Self-Esteem Factors and Artifacts

Supplemental Material

In order to conserve space and facilitate presentation, some of the detailed results for Models 4 and 5 (submodels of Model 3) and for Models 7 and 8 (submodels of Model 6) were excluded from the published article “Longitudinal Tests of Competing Factor Structures for the Rosenberg

Self-Esteem Scale: Traits, Ephemeral Artifacts, and Stable Response Styles” by Herbert W. Marsh, L. Francesca Scalas, and Benjamin Nagengast. These materials are presented here in full.

Supplemental Table 1 (extended version of Table 3 from published article)

Confirmatory Factor Analyses and Invariance Tests

2 / df / cf / TLI / CFI / RMSEA
Model 1 (One trait factor, no correlated uniqueness)
1.1 wave1 / 651.57** / 35 / .700 / .767 / .089
1.2 wave2 / 624.03** / 35 / .710 / .775 / .095
1.3 wave3 / 539.94** / 35 / .752 / .807 / .090
1.4 wave4 / 542.04** / 35 / .753 / .808 / .095
1.5 Longitudinal CFA
1.5a Unconstrained model (UM) / 2930.10** / 674 / 1.203 / .838 / .860 / .039
1.5b Factor Loadings (FL) / 2971.55** / 701 / 1.200 / .843 / .859 / .038
1.5c FL & Variances (Var) / 2975.17** / 704 / 1.199 / .844 / .859 / .038
1.5d FL-Var-Uniquenesses (Uniq) / 3134.95** / 724 / 1.203 / .839 / .850 / .039
Model 2 (Two-trait factors: negative & positive correlated factors)
2.1 wave1 / 111.70** / 34 / .961 / .971 / .032
2.2 wave2 / 120.16** / 34 / .956 / .967 / .037
2.3 wave3 / 161.46** / 34 / .936 / .951 / .046
2.4wave4 / 133.00** / 34 / .950 / .962 / .043
2.5 Longitudinal CFA
2.5a UM / 1116.35** / 652 / 1.199 / .965 / .971 / .018
2.5b FL / 1152.80** / 676 / 1.194 / .966 / .970 / .018
2.5c FL & Var / 1161.67** / 682 / 1.194 / .966 / .970 / .018
2.5d FL-Var-Uniq / 1313.80** / 702 / 1.200 / .958 / .962 / .020
Model 3 (One trait factor with correlated uniqueness among both negative & positive items)
3.1 wave1a / --- / --- / --- / --- / --- / ---
3.2 wave2 / 24.23* / 14 / .987 / .996 / .020
3.3 wave3 / 22.74 / 14 / .989 / .997 / .019
3.4 wave4 / 19.05 / 14 / .994 / .998 / .015
3.5 Longitudinal CFA
3.5a UM / 1337.64** / 590 / 1.180 / .939 / .954 / .024
3.5b FL / 1365.49** / 617 / 1.175 / .941 / .954 / .023
3.5c FL & Var / 1373.87** / 620 / 1.175 / .941 / .953 / .023
3.5d FL-Var-Uniq / 1511.19** / 640 / 1.176 / .934 / .946 / .025
2 / df / cf / TLI / CFI / RMSEA
Model 4 (One trait factor with correlated uniqueness among negative items)
4.1 wave1 / 98.33** / 29 / .959 / .974 / .033
4.2 wave2 / 113.46** / 29 / .950 / .968 / .039
