450 0.2595520 0.7404480
#> 8 950 194 756 129.789957 820.21004 0.2042105 0.7957895
#> 9 213 49 164 18.553175 194.44683 0.2300469 0.7699531
#> 10 26 5 21 1.347068 24.65293 0.1923077 0.8076923
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.85894321 0.1410568 -0.014270553 0.014270553
#> 2 0.78295630 0.2170437 -0.034404738 0.034404738
#> 3 0.68617187 0.3138281 -0.017140150 0.017140150
#> 4 0.54918340 0.4508166 -0.004542894 0.004542894
#> 5 0.42686868 0.5731313 0.004752943 -0.004752943
#> 6 0.30695664 0.6930434 0.028052154 -0.028052154
#> 7 0.21034936 0.7896506 0.049202680 -0.049202680
#> 8 0.13662101 0.8633790 0.067589519 -0.067589519
#> 9 0.08710411 0.9128959 0.142942842 -0.142942842
#> 10 0.05181031 0.9481897 0.140497386 -0.140497386
#>
#> $V172
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 66 58 8 62.11728 3.882718 0.8787879 0.1212121
#> 2 417 331 86 373.90608 43.093921 0.7937650 0.2062350
#> 3 1332 1029 303 1113.35331 218.646690 0.7725225 0.2274775
#> 4 3639 2510 1129 2722.70719 916.292814 0.6897499 0.3102501
#> 5 4962 2957 2005 3079.63866 1882.361340 0.5959291 0.4040709
#> 6 4827 2378 2449 2324.55470 2502.445303 0.4926455 0.5073545
#> 7 4181 1484 2697 1433.87328 2747.126721 0.3549390 0.6450610
#> 8 2720 752 1968 622.87207 2097.127926 0.2764706 0.7235294
#> 9 683 155 528 93.16829 589.831706 0.2269400 0.7730600
#> 10 217 22 195 18.82221 198.177788 0.1013825 0.8986175
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.9411709 0.05882906 -0.06238307 0.06238307
#> 2 0.8966573 0.10334274 -0.10289227 0.10289227
#> 3 0.8358508 0.16414917 -0.06332831 0.06332831
#> 4 0.7482020 0.25179797 -0.05845210 0.05845210
#> 5 0.6206446 0.37935537 -0.02471557 0.02471557
#> 6 0.4815734 0.51842662 0.01107216 -0.01107216
#> 7 0.3429498 0.65705016 0.01198917 -0.01198917
#> 8 0.2289971 0.77100291 0.04747350 -0.04747350
#> 9 0.1364104 0.86358961 0.09052958 -0.09052958
#> 10 0.0867383 0.91326170 0.01464419 -0.01464419
#>
#> $V176
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 34 30 4 32.64428 1.355724 0.8823529 0.1176471
#> 2 253 208 45 234.86038 18.139617 0.8221344 0.1778656
#> 3 953 773 180 839.06830 113.931704 0.8111228 0.1888772
#> 4 3167 2387 780 2552.06750 614.932500 0.7537101 0.2462899
#> 5 4775 3145 1630 3285.34265 1489.657353 0.6586387 0.3413613
#> 6 4843 2649 2194 2652.26790 2190.732104 0.5469750 0.4530250
#> 7 4425 1761 2664 1747.81331 2677.186687 0.3979661 0.6020339
#> 8 3381 998 2383 884.31622 2496.683785 0.2951789 0.7048211
#> 9 1007 215 792 158.16623 848.833767 0.2135055 0.7864945
#> 10 515 70 445 51.38197 463.618027 0.1359223 0.8640777
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.96012578 0.03987422 -0.0777728360 0.0777728360
#> 2 0.92830191 0.07169809 -0.1061675203 0.1061675203
#> 3 0.88044942 0.11955058 -0.0693266487 0.0693266487
#> 4 0.80583123 0.19416877 -0.0521210925 0.0521210925
#> 5 0.68802987 0.31197013 -0.0293911303 0.0293911303
#> 6 0.54764978 0.45235022 -0.0006747668 0.0006747668
#> 7 0.39498606 0.60501394 0.0029800422 -0.0029800422
#> 8 0.26155463 0.73844537 0.0336243078 -0.0336243078
#> 9 0.15706677 0.84293323 0.0564386963 -0.0564386963
#> 10 0.09977082 0.90022918 0.0361515080 -0.0361515080
#>
#> $V185
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 840 615 225 639.165283 200.8347 0.73214286 0.2678571
#> 2 1540 878 662 912.443545 627.5565 0.57012987 0.4298701
#> 3 2613 1114 1499 1126.441351 1486.5586 0.42632989 0.5736701
#> 4 4208 1288 2920 1173.914686 3034.0853 0.30608365 0.6939163
#> 5 3287 640 2647 541.119390 2745.8806 0.19470642 0.8052936
#> 6 2362 316 2046 220.376072 2141.6239 0.13378493 0.8662151
#> 7 777 81 696 37.603521 739.3965 0.10424710 0.8957529
#> 8 253 17 236 6.565049 246.4350 0.06719368 0.9328063
#> 9 85 1 84 1.061403 83.9386 0.01176471 0.9882353
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.76091105 0.2390889 -0.0287681938 0.0287681938
#> 2 0.59249581 0.4075042 -0.0223659385 0.0223659385
#> 3 0.43109122 0.5689088 -0.0047613284 0.0047613284
#> 4 0.27897212 0.7210279 0.0271115291 -0.0271115291
#> 5 0.16462409 0.8353759 0.0300823273 -0.0300823273
#> 6 0.09330062 0.9066994 0.0404843050 -0.0404843050
#> 7 0.04839578 0.9516042 0.0558513240 -0.0558513240
#> 8 0.02594881 0.9740512 0.0412448655 -0.0412448655
#> 9 0.01248709 0.9875129 -0.0007223891 0.0007223891
#>
#> $V186
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 426 372 54 395.970241 30.02976 0.8732394 0.1267606
