Manual

CAARS 2 Manual

Appendix N: Between-Subjects Measurement Invariance — Translation Study Analyses, Tables


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Table N.1. Between-Subjects Measurement Invariance by Language Version (French vs. English): CAARS 2 Self-Report

Scale Invariance Model χ2 df RMSEA CFI TLI SRMR Satorra-Bentler χ2 df ΔCFI
Inattention/​Executive Dysfunction Configural 1733.34*** 810 .066 .954 .951 .070
Weak 1756.82*** 839 .065 .955 .953 .070 22.72 29 .002
Strong 1755.77*** 868 .063 .956 .956 .071 36.25 29 .003
Strict 1760.44*** 891 .061 .957 .958 .071 33.90 23 .002
Hyperactivity Configural 568.80*** 130 .114 .937 .925 .087
Weak 583.69*** 143 .109 .937 .931 .087 9.01 13 .006
Strong 570.87*** 155 .101 .941 .940 .087 15.73 12 .009
Strict 563.76*** 162 .098 .943 .945 .087 11.10 7 .005
Impulsivity Configural 454.06*** 130 .098 .924 .909 .079
Weak 475.31*** 143 .094 .922 .915 .079 18.18 13 .006
Strong 465.68*** 155 .088 .927 .927 .079 17.98 12 .012
Strict 468.31*** 167 .083 .930 .934 .081 21.00 12 .012
Emotional Dysregulation Configural 174.254*** 54 .092 .986 .981 .045
Weak 180.742*** 63 .085 .986 .984 .045 5.37 9 .003
Strong 178.013*** 71 .076 .987 .987 .045 8.29 8 .003
Strict 186.31*** 77 .074 .987 .988 .045 11.51 6 .001
Negative Self-Concept Configural 141.43*** 28 .125 .981 .971 .044
Weak 154.51*** 35 .114 .980 .976 .044 7.87 7 .005
Strong 145.50*** 41 .099 .982 .982 .045 3.44 6 .006
Strict 150.33*** 44 .096 .982 .983 .045 6.12 3 .001
Note. N = 274 French version; N = 274 English version. RMSEA = Root mean square error of approximation; CFI = Comparative Fit Index; TLI = Tucker-Lewis Index; SRMR = Standardized root mean square residual; ∆CFI = change in CFI. *p < .05, **p < .01, ***p < .001. Exploration of partial invariance models for the Inattention/Executive Dysfunction, Hyperactivity, Emotional Dysregulation, and Negative Self-Concept scale revealed that six, five, three, and two intercepts had to be released, respectively, for the strict invariance hypothesis to hold.
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Table N.2. Between-Subjects Measurement Invariance by Language Version (French vs. English): CAARS 2 Observer

Scale Invariance Model χ2 df RMSEA CFI TLI SRMR Satorra-Bentler χ2 df ΔCFI
Inattention/​Executive Dysfunction Configural 1255.13*** 810 .054 .975 .974 .065
Weak 1279.74*** 839 .052 .976 .975 .065 29.14 29 .001
Strong 1281.81*** 868 .050 .977 .977 .065 22.98 29 .001
Strict 1301.93*** 893 .049 .977 .978 .065 37.15 25 .000
Hyperactivity Configural 510.17*** 130 .124 .933 .920 .101
Weak 528.25*** 142 .119 .932 .925 .101 10.45 12 -.001
Strong 532.32*** 153 .114 .933 .932 .101 14.44 11 .001
Strict 523.63*** 165 .107 .937 .940 .101 17.12 12 .004
Impulsivity Configural 393.54*** 130 .103 .955 .946 .074
Weak 414.26*** 143 .100 .954 .949 074 18.93 13 -.001
Strong 410.87*** 155 .093 .956 .956 075 13.13 12 .002
Strict 412.59*** 165 .089 .958 .960 075 14.50 10 .002
Emotional Dysregulation Configural 255.60*** 54 .140 .972 .963 .062
Weak 265.98*** 63 .130 .972 .968 .062 6.77 9 .000
Strong 261.91*** 71 .119 .974 .973 .062 8.62 8 .002
Strict 262.41*** 78 .111 .974 .976 .062 10.74 7 .000
Negative Self-Concept Configural 68.69*** 28 .087 .986 .978 .048
Weak 74.54*** 35 .077 .986 .983 .048 4.97 7 .000
Strong 83.49*** 40 .075 .985 .984 .048 9.73 5 -.001
Strict 91.69*** 46 .072 .984 .985 .048 10.67 6 -.001
Note. N = 195 French version; N = 195 English version. RMSEA = Root mean square error of approximation; CFI = Comparative Fit Index; TLI = Tucker-Lewis Index; SRMR = Standardized root mean square residual; ∆CFI = change in CFI. *p < .05, **p < .01, ***p < .001. Exploration of partial invariance models for the Hyperactivity and Negative Self-Concept scale revealed that one factor loading in each scale had to be released to meet the strong invariance hypothesis. To meet the strict invariance hypothesis, four item intercepts had to be released for the Inattention/Executive Dysfunction Scale, two for the Impulsivity Scale, and one for the Emotional Dysregulation Scale.
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Table N.3. Between-Subjects Measurement Invariance by Language Version (Spanish vs. English): CAARS 2 Self-Report