4.3 wave3 / 139.87** / 29 / .934 / .958 / .046
4.4 wave4 / 120.62** / 29 / .946 / .965 / .044
4.5 Longitudinal CFA
4.5a UM / 1725.02** / 650 / 1.194 / .920 / .933 / .027
4.5b FL / 1773.01** / 677 / 1.189 / .922 / .932 / .027
4.5c FL & Var / 1776.52** / 680 / 1.188 / .922 / .932 / .027
4.5d FL-Var-Uniq / 1932.87** / 700 / 1.191 / .915 / .923 / .028
Model 5 (One trait factor with correlated uniqueness among positive items)
5.1 wave1 / 32.95* / 20 / .989 / .995 / .017
5.2 wave2 / 32.62* / 20 / .989 / .995 / .018
5.3 wave3 / 44.24* / 20 / .979 / .991 / .026
5.4 wave4 / 34.67* / 20 / .987 / .994 / .021
5.5 Longitudinal CFA
5.5a UM / 1745.63** / 614 / 1.185 / .911 / .930 / .029
5.5b FL / 1786.80** / 641 / 1.184 / .913 / .929 / .028
5.5c FL & Var / 1788.70** / 644 / 1.183 / .914 / .929 / .028
5.5d FL-Var-Uniq / 1927.05** / 664 / 1.187 / .908 / .922 / .029
Model 6 (One trait factor plus negative and positive latent method factor)
6.1 wave1 / 69.62** / 25 / .970 / .983 / .028
6.2 wave2 / 70.62** / 25 / .969 / .983 / .031
6.3 wave3 / 88.48** / 25 / .956 / .976 / .038
6.4 wave4 / 78.83** / 25 / .963 / .980 / .037
6.5 Longitudinal CFA
6.5-0 No Correlations for the same method factor over time / 1483.37** / 634 / 1.186 / .935 / .947 / .025
6.5a UM / 916.52** / 622 / 1.182 / .977 / .982 / .015
6.5b FL / 962.06** / 673 / 1.188 / .979 / .982 / .014
6.5c FL & Var / 1000.90** / 682 / 1.189 / .977 / .980 / .015
6.5d FL-Var-Uniq / 1161.90** / 702 / 1.196 / .968 / .971 / .017
2 / df / cf / TLI / CFI / RMSEA
Model 7 (One trait factor plus negative latent method factor)
7.1 wave1 / 109.00** / 31 / .957 / .970 / .034
7.2 wave2 / 119.02** / 31 / .951 / .966 / .039
7.3 wave3 / 153.38** / 31 / .932 / .953 / .047
7.4 wave4 / 130.43** / 31 / .945 / .962 / .045
7.5 Longitudinal CFA
7.5a UM / 1213.85** / 688 / 1.192 / .963 / .967 / .019
7.5b FL / 1226.67** / 694 / 1.192 / .963 / .967 / .019
7.5c FL & Var / 1388.27** / 714 / 1.199 / .954 / .958 / .021
7.5d FL-Var-Uniq / 109.00** / 31 / .957 / .970 / .034
Model 8 (One trait factor plus positive latent method factor)
8.1 wave1 / 79.29** / 29 / .970 / .981 / .028
8.2 wave2 / 70.66** / 29 / .975 / .984 / .028
8.3 wave3 / 109.04** / 29 / .953 / .969 / .039
8.4 wave4 / 69.55** / 29 / .976 / .985 / .029
8.5 Longitudinal CFA
8.5a UM / 994.87** / 644 / 1.196 / .974 / .978 / .016
8.5b FL / 1055.77** / 686 / 1.193 / .974 / .977 / .016
8.5c FL & Var / 1077.92** / 692 / 1.192 / .973 / .976 / .016
8.5d FL-Var-Uniq / 1239.719** / 712 / 1.199 / .964 / .967 / .018

