Table 3.
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.