#> 2 1230 1021 209 1064.755950 165.24405 0.8300813 0.1699187
#> 3 2495 1849 646 1943.114708 551.88529 0.7410822 0.2589178
#> 4 4490 2839 1651 2925.008568 1564.99143 0.6322940 0.3677060
#> 5 4430 2247 2183 2198.053318 2231.94668 0.5072235 0.4927765
#> 6 5172 1838 3334 1776.638854 3395.36115 0.3553751 0.6446249
#> 7 3699 946 2753 782.351535 2916.64847 0.2557448 0.7442552
#> 8 1849 328 1521 240.488195 1608.51181 0.1773932 0.8226068
#> 9 558 76 482 43.538047 514.46195 0.1362007 0.8637993
#> 10 145 16 129 5.996887 139.00311 0.1103448 0.8896552
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.92950761 0.07049239 -0.05626817 0.05626817
#> 2 0.86565524 0.13434476 -0.03557394 0.03557394
#> 3 0.77880349 0.22119651 -0.03772133 0.03772133
#> 4 0.65144957 0.34855043 -0.01915558 0.01915558
#> 5 0.49617456 0.50382544 0.01104891 -0.01104891
#> 6 0.34351099 0.65648901 0.01186410 -0.01186410
#> 7 0.21150352 0.78849648 0.04424127 -0.04424127
#> 8 0.13006392 0.86993608 0.04732926 -0.04732926
#> 9 0.07802517 0.92197483 0.05817554 -0.05817554
#> 10 0.04135784 0.95864216 0.06898699 -0.06898699
#>
#> $V187
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 137 103 34 123.162022 13.83798 0.7518248 0.2481752
#> 2 568 445 123 475.142273 92.85773 0.7834507 0.2165493
#> 3 1766 1241 525 1343.242718 422.75728 0.7027180 0.2972820
#> 4 4066 2585 1481 2664.223102 1401.77690 0.6357600 0.3642400
#> 5 4257 2257 2000 2274.322306 1982.67769 0.5301856 0.4698144
#> 6 4671 1964 2707 1927.387137 2743.61286 0.4204667 0.5795333
#> 7 3358 1117 2241 996.377436 2361.62256 0.3326385 0.6673615
#> 8 1689 476 1213 346.536448 1342.46355 0.2818236 0.7181764
#> 9 350 89 261 47.241324 302.75868 0.2542857 0.7457143
#> 10 67 12 55 5.494661 61.50534 0.1791045 0.8208955
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.89899286 0.1010071 -0.147168044 0.147168044
#> 2 0.83651809 0.1634819 -0.053067382 0.053067382
#> 3 0.76061309 0.2393869 -0.057895084 0.057895084
#> 4 0.65524425 0.3447558 -0.019484285 0.019484285
#> 5 0.53425471 0.4657453 -0.004069135 0.004069135
#> 6 0.41262837 0.5873716 0.007838335 -0.007838335
#> 7 0.29671752 0.7032825 0.035920954 -0.035920954
#> 8 0.20517256 0.7948274 0.076651007 -0.076651007
#> 9 0.13497521 0.8650248 0.119310503 -0.119310503
#> 10 0.08200987 0.9179901 0.097094610 -0.097094610
#>
#> $V201
#> total obs.freq.0 obs.freq.1 obs.freq.2 obs.freq.3 exp.freq.0 exp.freq.1
#> 1 38 33 1 1 3 21.74482 11.54804
#> 2 271 170 92 3 6 133.47491 87.44788
#> 3 442 252 135 30 25 185.48923 145.04012
#> 4 934 442 354 57 81 323.56372 300.62245
#> 5 1782 559 540 202 481 474.30099 535.05881
#> 6 1282 178 421 150 533 250.91952 341.75891
#> 7 1088 102 203 152 631 155.24163 250.08344
#> 8 760 0 114 79 567 72.59432 141.37026
#> 9 584 0 0 54 530 34.85516 83.03033
#> 10 203 0 0 0 203 6.28567 19.40046
#> exp.freq.2 exp.freq.3 obs.prop.0 obs.prop.1 obs.prop.2 obs.prop.3 exp.prob.0
#> 1 1.911186 2.795956 0.8684211 0.02631579 0.02631579 0.07894737 0.57223205
#> 2 17.854230 32.222982 0.6273063 0.33948339 0.01107011 0.02214022 0.49252733
#> 3 35.342701 76.127947 0.5701357 0.30542986 0.06787330 0.05656109 0.41965890
#> 4 87.041260 222.772564 0.4732334 0.37901499 0.06102784 0.08672377 0.34642797
#> 5 188.101033 584.539168 0.3136925 0.30303030 0.11335578 0.26992144 0.26616217
#> 6 145.059911 544.261660 0.1388456 0.32839314 0.11700468 0.41575663 0.19572506
#> 7 125.546273 557.128657 0.0937500 0.18658088 0.13970588 0.57996324 0.14268532
#> 8 85.793742 460.241679 0.0000000 0.15000000 0.10394737 0.74605263 0.09551884
#> 9 61.638014 404.476505 0.0000000 0.00000000 0.09246575 0.90753425 0.05968348
#> 10 18.660136 158.653732 0.0000000 0.00000000 0.00000000 1.00000000 0.03096389
#> exp.prob.1 exp.prob.2 exp.prob.3 raw.rsd.0 raw.rsd.1 raw.rsd.2
#> 1 0.30389579 0.05029437 0.0735778 0.29618900 -0.277579996 -0.023978577
#> 2 0.32268591 0.06588277 0.1189040 0.13477894 0.016797486 -0.054812657
#> 3 0.32814506 0.07996086 0.1722352 0.15047684 -0.022715198 -0.012087560
#> 4 0.32186558 0.09319193 0.2385145 0.12680544 0.057149408 -0.032164090
#> 5 0.30025747 0.10555614 0.3280242 0.04753031 0.002772832 0.007799645
#> 6 0.26658261 0.11315126 0.4245411 -0.05687950 0.061810524 0.003853424
#> 7 0.22985610 0.11539180 0.5120668 -0.04893532 -0.043275218 0.024314087
#> 8 0.18601350 0.11288650 0.6055812 -0.09551884 -0.036013496 -0.008939134
