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. Author manuscript; available in PMC: 2010 May 27.
Published in final edited form as: Appl Psychol Meas. 2010 Mar 1;34(2):122–142. doi: 10.1177/0146621609338592

Table 3.

Standard Deviation of Parameter Estimates under Various Data Conditions and Approaches and Corresponding Sample Sizes (n)

Dataset Conditions\Approaches Latent Scores Single Parcels Even-Split Parcels Item-Construct Balance
Cat. Distribution (%) N γ1 γ2 φ n γ1 γ2 φ n γ1 γ2 φ n γ1 γ2 φ n
Two 100 .65 .69 .06 100 .40 .38 .00 100 .85 .82 .00 99 .89 .92 .00 100
70, 30 350 .20 .26 .03 100 .19 .20 .00 100 .35 .39 .00 100 .33 .39 .00 100
600 .16 .16 .02 100 .15 .14 .00 100 .28 .28 .00 100 .28 .27 .00 100
85, 15 100 1.02 .10 .07 100 .43 .54 .00 100 1.19 1.62 .00 100 1.19 1.61 .00 100
350 .31 .32 .03 100 .28 .26 .00 100 .65 .61 .00 100 .56 .62 .00 100
600 .25 .24 .02 100 .21 .22 .00 100 .43 .49 .00 100 .51 .50 .00 100
Three 20, 60, 20 100 .49 .62 .05 100 .23 .26 .01 100 .46 .48 .01 100 .46 .57 .01 100
350 .18 .19 .02 100 .13 .12 .00 100 .22 .21 .01 100 .22 .21 .01 100
600 .14 .16 .02 100 .09 .10 .00 100 .15 .19 .00 100 .16 .18 .01 100
70, 20, 10 100 .78 1.37 .06 100 .26 .30 .01 100 .64 .80 .01 98 .58 .77 .01 100
350 .20 .22 .02 100 .15 .16 .00 100 .29 .30 .00 100 .28 .31 .00 100
600 .16 .15 .02 100 .12 .11 .00 100 .20 .20 .00 100 .22 .20 .00 100
Five 5, 15, 60, 15, 5 100 .33 .32 .04 100 .14 .12 .03 100 .21 .20 .03 100 .23 .20 .04 100
350 .15 .15 .02 100 .07 .07 .02 100 .11 .10 .02 100 .10 .10 .02 100
600 .11 .13 .01 100 .06 .06 .01 100 .08 .09 .01 100 .08 .09 .01 100
5, 10, 20, 40, 25 100 .29 .41 .05 100 .12 .15 .03 100 .22 .22 .04 99 .19 .25 .04 100
350 .15 .16 .03 100 .07 .07 .02 100 .11 .12 .02 100 .11 .12 .02 100
600 .11 .13 .02 100 .05 .06 .01 100 .08 .10 .02 100 .08 .09 .02 100
Seven 5, 10, 20, 30, 20, 10, 5 100 .37 .41 .04 100 .11 .12 .05 100 .17 .20 .06 100 .18 .18 .07 100
350 .15 .17 .03 100 .06 .06 .03 100 .09 .10 .03 100 .08 .09 .04 100
600 .11 .10 .02 100 .04 .04 .02 100 .06 .06 .03 100 .06 .06 .03 100
3, 7, 12, 18, 35, 20, 5 100 .42 .35 .04 100 .10 .11 .05 100 .18 .19 .07 100 .17 .18 .07 100
350 .16 .18 .02 100 .06 .06 .03 100 .09 .10 .04 100 .08 .10 .04 100
600 .12 .15 .02 100 .04 .05 .02 100 .07 .08 .03 100 .06 .08 .03 100
Randomized to Four Parcels Randomized to Six Parcels Four Parcels of Adjacent Loadings Six Parcels of Adjacent Loadings Four Items of Diverse Loadings Four Items of High Loadings
