Table 23.6, 23.16 Person measures for item clusters in contrast

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|                         CONTRAST 1  CLUSTER MEASURES                                                      |

|                 |   CLUSTER 1   |   CLUSTER 2   |   CLUSTER 3   |   BASELINE    |                         |

|     KID  STATUS | MEASURE  S.E. | MEASURE  S.E. | MEASURE  S.E. | MEASURE  S.E. | KID LABEL               |

|-----------------+---------------+---------------+---------------+---------------+-------------------------|

|       1     1   |     .49   .71 |     .01   .62 |    1.15   .58 |     .61   .34 | M Rossner, Marc Daniel  |

|       2     0   |    5.68  1.85 |    4.30  1.85 |    4.06  1.84 |    6.07  1.84 | M Rossner, Lawrence F.  |

|       3     1   |    1.36   .63 |     .77   .62 |    1.15   .58 |    1.10   .36 | M Rossner, Toby G.      |

....

|      73     1   |    1.75   .62 |    1.62   .70 |    -.95   .45 |     .38   .34 | M Sandberg, Ryne        |

|      74     1   |    -.08   .81 |    2.18   .80 |    2.80  1.04 |    1.50   .37 | M Patriarca, Ray        |

|      75     1   |     .49   .71 |    -.85   .70 |     .56   .51 |     .15   .34 | M Pauling, Linus        |

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      RELIABILITY:      .63             .68             .71             .89

 

Approximate relationships between the KID measures

 PCA      ACT       Pearson       Disattenuated Pearson+Extr  Disattenuated+Extr

Contrast  Clusters  Correlation   Correlation   Correlation   Correlation  Cluster Sizes

 1        1 - 2      0.2951        0.4683        0.3592        0.5497      6       6

 1        1 - 3      0.1411        0.2191        0.1958        0.2941      6       13

 1        2 - 3      0.8065        1.0000        0.8123        1.0000      6       13

 1        1 - B      0.4541                      0.5506                    6       25

 1        2 - B      0.9030                      0.8928                    6       25

 1        3 - B      0.8934                      0.8652                    13      25

 

This subtable shows the estimated person measures and standard errors for each cluster of items in the PCA contrast and the baseline measures, the estimates from the main analysis. The cluster correlations, explained in Table 23.1, are computed from these measures and reported in Table 23.0. Scatterplots of the person measures in Table 23.6 for each item cluster in Table 23.1 are shown in the Cluster Measure Plot.

 

The Reliability is the Spearman Reliability of the person measures estimated from each cluster of items.

 

For Smith's (2002) "dimensionality" method:

1. Analyze all the data. Table 23.1 identifies Item cluster 1 and Item cluster 3

2. Table 23.6 has the person measures and S.E.s.

3. Conduct t-tests.

 

Smith EV Jr. Detecting and evaluating the impact of multidimensionality using item fit statistics and principal component analysis of residuals. J Appl Meas. 2002; 3(2):205-31.

 

Table 23.0 Variance components scree plot for items

Table 23.1, 23.11 Principal components plots of item loadings

Table 23.2, 23.12 Item Principal components analysis/contrast of residuals

Table 23.3, 23.13 Item contrast by persons

Table 23.4, 23.14 Item contrast loadings sorted by measure

Table 23.5, 23.15 Item contrast loadings sorted by entry number

Table 23.6, 23.16 Person measures for item clusters in contrast. Cluster Measure Plot for Table 23.6.

Table 23.99 Largest residual correlations for items

Youtube video explaining Table 23