#> 9 0.14217522 0.10554454 0.6925968 -0.05968348 -0.142175216 -0.013078790
#> 10 0.09556878 0.09192185 0.7815455 -0.03096389 -0.095568783 -0.091921852
#> raw.rsd.3
#> 1 0.005369571
#> 2 -0.096763772
#> 3 -0.115674087
#> 4 -0.151790754
#> 5 -0.058102788
#> 6 -0.008784446
#> 7 0.067896455
#> 8 0.140471474
#> 9 0.214937491
#> 10 0.218454524
#>
#> $V202
#> total obs.freq.0 obs.freq.1 obs.freq.2 obs.freq.3 exp.freq.0 exp.freq.1
#> 1 775 775 0 0 0 559.447133 185.03778
#> 2 770 550 220 0 0 468.824055 237.01445
#> 3 1457 840 524 93 0 719.826935 519.40759
#> 4 2171 1016 910 236 9 786.348925 823.81848
#> 5 3525 647 1463 899 516 811.352068 1253.13473
#> 6 2698 169 641 875 1013 331.323585 762.47827
#> 7 1486 33 171 387 895 86.799790 290.99760
#> 8 372 1 18 48 305 8.596281 42.25366
#> exp.freq.2 exp.freq.3 obs.prop.0 obs.prop.1 obs.prop.2 obs.prop.3
#> 1 26.24556 4.269527 1.000000000 0.0000000 0.00000000 0.000000000
#> 2 51.38471 12.776778 0.714285714 0.2857143 0.00000000 0.000000000
#> 3 160.72471 57.040762 0.576527111 0.3596431 0.06382979 0.000000000
#> 4 370.11946 190.713138 0.467987103 0.4191617 0.10870567 0.004145555
#> 5 830.00430 630.508904 0.183546099 0.4150355 0.25503546 0.146382979
#> 6 752.48309 851.715059 0.062638992 0.2375834 0.32431431 0.375463306
#> 7 418.36399 689.838615 0.022207268 0.1150740 0.26043069 0.602288022
#> 8 90.68049 230.469575 0.002688172 0.0483871 0.12903226 0.819892473
#> exp.prob.0 exp.prob.1 exp.prob.2 exp.prob.3 raw.rsd.0 raw.rsd.1
#> 1 0.72186727 0.2387584 0.03386524 0.005509067 0.27813273 -0.23875842
#> 2 0.60886241 0.3078110 0.06673339 0.016593218 0.10542330 -0.02209669
#> 3 0.49404731 0.3564911 0.11031209 0.039149459 0.08247980 0.00315196
#> 4 0.36220586 0.3794650 0.17048340 0.087845757 0.10578124 0.03969669
#> 5 0.23017080 0.3554992 0.23546221 0.178867774 -0.04662470 0.05953625
#> 6 0.12280340 0.2826087 0.27890404 0.315683862 -0.06016441 -0.04502530
#> 7 0.05841170 0.1958261 0.28153701 0.464225178 -0.03620443 -0.08075209
#> 8 0.02310828 0.1135851 0.24376475 0.619541869 -0.02042011 -0.06519800
#> raw.rsd.2 raw.rsd.3
#> 1 -0.03386524 -0.005509067
#> 2 -0.06673339 -0.016593218
#> 3 -0.04648230 -0.039149459
#> 4 -0.06177773 -0.083700202
#> 5 0.01957325 -0.032484795
#> 6 0.04541027 0.059779444
#> 7 -0.02110632 0.138062843
#> 8 -0.11473249 0.200350604
#>
#> $V211
#> total obs.freq.0 obs.freq.1 obs.freq.2 obs.freq.3 exp.freq.0 exp.freq.1
#> 1 135 101 22 12 0 65.69728 43.98025
#> 2 369 234 99 28 8 146.94513 124.79548
#> 3 948 380 370 148 50 290.36831 314.35598
#> 4 1392 415 499 296 182 318.05316 429.25679
#> 5 2142 218 652 739 533 344.68686 580.71800
#> 6 1299 111 213 416 559 136.64613 290.23285
#> 7 914 0 146 232 536 60.21927 160.32232
#> 8 837 0 0 211 626 32.38527 108.94207
#> 9 339 0 0 0 339 6.25990 28.42711
#> exp.freq.2 exp.freq.3 obs.prop.0 obs.prop.1 obs.prop.2 obs.prop.3 exp.prob.0
#> 1 17.43195 7.890518 0.74814815 0.1629630 0.08888889 0.00000000 0.48664648
#> 2 62.15991 35.099478 0.63414634 0.2682927 0.07588076 0.02168022 0.39822529
#> 3 199.60071 143.674999 0.40084388 0.3902954 0.15611814 0.05274262 0.30629569
#> 4 339.78365 304.906407 0.29813218 0.3584770 0.21264368 0.13074713 0.22848646
#> 5 573.81736 642.777779 0.10177404 0.3043884 0.34500467 0.24883287 0.16091824
#> 6 361.54607 510.574950 0.08545035 0.1639723 0.32024634 0.43033102 0.10519332
#> 7 250.33427 443.124141 0.00000000 0.1597374 0.25382932 0.58643326 0.06588542
#> 8 214.93717 480.735492 0.00000000 0.0000000 0.25209080 0.74790920 0.03869208
#> 9 75.71219 228.600798 0.00000000 0.0000000 0.00000000 1.00000000 0.01846578
#> exp.prob.1 exp.prob.2 exp.prob.3 raw.rsd.0 raw.rsd.1 raw.rsd.2
#> 1 0.32577965 0.1291256 0.05844828 0.26150167 -0.16281669 -0.040236697
#> 2 0.33819914 0.1684550 0.09512054 0.23592106 -0.06990646 -0.092574281
#> 3 0.33159913 0.2105493 0.15155591 0.09454819 0.05869622 -0.054431128
#> 4 0.30837413 0.2440974 0.21904196 0.06964572 0.05010288 -0.031453771
#> 5 0.27111018 0.2678886 0.30008300 -0.05914419 0.03327825 0.077116077
#> 6 0.22342791 0.2783265 0.39305231 -0.01974298 -0.05945562 0.041919881
#> 7 0.17540735 0.2738887 0.48481854 -0.06588542 -0.01566993 -0.020059378
#> 8 0.13015779 0.2567947 0.57435543 -0.03869208 -0.13015779 -0.004703902
#> 9 0.08385578 0.2233398 0.67433864 -0.01846578 -0.08385578 -0.223339804
#> raw.rsd.3
#> 1 -0.05844828
#> 2 -0.07344032
#> 3 -0.09881329
#> 4 -0.08829483
#> 5 -0.05125013