γ1 γ2 φ n γ1 γ2 φ n γ1 γ2 φ n γ1 γ2 φ n γ1 γ2 φ n γ1 γ2 φ n
1.39 1.21 .00 100 .90 1.03 .00 100 .76 .74 .01 100 .08 .81 .01 100 1.02 2.19 .11 82 .66 .97 .09 96
.41 .40 .00 100 .46 .39 .00 100 .31 .34 .00 100 .30 .34 .00 100 .18 .60 .05 98 .18 .18 .05 100
.32 .30 .00 100 .31 .26 .00 100 .25 .23 .00 100 .25 .22 .00 100 .19 .18 .05 100 .14 .13 .04 100
1.29 2.47 .00 100 1.56 1.58 .00 98 1.57 1.68 .00 99 1.20 1.65 .00 100 .65 1.87 .14 84 .65 1.32 .14 83
.64 .59 .00 100 .71 .64 .00 100 .48 .50 .00 100 .49 .50 .00 100 .49 .56 .06 98 .26 .35 .05 100
.49 .51 .00 100 .56 .49 .00 100 .35 .39 .00 100 .37 .38 .00 100 .24 .24 .11 100 .18 .17 .04 100
.58 .65 .01 100 .59 .51 .01 100 .41 .44 .02 100 .39 .44 .02 100 1.02 .76 .10 86 .43 .96 .08 98
.24 .21 .01 100 .24 .22 .01 100 .18 .19 .01 100 .18 .19 .01 100 .20 .25 .04 100 .17 .18 .03 100
.18 .18 .00 100 .18 .17 .01 100 .12 .15 .01 100 .13 .15 .01 100 .12 .18 .03 100 .13 .13 .03 100
.74 .91 .01 100 .78 .77 .01 100 .50 .70 .02 100 .52 .73 .02 100 3.05 3.48 .13 81 .82 1.00 .09 96
.34 .31 .00 100 .33 .33 .00 100 .22 .25 .01 100 .22 .25 .01 100 .34 .33 .05 99 .17 .25 .04 100
.25 .22 .00 100 .26 .22 .00 100 .18 .17 .01 100 .18 .17 .01 100 .15 .17 .04 100 .11 .13 .32 100
.24 .26 .04 100 .28 .21 .04 100 .19 .18 .05 100 .19 .17 .05 100 .64 1.48 .07 96 .04 .36 .06 100
.12 .11 .02 100 .13 .10 .02 100 .09 .09 .03 100 .09 .09 .03 100 .17 .20 .04 100 .13 .13 .03 100
.09 .09 .01 100 .09 .09 .01 100 .07 .07 .02 100 .07 .07 .02 100 .14 .13 .03 100 .09 .11 .02 100
.21 .27 .03 100 .27 .28 .04 100 .16 .22 .05 100 .16 .22 .05 100 .48 .86 .08 96 .29 .40 .07 99
.12 .12 .02 100 .13 .12 .02 100 .09 .10 .03 100 .09 .10 .03 100 .18 .17 .04 100 .15 .13 .03 100
.09 .10 .01 100 .10 .10 .01 100 .07 .08 .02 100 .06 .08 .02 100 .12 .15 .03 100 .10 .10 .03 100
.19 .20 .06 100 .21 .22 .06 100 .14 .18 .09 100 .15 .19 .09 100 .53 .59 .07 97 .30 .39 .06 98
.10 .10 .03 100 .10 .10 .03 100 .08 .08 .05 100 .08 .08 .05 100 .15 .21 .04 100 .12 .12 .04 100
.07 .06 .03 100 .07 .06 .03 100 .05 .05 .04 100 .05 .05 .05 100 .11 .13 .03 100 .10 .09 .02 100
.18 .20 .06 100 .06 .13 .15 100 .14 .17 .09 100 .15 .17 .09 100 .53 .76 .08 96 .37 .30 .06 99
.10 .11 .03 100 .10 .10 .04 100 .07 .08 .05 100 .07 .08 .05 100 .17 .21 .04 100 .15 .13 .03 100
.08 .07 .02 100 .08 .08 .03 100 .06 .07 .04 100 .06 .06 .04 100 .14 .16 .03 100 .10 .11 .02 100
Four Items of Medium Loadings Four Items of Low Loadings Six Items of Diverse Loadings Six Items of High Loadings Six Items of Medium Loadings Six Items of Low Loadings