Scale Invariance Model χ2 df RMSEA CFI TLI SRMR Satorra-Bentler χ2 df ΔCFI
Inattention/​Executive Dysfunction Configural 1441.51*** 810 .053 .974 .972 .056
Weak 1465.66*** 840 .051 .974 .973 .056 30.15 30 .000
Strong 1468.67*** 869 .050 .975 .975 .056 33.77 29 .001
Strict 1475.00*** 896 .048 .976 .977 .056 36.47 27 .001
Hyperactivity Configural 501.77*** 130 .101 .944 .933 .077
Weak 514.84*** 141 .097 .944 .938 .077 11.87 11 .000
Strong 510.05*** 153 .091 .946 .945 .077 19.20 12 .002
Strict 499.11*** 163 .086 .949 .951 .078 14.93 10 .003
Impulsivity Configural 363.97*** 130 .080 .956 .947 .066
Weak 374.31*** 143 .076 .956 .952 .066 6.97 13 .000
Strong 370.15*** 155 .070 .959 .959 .067 15.56 12 .003
Strict 368.81*** 167 .066 .962 .964 .068 16.43 12 .003
Emotional Dysregulation Configural 218.84*** 54 .104 .969 .959 .054
Weak 229.38*** 63 .097 .969 .965 .054 6.90 9 .000
Strong 223.60*** 71 .087 .972 .971 .054 10.49 8 .003
Strict 223.39*** 79 .081 .973 .975 .055 12.17 8 .001
Negative Self-Concept Configural 94.63*** 28 .092 .986 .979 .046
Weak 103.54*** 35 .083 .986 .983 .046 6.76 7 .000
Strong 95.02*** 41 .068 .989 .988 .047 5.00 6 .003
Strict 95.84*** 45 .063 .989 .990 .047 4.64 4 .000
Note. N = 283 Spanish version; N = 283 English version. RMSEA = Root mean square error of approximation; CFI = Comparative Fit Index; TLI = Tucker-Lewis Index; SRMR = Standardized root mean square residual; ∆CFI = change in CFI. *p < .05, **p < .01, ***p < .001. Exploration of partial invariance models found that two item intercepts had to be released for the Inattention/Executive Dysfunction, Hyperactivity, and Negative Self-Concept scale for the strict invariance model to hold.
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Table N.4. Between-Subjects Measurement Invariance by Language Version (Spanish vs. English): CAARS 2 Observer

Scale Invariance Model χ2 df RMSEA CFI TLI SRMR Satorra-Bentler χ2 df ΔCFI
Inattention/​Executive Dysfunction Configural 1366.89*** 810 .055 .980 .979 .056
Weak 1394.48*** 840 .054 .980 .980 .056 31.37 30 .000
Strong 1395.46*** 869 .052 .982 .981 .056 22.75 29 .002
Strict 1407.05*** 896 .050 .982 .983 .056 37.69 27 .000
Hyperactivity Configural 445.78*** 130 .103 .965 .958 .073
Weak 461.34*** 143 .099 .964 .961 .073 8.59 13 -.001
Strong 455.62*** 154 .093 .966 .966 .074 7.18 11 .002
Strict 450.05*** 165 .087 .968 .970 .074 16.51 11 .002
Impulsivity Configural 225.72*** 130 .057 .989 .987 .047
Weak 239.64*** 143 .055 .989 .988 .047 12.88 13 .000
Strong 246.99*** 154 .052 .990 .989 .047 12.40 11 .001
Strict 258.85*** 165 .050 .989 .990 .048 16.46 11 -.001
Emotional Dysregulation Configural 219.12*** 54 .116 .982 .977 .049
Weak 231.52*** 63 .109 .982 .979 .049 9.30 9 .000
Strong 233.83*** 71 .101 .983 .982 .049 9.28 8 .001
Strict 239.49*** 77 .096 .983 .984 .049 10.95 6 .000
Negative Self-Concept Configural 87.98*** 28 .097 .972 .959 .059
Weak 94.01*** 35 .086 .973 .967 .059 3.34 7 .001
Strong 96.59*** 38 .082 .973 .970 .059 4.33 3 .000
Strict 105.44*** 43 .080 .971 .972 .060 10.21 5 -.002
Note. N = 230 Spanish version; N = 230 English version. RMSEA = Root mean square error of approximation; CFI = Comparative Fit Index; TLI = Tucker-Lewis Index; SRMR = Standardized root mean square residual; ∆CFI = change in CFI. *p < .05, **p < .01, ***p < .001. Exploration of partial invariance models found that one loading had to be released for the Hyperactivity and Impulsivity scale, and three loadings had to be released for the Negative Self-Concept scale for the strong invariance model to hold. Further, one item intercept had to be released for the Hyperactivity, Impulsivity, and Negative Self-Concept scales, and two item intercepts for the Inattention/Executive Dysfunction and Emotional Dysregulation scales for strict invariance to hold.
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Table N.5. Differential Test Functioning by Language Version (French vs. English)

Scale Self-Report Observer
Inattention/​Executive Dysfunction -0.03 -0.05
Hyperactivity -0.11 -0.02
Impulsivity -0.03 -0.03
Emotional Dysregulation 0.00 -0.11
Negative Self-Concept 0.02 0.10
Note. Values presented are Expected Test Score Standardized Differences (ETSSD); guidelines for interpretation: small effect size ≥ |0.20|; medium effect size ≥ |0.50|; large effect size ≥ |0.80|. Positive ETSSD values indicate that individuals with equal amounts of the constructs being measured who took the French translation as part of the translation study sample scored higher than individuals who took the English version.
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Table N.6. Differential Test Functioning by Language Version (Spanish vs. English)

Scale Self-Report Observer
Inattention/​Executive Dysfunction -0.02 0.00
Hyperactivity -0.01 -0.03
Impulsivity -0.07 0.01
Emotional Dysregulation -0.11 0.00
Negative Self-Concept -0.05 0.11
Note. Values presented are expected test score standardized differences (ETSSD); guidelines for interpretation: small effect size ≥ |0.20|; medium effect size ≥ |0.50|; large effect size ≥ |0.80|. Positive ETSSD values indicate that individuals with equal amounts of the constructs being measured who took the Spanish translation as part of the translation study sample scored higher than individuals who took the English version.