#> 6 0.03727871
#> 7 0.10161473
#> 8 0.17355377
#> 9 0.32566136
#>
#> $V214
#> total obs.freq.0 obs.freq.1 obs.freq.2 obs.freq.3 exp.freq.0 exp.freq.1
#> 1 351 317 34 0 0 253.794941 42.834200
#> 2 218 172 24 22 0 134.918384 29.668287
#> 3 370 265 41 46 18 191.133607 52.208898
#> 4 1303 1016 187 75 25 534.637002 179.995633
#> 5 2248 713 373 799 363 667.221101 282.639875
#> 6 2130 85 175 854 1016 424.998919 226.369418
#> 7 1269 15 24 253 977 162.265520 107.710347
#> 8 265 0 9 83 173 21.564078 17.504119
#> 9 150 0 0 13 137 7.204947 7.270299
#> 10 44 0 0 0 44 1.110013 1.439040
#> exp.freq.2 exp.freq.3 obs.prop.0 obs.prop.1 obs.prop.2 obs.prop.3 exp.prob.0
#> 1 38.467628 15.90323 0.90313390 0.09686610 0.00000000 0.00000000 0.72306251
#> 2 34.714497 18.69883 0.78899083 0.11009174 0.10091743 0.00000000 0.61889167
#> 3 75.883798 50.77370 0.71621622 0.11081081 0.12432432 0.04864865 0.51657732
#> 4 322.449701 265.91766 0.77973906 0.14351497 0.05755948 0.01918649 0.41031236
#> 5 637.080262 661.05876 0.31717082 0.16592527 0.35542705 0.16147687 0.29680654
#> 6 641.571021 837.06064 0.03990610 0.08215962 0.40093897 0.47699531 0.19953001
#> 7 380.439550 618.58458 0.01182033 0.01891253 0.19936958 0.76989756 0.12786881
#> 8 75.604336 150.32747 0.00000000 0.03396226 0.31320755 0.65283019 0.08137388
#> 9 39.036491 96.48826 0.00000000 0.00000000 0.08666667 0.91333333 0.04803298
#> 10 9.926924 31.52402 0.00000000 0.00000000 0.00000000 1.00000000 0.02522758
#> exp.prob.1 exp.prob.2 exp.prob.3 raw.rsd.0 raw.rsd.1 raw.rsd.2
#> 1 0.12203476 0.1095944 0.04530835 0.18007139 -0.02516866 -0.10959438
#> 2 0.13609306 0.1592408 0.08577446 0.17009915 -0.02600132 -0.05832338
#> 3 0.14110513 0.2050913 0.13722621 0.19963890 -0.03029432 -0.08076702
#> 4 0.13813940 0.2474672 0.20408109 0.36942671 0.00537557 -0.18990768
#> 5 0.12572948 0.2833987 0.29406529 0.02036428 0.04019578 0.07202835
#> 6 0.10627672 0.3012071 0.39298622 -0.15962391 -0.02411710 0.09973192
#> 7 0.08487813 0.2997948 0.48745830 -0.11604848 -0.06596560 -0.10042518
#> 8 0.06605328 0.2852994 0.56727346 -0.08137388 -0.03209102 0.02790817
#> 9 0.04846866 0.2602433 0.64325508 -0.04803298 -0.04846866 -0.17357661
#> 10 0.03270546 0.2256119 0.71645506 -0.02522758 -0.03270546 -0.22561190
#> raw.rsd.3
#> 1 -0.04530835
#> 2 -0.08577446
#> 3 -0.08857756
#> 4 -0.18489460
#> 5 -0.13258842
#> 6 0.08400909
#> 7 0.28243926
#> 8 0.08555673
#> 9 0.27007825
#> 10 0.28354494
#>
#> $V217
#> total obs.freq.0 obs.freq.1 obs.freq.2 obs.freq.3 exp.freq.0 exp.freq.1
#> 1 909 872 32 5 0 652.823460 148.604849
#> 2 2243 1552 485 192 14 1348.046871 424.894714
#> 3 3118 1497 671 600 350 1335.829332 616.252804
#> 4 3119 525 610 989 995 820.080996 541.849213
#> 5 1882 36 116 567 1163 250.970188 239.400313
#> 6 538 0 4 35 499 31.891121 43.586768
#> 7 70 0 2 1 67 1.388533 2.903588
#> exp.freq.2 exp.freq.3 obs.prop.0 obs.prop.1 obs.prop.2 obs.prop.3
#> 1 75.99131 31.58038 0.95929593 0.035203520 0.00550055 0.000000000
#> 2 299.28184 170.77657 0.69193045 0.216228266 0.08559964 0.006241641
#> 3 635.31564 530.60222 0.48011546 0.215202053 0.19243105 0.112251443
#> 4 800.06054 957.00925 0.16832318 0.195575505 0.31708881 0.319012504
#> 5 510.32871 881.30079 0.01912859 0.061636557 0.30127524 0.617959617
#> 6 133.12581 329.39630 0.00000000 0.007434944 0.06505576 0.927509294
#> 7 13.62404 52.08384 0.00000000 0.028571429 0.01428571 0.957142857
#> exp.prob.0 exp.prob.1 exp.prob.2 exp.prob.3 raw.rsd.0 raw.rsd.1
#> 1 0.71817762 0.16348168 0.0835988 0.03474190 0.24111831 -0.12827816
#> 2 0.60100173 0.18943144 0.1334293 0.07613757 0.09092872 0.02679683
#> 3 0.42842506 0.19764362 0.2037574 0.17017390 0.05169040 0.01755843
#> 4 0.26293075 0.17372530 0.2565119 0.30683208 -0.09460757 0.02185020
#> 5 0.13335292 0.12720527 0.2711630 0.46827885 -0.11422433 -0.06556871
#> 6 0.05927718 0.08101630 0.2474457 0.61226079 -0.05927718 -0.07358135
#> 7 0.01983618 0.04147983 0.1946291 0.74405490 -0.01983618 -0.01290840
#> raw.rsd.2 raw.rsd.3
#> 1 -0.07809825 -0.03474190
#> 2 -0.04782962 -0.06989593
#> 3 -0.01132638 -0.05792246
#> 4 0.06057693 0.01218043
#> 5 0.03011227 0.14968077
#> 6 -0.18238998 0.31524851
#> 7 -0.18034337 0.21308796
#>
#> $V220
#> total obs.freq.0 obs.freq.1 obs.freq.2 obs.freq.3 exp.freq.0 exp.freq.1
#> 1 668 668 0 0 0 473.75960 73.39859
#> 2 814 706 108 0 0 529.13005 93.91865
#> 3 970 749 115 106 0 576.05411 114.63599