γ1 γ2 φ n γ1 γ2 φ n γ1 γ2 φ n γ1 γ2 φ n γ1 γ2 φ n γ1 γ2 φ n
1.44 .93 .09 78 1.91 2.46 .09 61 .82 .89 .09 95 .47 .65 .08 100 1.38 2.47 .09 88 1.79 2.01 .08 78
.26 .33 .05 99 1.25 .97 .04 94 .17 .25 .05 100 .13 .17 .04 100 .19 .24 .04 100 .60 .60 .04 100
.18 .20 .04 100 .34 .35 .03 99 .14 .14 .04 100 .12 .11 .03 100 .16 .18 .03 100 .23 .32 .03 100
1.47 1.41 .15 74 1.62 1.3 .12 53 1.31 1.11 .12 91 .44 1.19 .12 91 1.17 1.56 .10 79 1.11 1.42 .11 67
.41 .66 .05 99 .89 1.56 .05 87 .22 .28 .06 100 .19 .20 .04 100 .26 .45 .05 100 .79 1.35 .05 95
.24 .41 .04 100 .74 .58 .04 99 .21 .19 .04 100 .14 .14 .03 100 .18 .22 .03 100 .44 .34 .03 100
.96 1.37 .09 92 1.9 1.2 .07 69 .61 .92 .08 97 .31 .39 .07 98 .97 .99 .08 97 1.48 1.89 .07 84
.22 .36 .03 100 .93 .48 .03 99 .16 .16 .04 100 .14 .13 .03 100 .19 .27 .03 100 .39 .34 .03 100
.13 .18 .03 100 .38 .39 .03 100 .12 .14 .03 100 .12 .12 .03 100 .12 .15 .02 100 .25 .28 .02 100
.99 1.16 .07 86 2.56 1.78 .09 76 .66 .80 .10 97 .43 .73 .09 99 .91 .69 .08 95 4.42 17.5 .08 86
.29 .33 .04 100 .68 .69 .04 96 .15 .20 .04 100 .14 .15 .04 100 .20 .21 .04 100 .71 .92 .04 98
.16 .22 .03 100 .32 .36 .03 100 .13 .13 .03 100 .10 .10 .03 100 .14 .18 .03 100 .21 .23 .03 100
.84 1.06 .06 96 1.17 1.64 .06 86 .60 .50 .06 100 .27 .27 .06 100 .37 .47 .05 99 1.4 1.64 .05 95
.21 .20 .03 100 .34 .44 .03 99 .16 .13 .03 100 .12 .13 .03 100 .17 .17 .03 100 .23 .35 .03 100
.12 .13 .02 100 .25 .23 .02 100 .11 .10 .02 100 .08 .10 .02 100 .12 .12 .02 100 .17 .21 .02 100
.54 .43 .07 100 1.25 1.33 .07 87 .46 .61 .07 99 .23 .30 .06 100 .45 .33 .06 100 1.47 1.66 .06 95
.16 .19 .04 100 .39 .63 .03 100 .14 .18 .03 100 .12 .11 .03 100 .15 .18 .03 100 .24 .39 .03 100
.11 .16 .02 100 .31 .38 .02 100 .10 .12 .02 100 .10 .09 .02 100 .11 .15 .02 100 .17 .27 .02 100
.39 .57 .06 96 1.12 1.48 .06 93 .35 .38 .05 100 .30 .43 .05 100 .58 1.19 .06 100 12.9 4.92 .05 96
.19 .23 .03 100 .38 .40 .03 100 .15 .16 .03 100 .11 .11 .04 100 .17 .17 .03 100 .28 .37 .02 100
.13 .15 .02 100 .25 .24 .02 100 .10 .10 .03 100 .09 .08 .02 100 .11 .12 .02 100 .17 .18 .02 100
.59 .70 .07 96 1.79 2.19 .07 84 .50 .74 .06 100 .33 .26 .05 100 .46 .52 .05 100 .61 1.16 .05 90
.19 .22 .03 100 .29 .50 .03 100 .13 .16 .03 100 .13 .13 .03 100 .18 .18 .03 100 .26 .43 .03 100
.14 .13 .02 100 .29 .25 .02 100 .11 .13 .02 100 .09 .10 .02 100 .12 .12 .02 100 .19 .24 .02 100

Note: Cat. = Number of categories.