1 Supplemental file 1 - further results
We include four tables with additional information on the analysis of items by graphical loglinear Rasch models (GLLRM).
Table S1 shows item fit statistics comparing observed correlations between an item and the rest score over the remaining items with the expected correlations under the GLLRM. These are not the only item fit statistics calculated during the analysis. However, they are particular important because significant differences between observed and expected correlations may suggest that a discrimination parameter may be needed to improve the fit of the model to data.
Under GLLRMs, the sum over items over locally dependent items have partial credit
distributions. In TCA, TCA+TCA3 and TCA2+TCA4 are partial credit super-items. For this reason, table S1 includes item fit statistics for super items. FAH consists of three pairs of locally dependent items, (FAH1, FAH3), (FAH2, FAH3) and (FAH2, FAH5). For this reason, FAH1+FAH2+FAH3+FAH5 is a partial credit super-item. The restscore for this item is defined by FAH4. The item fit statistics for FAH1+FAH2+FAH3+FAH5 therefore has to be the same as the item fit for FAH4. We include both statistics to make it clear what happens but acknowledge that the information provided by the fit statistic for
FAH1+FAH2+FAH3+FAH5 is redundant.
There are weak significant differences in three cases. The Benjamini-Hochberg procedure dismisses all three cases for which reason we conclude that there is no evidence against the GLLRM in Table S1.
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Table S1. Item fit statistics for the TCA, FAH, IA, and WS items Test and Class Anxiety (TCA)
items observed expected p
TCA1 0.54 0.58 0.369
TCA2 0.49 0.48 0.902
TCA3 0.60 0.57 0.475
TCA4 0.49 0.49 0.871
TCA5 0.36 0.39 0.588
TCA7 0.59 0.44 0.015
TCA8 0.32 0.38 0.277
TCA 1+3 0.44 0.46 0.764
TCA 2+4 0.32 0.38 0.277
Fear of Asking for Help (FAH)
items observed expected p
FAH1 0.63 0.62 0.801
FAH2 0.82 0.78 0.337
FAH3 0.80 0.76 0.352
FAH4 0.49 0.50 0.863
FAH5 0.56 0.63 0.170
FAH1+2+3+5 0.49 0.50 0.863
Interpretation Anxiety (IA)
items observed expected p
IA1 0.56 0.59 0.390
IA2 0.59 0.59 0.984
IA3 0.55 0.59 0.337
IA4 0.56 0.59 0.568
IA5 0.71 0.59 0.011
IA6 0.65 0.59 0.167
IA7 0.57 0.59 0.699
Worth of Statistics (WS)
items observed expected p
WS2 0.48 0.53 0.309
WS3R 0.64 0.54 0.047
WS5 0.59 0.62 0.602
WS6 0.66 0.61 0.261
WS7 0.50 0.53 0.538
WS5+6 0.58 0.55 0.518
Note. = Item-restscore correlations for the respective subscale Rasch or graphical log-linear Rasch models in Figure 1 and Table 2. -correlations are Goodman and Kruskal’s rank correlation for ordinal data.
Table S2 contains the results of testing whether the local dependence and/or DIF terms included in the GLLRMs are indeed necessary as well as the strength of the local dependence and the DIF in the form of gamma correlation coefficients. The evidence for local dependency of items and DIF is very strong in all cases, and all correlations are strong or very strong.
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Table S2. Conditional likelihood ratio tests of local independence and no DIF under the GLLRMs for the three subscales not fitting the Rasch model
LD and DIF terms within subscales
CLR Df p
Test and Class Anxiety
TCA1 & TCA3 65.39 9 < 0.0000 0.62
TCA2 & TCA4 26.32 9 0.0018 0.35
TCA5 & Age groups 19.05 6 0.0041 -0.33
TCA8 & Age groups 28.05 6 0.0001 -0.36
Fear of Asking for Help
FAH1 & FAH3 43.67 9 < 0.0000 0.54
FAH2 & FAH3 43.78 9 < 0.0000 0.66
FAH2 & FAH5 38.05 9 < 0.0000 0.67
Worth of Statistics
WS5 & WS6 25.03 6 0.0003 0.47
Note. -correlations are Goodman and Kruskal’s rank correlation for ordinal data.
Table S3 contains the category thresholds for all items; conditionally independent items as well as the super items made up of locally dependent items. It is noticeable that local dependence of items creates reversed thresholds in some cases, as can be seen in the thresholds for the super items in the Test and Class Anxiety subscale.
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Table S3. Item thresholds for conditionally independent items and super items made up of locally dependent items
Thresholds
items within subscales 1 2 3 4 5 6 7 8 9 10 11 12
Test and Class Anxiety
TCA5, age group 1 -1.99 -0.19 0.17
TCA5, age group 2 -1.84 0.16 2.02
TCA5, age group 3 -1.52 0.54 1.80
TCA7 0.41 1.31 2.59
TCA8, age group 1 -1.34 -0.32 2.54
TCA8, age group 2 -1.09 1.01 ---
TCA8, age group 3 -0.51 0.95 1.31
TCA1+TCA3 -2.26 -2.60 -1.25 -0.89 -0.01 0.50
TCA2+TCA4 -1.15 -0.74 0.31 1.61 2.53 0.75
Fear of Asking for Help -0.92 -0.91 -0.51 -0.44 -0.12 0.12 0.49 0.40 0.66 1.16 1.97 ---
FAH4 -1.28 -0.84 -0.05
FAH1+FAH2+FAH3+FAH5 Interpretation Anxiety
IA1 -3.12 -0.31 2.27
IA2 -2.92 -0.18 2.36
IA3 -1.90 0.35 3.05
IA4 -4.72 -1.21 1.04
IA5 -3.45 0.02 2.45
IA6 -1.69 0.64 2.61
IA7 -0.31 1.89 3.12
Worth of Statistics -3.45 0.02 2.45
WS2 -2.05 -0.17 3.09
WS3r -1.70 -0.46 2.41
WS7 -2.03 -0.81 1.82
WS5+WS6 --- -2.25 -1.54 0.07 0.92 2.70
Note. --- signifies values not occurring in the data.
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Two TCA items function differently in different age groups. Table S4 shows the DIF equated TCA scores where the direct effect of Age on the TCA scores as been taken into account to make the scores comparable across age groups. To calculate such scores, we select the
youngest age category as the reference, estimate the person parameters in the other age groups and calculate the expected score under the assumption that the item parameters had been the same as the item parameters in the reference group. The degree to which the differences between the observed and DIF equated scores are important depends on the application of the results. In this case, about one point should be added to scores above 13-14 in age groups 21 and 22+ to make them comparable with scores in the reference group. Table 3 in the article compares the averages of observed and DIF equated scores in the three age groups.
Table S4. DIF-equation table for the TCA raw score to adjust for age-DIF Raw score
Age 18-20
Equated score Age 21
Equated score Age 22+
7.00 7.00 7.00
8.00 8.07 8.18
9.00 9.13 9.31
10.00 10.21 10.44
11.00 11.30 11.58
12.00 12.40 12.71
13.00 13.52 13.84
14.00 14.64 14.96
15.00 15.77 16.05
16.00 16.89 17.11
17.00 18.00 18.12
18.00 19.07 19.09
19.00 20.12 20.01
20.00 21.13 20.89
21.00 22.12 21.75
22.00 23.09 22.59
23.00 24.05 23.45
24.00 25.01 24.30
25.00 25.97 25.17
26.00 26.95 26.06
27.00 27.00 27.00