#> 4 954 625 150 110 69 506.09850 113.40446
#> 5 908 338 140 206 224 433.08278 106.76677
#> 6 1291 494 133 197 467 531.98578 146.95643
#> 7 967 130 144 193 500 335.09925 104.05904
#> 8 795 0 42 230 523 227.78915 79.23713
#> 9 630 0 0 68 562 145.34100 56.79509
#> 10 162 0 0 0 162 30.80343 13.24365
#> exp.freq.2 exp.freq.3 obs.prop.0 obs.prop.1 obs.prop.2 obs.prop.3 exp.prob.0
#> 1 56.21308 64.62874 1.0000000 0.00000000 0.0000000 0.00000000 0.7092210
#> 2 82.40645 108.54485 0.8673219 0.13267813 0.0000000 0.00000000 0.6500369
#> 3 112.77131 166.53860 0.7721649 0.11855670 0.1092784 0.00000000 0.5938702
#> 4 125.61607 208.88097 0.6551363 0.15723270 0.1153040 0.07232704 0.5305016
#> 5 130.11316 238.03729 0.3722467 0.15418502 0.2268722 0.24669604 0.4769634
#> 6 200.67677 411.38102 0.3826491 0.10302091 0.1525949 0.36173509 0.4120726
#> 7 159.73723 368.10448 0.1344364 0.14891417 0.1995863 0.51706308 0.3465349
#> 8 136.25246 351.72126 0.0000000 0.05283019 0.2893082 0.65786164 0.2865272
#> 9 109.71183 318.15208 0.0000000 0.00000000 0.1079365 0.89206349 0.2307000
#> 10 28.14728 89.80564 0.0000000 0.00000000 0.0000000 1.00000000 0.1901446
#> exp.prob.1 exp.prob.2 exp.prob.3 raw.rsd.0 raw.rsd.1 raw.rsd.2
#> 1 0.10987813 0.08415131 0.09674961 0.29077905 -0.1098781285 -0.084151314
#> 2 0.11537918 0.10123642 0.13334748 0.21728495 0.0172989565 -0.101236424
#> 3 0.11818143 0.11625908 0.17168928 0.17829473 0.0003752725 -0.006980729
#> 4 0.11887260 0.13167303 0.21895280 0.12463470 0.0383601029 -0.016369042
#> 5 0.11758455 0.14329643 0.26215561 -0.10471672 0.0366004766 0.083575815
#> 6 0.11383147 0.15544289 0.31865300 -0.02942354 -0.0108105553 -0.002847999
#> 7 0.10761018 0.16518844 0.38066647 -0.21209850 0.0413039899 0.034397905
#> 8 0.09966934 0.17138674 0.44241668 -0.28652724 -0.0468391524 0.117921436
#> 9 0.09015094 0.17414577 0.50500330 -0.23069999 -0.0901509432 -0.066209258
#> 10 0.08175093 0.17374861 0.55435583 -0.19014463 -0.0817509344 -0.173748613
#> raw.rsd.3
#> 1 -0.09674961
#> 2 -0.13334748
#> 3 -0.17168928
#> 4 -0.14662576
#> 5 -0.01545957
#> 6 0.04308209
#> 7 0.13639661
#> 8 0.21544495
#> 9 0.38706020
#> 10 0.44564417
#>
#> $V222
#> total obs.freq.0 obs.freq.1 obs.freq.2 obs.freq.3 exp.freq.0 exp.freq.1
#> 1 394 345 45 4 0 284.596081 93.20502
#> 2 1394 931 419 28 16 802.986135 439.68162
#> 3 3200 1563 1205 244 188 1333.490397 1119.03319
#> 4 3861 859 1429 588 985 951.026569 1229.78715
#> 5 3760 173 746 601 2240 395.801024 818.96704
#> 6 2455 0 108 281 2066 91.813756 296.06164
#> 7 934 0 0 60 874 11.677873 56.96378
#> 8 425 0 0 0 425 1.381017 10.86376
#> exp.freq.2 exp.freq.3 obs.prop.0 obs.prop.1 obs.prop.2 obs.prop.3
#> 1 9.927696 6.271204 0.87563452 0.11421320 0.01015228 0.00000000
#> 2 75.661490 75.670754 0.66786227 0.30057389 0.02008608 0.01147776
#> 3 295.122521 452.353892 0.48843750 0.37656250 0.07625000 0.05875000
#> 4 499.773884 1180.412400 0.22248122 0.37011137 0.15229215 0.25511526
#> 5 532.552274 2012.679661 0.04601064 0.19840426 0.15984043 0.59574468
#> 6 300.028719 1767.095888 0.00000000 0.04399185 0.11446029 0.84154786
#> 7 87.325305 778.033045 0.00000000 0.00000000 0.06423983 0.93576017
#> 8 26.857641 385.897579 0.00000000 0.00000000 0.00000000 1.00000000
#> exp.prob.0 exp.prob.1 exp.prob.2 exp.prob.3 raw.rsd.0 raw.rsd.1
#> 1 0.722325079 0.23656096 0.02519720 0.01591676 0.153309439 -0.12234776
#> 2 0.576030226 0.31541006 0.05427653 0.05428318 0.091832041 -0.01483617
#> 3 0.416715749 0.34969787 0.09222579 0.14136059 0.071721751 0.02686463
#> 4 0.246316128 0.31851519 0.12944157 0.30572712 -0.023834905 0.05159618
#> 5 0.105266230 0.21781038 0.14163624 0.53528714 -0.059255592 -0.01940613
#> 6 0.037398679 0.12059537 0.12221129 0.71979466 -0.037398679 -0.07660352
#> 7 0.012503076 0.06098905 0.09349604 0.83301183 -0.012503076 -0.06098905
#> 8 0.003249452 0.02556180 0.06319445 0.90799430 -0.003249452 -0.02556180
#> raw.rsd.2 raw.rsd.3
#> 1 -0.015044915 -0.01591676
#> 2 -0.034190452 -0.04280542
#> 3 -0.015975788 -0.08261059
#> 4 0.022850587 -0.05061186
#> 5 0.018204183 0.06045754
#> 6 -0.007751006 0.12175320
#> 7 -0.029256215 0.10274835
#> 8 -0.063194450 0.09200570
#>
#> $V223
#> total obs.freq.0 obs.freq.1 obs.freq.2 obs.freq.3 exp.freq.0 exp.freq.1
#> 1 173 169 4 0 0 150.41445 15.45807
#> 2 415 385 25 5 0 334.82686 47.63071
#> 3 1676 1368 195 113 0 1198.01840 235.50067
#> 4 3762 2611 653 340 158 2167.05329 603.67504