Note. See Figure 1 for a description of the various models. df = degrees of freedom; cf = MLR correction factor; TLI = Tucker-Lewis Index; CFI = Comparative Fit Index; RMSEA = root-mean-square error of approximation. In the various models, factor loadings (FL) and factor variances (Var) were constrained to be equal across all four waves. Uniquenesses (Uniq) were constrained to be equal across waves 2-4, but freely estimated in wave 1 (following Marsh & Grayson,1994).

a Model 3 when applied to data from Wave 1 resulted in improper solution that was not considered further.

* p < .05; ** p < .001; § the variance of GSE was fixed in order to achieve identification.

Supplemental Table 2 (extended version of Table 4 from published article)

Factor Loadings and Uniquenesses for Models in Wave 1

Model 1 / Model 2
Item / GSE / Uniqueness / POS / NEG / Uniqueness
1 / .59 / .66 / .62 / .62
2 / .62 / .61 / .66 / .56
3 / .60 / .64 / .62 / .62
5 / .54 / .71 / .53 / .72
7 / .48 / .77 / .49 / .76
9 / .47 / .78 / .47 / .78
4 / .32 / .90 / .52 / .73
6 / .35 / .88 / .59 / .65
8 / .33 / .89 / .53 / .72
10 / .41 / .84 / .63 / .60
M / .47 / .56 / .57
Model 3 / Model 4
Item / GSE / Uniqueness / GSE / Uniqueness
1 / .40 / .84 / .62 / .62
2 / .40 / .84 / .66 / .56
3 / .45 / .80 / .62 / .62
5 / .54 / .71 / .53 / .72
7 / .32 / .90 / .49 / .76
9 / .41 / .83 / .47 / .78
4 / .30 / .91 / .22 / .95
6 / .35 / .88 / .24 / .94
8 / .32 / .90 / .23 / .95
10 / .42 / .82 / .30 / .91
M / .39 / .44
Model 5 / Model 6
Item / GSE / uniqueness / GSE / Neg / Pos / uniqueness
1 / .25 / .94 / .57 / .28 / .60
2 / .24 / .94 / .61 / .32 / .52
3 / .28 / .92 / .58 / .22 / .62
5 / .33 / .89 / .51 / ns / .73
7 / .19 / .96 / .52 / ns / .74
9 / .25 / .94 / .60 / ns / .55
4 / .51 / .74 / .22 / .47 / .73
6 / .59 / .65 / .24 / .55 / .64
8 / .53 / .72 / .22 / .49 / .71
10 / .63 / .60 / .32 / .53 / .62
M / .38 / .44 / .51 / .27
Model 7 / Model 8
Item / GSE / Neg / uniqueness / GSE / Pos / uniqueness
1 / .62 / .62 / .24 / .58 / .61
2 / .66 / .56 / .24 / .63 / .54
3 / .62 / .62 / .28 / .55 / .62
5 / .53 / .72 / .34 / .41 / .72
7 / .49 / .76 / .19 / .46 / .76
9 / .47 / .78 / .25 / .39 / .79
4 / .22 / .47 / .73 / .51 / .74
6 / .24 / .55 / .64 / .59 / .65
8 / .23 / .48 / .71 / .53 / .72
10 / .30 / .54 / .62 / .63 / .60
M / .44 / .51 / .38 / .50

Note. See Figure 1 for a description of the various models. GSE = global self-esteem trait factor; NEG = negative self-esteem trait factor; POS = positive self-esteem trait factor; Neg = negative method factor; Pos = positive method factor.

Supplemental Table 3 (extended version of Table 6 from published article)

Correlationsfor Latent Factors Across Waves

Model 1 / Model2
GSE1 / GSE2 / GSE3 / GSE4 / POS1 / POS2 / POS3 / POS4 / NEG1 / NEG2 / NEG3 / NEG4
GSE1 / — / POS1 / —
GSE2 / .65 / — / POS2 / .62 / —
GSE3 / .59 / .76 / — / POS3 / .56 / .73 / —
GSE4 / .51 / .66 / .76 / — / POS4 / .49 / .66 / .73 / —
NEG1 / .44 / .34 / .39 / .37 / —
NEG2 / .34 / .49 / .47 / .42 / .59 / —
NEG3 / .33 / .44 / .58 / .51 / .52 / .66 / —
NEG4 / .22 / .29 / .43 / .58 / .46 / .66 / .70 / —
Model3 / Model4 / Model5
GSE1 / GSE2 / GSE3 / GSE4 / GSE1 / GSE2 / GSE3 / GSE4 / GSE1 / GSE2 / GSE3 / GSE4
GSE1 / — / GSE1 / — / GSE1 / —
GSE2 / .89 / — / GSE2 / .64 / — / GSE2 / .65 / —
GSE3 / .78 / .95 / — / GSE3 / .58 / .76 / — / GSE3 / .59 / .75 / —
GSE4 / .67 / .82 / .90 / — / GSE4 / .51 / .67 / .75 / — / GSE4 / .51 / .68 / .76 / —
Model6 / Model7 / Model8
GSE1 / GSE2 / GSE3 / GSE4 / GSE1 / GSE2 / GSE3 / GSE4 / GSE1 / GSE2 / GSE3 / GSE4
GSE1 / — / GSE1 / — / GSE1 / —
GSE2 / .71 / — / GSE2 / .64 / — / GSE2 / .62 / —
GSE3 / .64 / .82 / — / GSE3 / .58 / .75 / — / GSE3 / .56 / .72 / —
GSE4 / .55 / .68 / .80 / — / GSE4 / .50 / .65 / .74 / — / GSE4 / .49 / .66 / .75 / —
Pos1 / Pos2 / Pos3 / Pos4 / Neg1 / Neg2 / Neg3 / Neg4 / Pos1 / Pos2 / Pos3 / Pos4
Pos1 / — / Neg1 / — / Pos1 / —
Pos2 / .52 / — / Neg2 / .54 / — / Pos2 / .58 / —
Pos3 / .48 / .60 / — / Neg3 / .44 / .58 / — / Pos3 / .51 / .67 / —
Pos4 / .43 / .62 / .60 / — / Neg4 / .42 / .66 / .65 / — / Pos4 / .46 / .65 / .67 / —
Neg1 / Neg2 / Neg3 / Neg4
Neg1 / —
Neg2 / .49 / —
Neg3 / .39 / .49 / —
Neg4 / .39 / .65 / .60 / —