#> 5 3255 1205 542 920 588 1285.76857 519.69396
#> 6 3713 612 470 1199 1432 867.84595 496.99478
#> 7 2516 96 210 743 1467 308.63792 245.60750
#> 8 1234 12 16 231 975 70.07068 77.83838
#> 9 435 0 2 69 364 10.29288 16.09384
#> exp.freq.2 exp.freq.3 obs.prop.0 obs.prop.1 obs.prop.2 obs.prop.3
#> 1 5.819837 1.307636 0.976878613 0.023121387 0.00000000 0.00000000
#> 2 24.822381 7.720057 0.927710843 0.060240964 0.01204819 0.00000000
#> 3 169.594012 72.886910 0.816229117 0.116348449 0.06742243 0.00000000
#> 4 616.065011 375.206651 0.694045720 0.173577884 0.09037746 0.04199894
#> 5 769.524106 680.013368 0.370199693 0.166513057 0.28264209 0.18064516
#> 6 1042.679193 1305.480081 0.164826286 0.126582278 0.32291947 0.38567196
#> 7 716.017554 1245.737023 0.038155803 0.083465819 0.29531002 0.58306836
#> 8 316.767761 769.323182 0.009724473 0.012965964 0.18719611 0.79011345
#> 9 92.287390 316.325896 0.000000000 0.004597701 0.15862069 0.83678161
#> exp.prob.0 exp.prob.1 exp.prob.2 exp.prob.3 raw.rsd.0 raw.rsd.1
#> 1 0.86944771 0.08935302 0.03364068 0.007558592 0.10743091 -0.066231637
#> 2 0.80681170 0.11477279 0.05981297 0.018602548 0.12089914 -0.054531821
#> 3 0.71480812 0.14051353 0.10118974 0.043488610 0.10142100 -0.024165080
#> 4 0.57603756 0.16046652 0.16375997 0.099735952 0.11800816 0.013111365
#> 5 0.39501338 0.15966020 0.23641294 0.208913477 -0.02481369 0.006852854
#> 6 0.23373174 0.13385262 0.28081853 0.351597113 -0.06890545 -0.007270342
#> 7 0.12267008 0.09761824 0.28458567 0.495126003 -0.08451428 -0.014152426
#> 8 0.05678337 0.06307810 0.25669997 0.623438559 -0.04705889 -0.050112140
#> 9 0.02366179 0.03699732 0.21215492 0.727185967 -0.02366179 -0.032399624
#> raw.rsd.2 raw.rsd.3
#> 1 -0.03364068 -0.007558592
#> 2 -0.04776477 -0.018602548
#> 3 -0.03376731 -0.043488610
#> 4 -0.07338251 -0.057737015
#> 5 0.04622915 -0.028268316
#> 6 0.04210094 0.034074850
#> 7 0.01072434 0.087942360
#> 8 -0.06950386 0.166674893
#> 9 -0.05353423 0.109595642
#>
#> $V226
#> total obs.freq.0 obs.freq.1 obs.freq.2 obs.freq.3 exp.freq.0 exp.freq.1
#> 1 439 439 0 0 0 296.56451 73.90696
#> 2 771 591 153 27 0 460.26543 140.76126
#> 3 1250 727 229 231 63 630.83738 238.17158
#> 4 1585 690 368 360 167 642.20668 299.75893
#> 5 1939 600 369 581 389 613.21468 346.75748
#> 6 1486 295 226 528 437 339.05169 236.41948
#> 7 1203 67 143 358 635 188.92608 161.67764
#> 8 568 0 2 230 336 59.04750 61.75040
#> 9 246 0 0 1 245 15.61834 20.30524
#> exp.freq.2 exp.freq.3 obs.prop.0 obs.prop.1 obs.prop.2 obs.prop.3
#> 1 50.06356 18.46497 1.0000000 0.000000000 0.000000000 0.0000000
#> 2 117.01139 52.96192 0.7665370 0.198443580 0.035019455 0.0000000
#> 3 244.41769 136.57335 0.5816000 0.183200000 0.184800000 0.0504000
#> 4 380.31162 262.72277 0.4353312 0.232176656 0.227129338 0.1053628
#> 5 532.97800 446.04984 0.3094379 0.190304281 0.299638989 0.2006189
#> 6 448.09570 462.43313 0.1985195 0.152086137 0.355316285 0.2940781
#> 7 376.07822 476.31805 0.0556941 0.118869493 0.297589360 0.5278470
#> 8 175.52869 271.67341 0.0000000 0.003521127 0.404929577 0.5915493
#> 9 71.79002 138.28640 0.0000000 0.000000000 0.004065041 0.9959350
#> exp.prob.0 exp.prob.1 exp.prob.2 exp.prob.3 raw.rsd.0 raw.rsd.1
#> 1 0.6755456 0.16835299 0.1140400 0.04206144 0.324454423 -0.168352990
#> 2 0.5969720 0.18256973 0.1517657 0.06869250 0.169564942 0.015873847
#> 3 0.5046699 0.19053727 0.1955341 0.10925868 0.076930095 -0.007337267
#> 4 0.4051777 0.18912235 0.2399442 0.16575569 0.030153517 0.043054304
#> 5 0.3162531 0.17883315 0.2748726 0.23004117 -0.006815206 0.011471131
#> 6 0.2281640 0.15909790 0.3015449 0.31119322 -0.029644473 -0.007011765
#> 7 0.1570458 0.13439538 0.3126170 0.39594186 -0.101351690 -0.015525888
#> 8 0.1039569 0.10871549 0.3090294 0.47829825 -0.103956874 -0.105194360
#> 9 0.0634892 0.08254161 0.2918294 0.56213983 -0.063489200 -0.082541609
#> raw.rsd.2 raw.rsd.3
#> 1 -0.11403999 -0.04206144
#> 2 -0.11674628 -0.06869250
#> 3 -0.01073415 -0.05885868
#> 4 -0.01281490 -0.06039292
#> 5 0.02476637 -0.02942230
#> 6 0.05377140 -0.01711516
#> 7 -0.01502761 0.13190519
#> 8 0.09590019 0.11325104
#> 9 -0.28776432 0.43379513
#>
## Example 2
## Import the "-prm.txt" output file from flexMIRT
flex_sam <- system.file("extdata", "flexmirt_sample-prm.txt", package = "irtQ")
# Select the first two dichotomous items and the last polytomous item
x <- bring.flexmirt(file = flex_sam, "par")$Group1$full_df[c(1:2, 55), ]
# Generate ability values from a standard normal distribution
set.seed(10)
score <- rnorm(1000, mean = 0, sd = 1)
# Simulate response data
data <- simdat(x = x, theta = score, D = 1)
# Compute item fit statistics
fit2 <- irtfit(
x = x, score = score, data = data, group.method = "equal.freq",
n.width = 11, loc.theta = "average", range.score = c(-4, 4), D = 1, alpha = 0.05
)
# View the fit statistics
fit2$fit_stat
#> id X2 G2 df.X2 df.G2 crit.val.X2 crit.val.G2 p.X2 p.G2 outfit
#> 1 CMC1 8.541 8.684 8 11 15.51 19.68 0.382 0.651 1.007
#> 2 CMC2 8.812 10.095 7 10 14.07 18.31 0.266 0.432 0.843
#> 3 AFR3 42.396 43.817 39 44 54.57 60.48 0.327 0.479 0.950
#> infit N overSR.prop
#> 1 1.003 1000 0.000
#> 2 1.003 1000 0.000
#> 3 0.955 1000 0.036
# View the contingency tables used to compute fit statistics
fit2$contingency.fitstat
#> $CMC1
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 91 70 21 61.91419 29.08581 0.7692308 0.2307692
#> 2 91 56 35 58.97557 32.02443 0.6153846 0.3846154
#> 3 91 58 33 56.57872 34.42128 0.6373626 0.3626374
#> 4 91 55 36 54.61312 36.38688 0.6043956 0.3956044
#> 5 91 50 41 52.85925 38.14075 0.5494505 0.4505495
#> 6 90 53 37 49.96450 40.03550 0.5888889 0.4111111
#> 7 91 42 49 47.89655 43.10345 0.4615385 0.5384615
#> 8 91 44 47 45.00921 45.99079 0.4835165 0.5164835
#> 9 91 45 46 41.96040 49.03960 0.4945055 0.5054945
#> 10 91 36 55 38.18202 52.81798 0.3956044 0.6043956
#> 11 91 36 55 30.10521 60.89479 0.3956044 0.6043956
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.6803758 0.3196242 0.088855008 -0.088855008
#> 2 0.6480831 0.3519169 -0.032698520 0.032698520
#> 3 0.6217442 0.3782558 0.015618466 -0.015618466
#> 4 0.6001442 0.3998558 0.004251382 -0.004251382
#> 5 0.5808709 0.4191291 -0.031420344 0.031420344
#> 6 0.5551611 0.4448389 0.033727786 -0.033727786
#> 7 0.5263357 0.4736643 -0.064797264 0.064797264
#> 8 0.4946067 0.5053933 -0.011090181 0.011090181
#> 9 0.4611033 0.5388967 0.033402221 -0.033402221
#> 10 0.4195826 0.5804174 -0.023978208 0.023978208
#> 11 0.3308265 0.6691735 0.064777861 -0.064777861
#>
#> $CMC2
#> total obs.freq.0 obs.freq.1 exp.freq.0 exp.freq.1 obs.prop.0 obs.prop.1
#> 1 91 56 35 59.847423 31.15258 0.61538462 0.3846154
#> 2 91 41 50 40.052623 50.94738 0.45054945 0.5494505
#> 3 91 28 63 26.361491 64.63851 0.30769231 0.6923077
#> 4 91 14 77 18.322089 72.67791 0.15384615 0.8461538
#> 5 91 17 74 13.239430 77.76057 0.18681319 0.8131868
#> 6 90 11 79 8.575110 81.42489 0.12222222 0.8777778
#> 7 91 4 87 5.498524 85.50148 0.04395604 0.9560440
#> 8 91 6 85 3.409008 87.59099 0.06593407 0.9340659
#> 9 91 1 90 2.103482 88.89652 0.01098901 0.9890110
#> 10 182 0 182 1.535797 180.46420 0.00000000 1.0000000
#> exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1
#> 1 0.657663986 0.3423360 -0.042279370 0.042279370
#> 2 0.440138716 0.5598613 0.010410735 -0.010410735
#> 3 0.289686715 0.7103133 0.018005593 -0.018005593
#> 4 0.201341642 0.7986584 -0.047495489 0.047495489
#> 5 0.145488246 0.8545118 0.041324940 -0.041324940
#> 6 0.095278998 0.9047210 0.026943224 -0.026943224
#> 7 0.060423345 0.9395767 -0.016467301 0.016467301
#> 8 0.037461630 0.9625384 0.028472436 -0.028472436
#> 9 0.023115182 0.9768848 -0.012126171 0.012126171
#> 10 0.008438447 0.9915616 -0.008438447 0.008438447
#>
#> $AFR3
#> total obs.freq.0 obs.freq.1 obs.freq.2 obs.freq.3 obs.freq.4 exp.freq.0
#> 1 91 70 9 7 3 2 64.382932
#> 2 91 53 13 7 5 13 52.714982
#> 3 91 35 18 14 5 19 45.010677
#> 4 91 43 15 13 5 15 39.682474
#> 5 91 39 20 8 12 12 35.552292
#> 6 90 38 12 14 8 18 30.464603
#> 7 91 30 13 19 11 18 26.322302
#> 8 91 20 18 13 8 32 22.209861
#> 9 91 17 17 13 10 34 18.601260
#> 10 91 13 11 12 7 48 14.938697
#> 11 91 7 5 7 11 61 9.220059
#> exp.freq.1 exp.freq.2 exp.freq.3 exp.freq.4 obs.prop.0 obs.prop.1 obs.prop.2
#> 1 10.550129 6.381702 3.612889 6.072348 0.76923077 0.09890110 0.07692308
#> 2 13.386387 9.152465 5.591455 10.154711 0.58241758 0.14285714 0.07692308
#> 3 14.469492 10.824328 7.029807 13.665695 0.38461538 0.19780220 0.15384615
#> 4 14.785266 11.830812 8.068613 16.632834 0.47252747 0.16483516 0.14285714
#> 5 14.754971 12.480281 8.881067 19.331389 0.42857143 0.21978022 0.08791209
#> 6 14.232327 12.883558 9.684825 22.734686 0.42222222 0.13333333 0.15555556
#> 7 13.688501 13.270488 10.580120 27.138589 0.32967033 0.14285714 0.20879121
#> 8 12.704352 13.174325 11.168933 31.742529 0.21978022 0.19780220 0.14285714
#> 9 11.544767 12.751245 11.491416 36.611312 0.18681319 0.18681319 0.14285714
#> 10 10.056405 11.893203 11.501006 42.610689 0.14285714 0.12087912 0.13186813
#> 11 7.029158 9.345416 10.316679 55.088688 0.07692308 0.05494505 0.07692308
#> obs.prop.3 obs.prop.4 exp.prob.0 exp.prob.1 exp.prob.2 exp.prob.3 exp.prob.4
#> 1 0.03296703 0.02197802 0.7075048 0.11593548 0.07012859 0.03970208 0.0667291
#> 2 0.05494505 0.14285714 0.5792855 0.14710316 0.10057654 0.06144456 0.1115902
#> 3 0.05494505 0.20879121 0.4946228 0.15900541 0.11894866 0.07725063 0.1501725
#> 4 0.05494505 0.16483516 0.4360711 0.16247545 0.13000892 0.08866608 0.1827784
#> 5 0.13186813 0.13186813 0.3906845 0.16214254 0.13714595 0.09759414 0.2124328
#> 6 0.08888889 0.20000000 0.3384956 0.15813696 0.14315065 0.10760917 0.2526076
#> 7 0.12087912 0.19780220 0.2892561 0.15042309 0.14582953 0.11626506 0.2982263
#> 8 0.08791209 0.35164835 0.2440644 0.13960827 0.14477280 0.12273553 0.3488190
#> 9 0.10989011 0.37362637 0.2044095 0.12686557 0.14012357 0.12627930 0.4023221
#> 10 0.07692308 0.52747253 0.1641615 0.11050994 0.13069454 0.12638469 0.4682493
#> 11 0.12087912 0.67032967 0.1013193 0.07724349 0.10269687 0.11337010 0.6053702
#> raw.rsd.0 raw.rsd.1 raw.rsd.2 raw.rsd.3 raw.rsd.4
#> 1 0.061726017 -0.017034382 0.006794485 -0.006735045 -0.044751075
#> 2 0.003132066 -0.004246016 -0.023653459 -0.006499501 0.031266910
#> 3 -0.110007440 0.038796789 0.034897491 -0.022305576 0.058618736
#> 4 0.036456328 0.002359713 0.012848220 -0.033721026 -0.017943235
#> 5 0.037886906 0.057637678 -0.049233859 0.034273988 -0.080564714
#> 6 0.083726632 -0.024803631 0.012404906 -0.018720281 -0.052607626
#> 7 0.040414266 -0.007565948 0.062961675 0.004614064 -0.100424057
#> 8 -0.024284190 0.058193931 -0.001915655 -0.034823441 0.002829356
#> 9 -0.017596263 0.059947617 0.002733575 -0.016389191 -0.028695738
#> 10 -0.021304362 0.010369178 0.001173592 -0.049461610 0.059223202
#> 11 -0.024396252 -0.022298440 -0.025773797 0.007509020 0.064959469
#>
# Plot raw and standardized residuals for the first item (dichotomous)
plot(x = fit2, item.loc = 1, type = "both", ci.method = "wald",
show.table = TRUE, ylim.sr.adjust = TRUE)
#> interval point total obs.freq.0 obs.freq.1 obs.prop.0
#> 1 [-3.012164,-1.359216) -1.76327705 91 70 21 0.7692308
#> 2 [-1.359216,-0.8869352) -1.12022860 91 56 35 0.6153846
#> 3 [-0.8869352,-0.600789) -0.73065886 91 58 33 0.6373626
#> 4 [-0.600789,-0.3503181) -0.46176301 91 55 36 0.6043956
#> 5 [-0.3503181,-0.1182627) -0.24799010 91 50 41 0.5494505
#> 6 [-0.1182627,0.1417995) 0.00944368 90 53 37 0.5888889
#> 7 [0.1417995,0.4048853) 0.27078570 91 42 49 0.4615385
#> 8 [0.4048853,0.6625933) 0.53501489 91 44 47 0.4835165
#> 9 [0.6625933,0.9468582) 0.79571925 91 45 46 0.4945055
#> 10 [0.9468582,1.260075) 1.10229030 91 36 55 0.3956044
#> 11 [1.260075,3.54114] 1.73576474 91 36 55 0.3956044
#> obs.prop.1 exp.prob.0 exp.prob.1 raw.rsd.0 raw.rsd.1 se.0
#> 1 0.2307692 0.6803758 0.3196242 0.088855008 -0.088855008 0.04888477
#> 2 0.3846154 0.6480831 0.3519169 -0.032698520 0.032698520 0.05006275
#> 3 0.3626374 0.6217442 0.3782558 0.015618466 -0.015618466 0.05083677
#> 4 0.3956044 0.6001442 0.3998558 0.004251382 -0.004251382 0.05135217
#> 5 0.4505495 0.5808709 0.4191291 -0.031420344 0.031420344 0.05172411
#> 6 0.4111111 0.5551611 0.4448389 0.033727786 -0.033727786 0.05238291
#> 7 0.5384615 0.5263357 0.4736643 -0.064797264 0.064797264 0.05234149
#> 8 0.5164835 0.4946067 0.5053933 -0.011090181 0.011090181 0.05241119
#> 9 0.5054945 0.4611033 0.5388967 0.033402221 -0.033402221 0.05225540
#> 10 0.6043956 0.4195826 0.5804174 -0.023978208 0.023978208 0.05173188
#> 11 0.6043956 0.3308265 0.6691735 0.064777861 -0.064777861 0.04932293
#> se.1 std.rsd.0 std.rsd.1
#> 1 0.04888477 1.81764194 -1.81764194
#> 2 0.05006275 -0.65315069 0.65315069
#> 3 0.05083677 0.30722772 -0.30722772
#> 4 0.05135217 0.08278874 -0.08278874
#> 5 0.05172411 -0.60746032 0.60746032
#> 6 0.05238291 0.64387000 -0.64387000
#> 7 0.05234149 -1.23797144 1.23797144
#> 8 0.05241119 -0.21159947 0.21159947
#> 9 0.05225540 0.63921088 -0.63921088
#> 10 0.05173188 -0.46350931 0.46350931
#> 11 0.04932293 1.31334183 -1.31334183
# Plot raw and standardized residuals for the third item (polytomous)
plot(x = fit2, item.loc = 3, type = "both", ci.method = "wald",
show.table = FALSE, ylim.sr.adjust = TRUE)
# }