EDU-EDU2-Conley20080319-RRR by panniuniu

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									                                                             Patterns of Motivation Beliefs         47


                       Supplementary Materials (to be made available online)

Missing Data

        Cases were not excluded from further analysis because of missing data on one or more

variables. Traditional methods like listwise or pairwise deletion of cases with missing values or

single-value imputation (e.g., with the sample mean) can bias sample statistics and are not

recommended (Peugh & Enders, 2004). The IMPUTE module in the Sleipner package identifies

cases with missing data and searches for twin patterns in the data that meet a specified threshold

of similarity. All of the analyses in this study used average squared Euclidean distance as the

similarity measure, a .50 threshold for finding a twin, and a conservative criterion for the number

of variables for which missing data may be imputed (25%, or 2 values missing for a set of 8

clustering variables). A description of cases for which data were imputed can be found in Table

S-2.

        There were 1,844 cases with complete data. For the 26 cases with missing data (1.5% of

the sample), 16 had a twin that met the standard similarity criterion of .50, 1 had no twin that met

the specified threshold, and 9 had missing values in too many variables.

Checking the Reliability and Validity of the Cluster Solutions

        Sensitivity of the results to sampling variation was checked by performing identical

analyses on two independent samples randomly selected from the same population and

comparing the two classifications. The utility of the classification was verified by examining the

amount of error explained by the chosen solution, and sensitivity of the results to the choice of

clustering method was checked by comparing the classifications from different clustering

algorithms. In a final validity check, between-cluster differences on theoretically-related

constructs provided evidence of the validity of the cluster solutions. Strong support was obtained

for the reliability and validity of the cluster solutions.
                                                              Patterns of Motivation Beliefs      48


       Random halves. An identical set of analyses was conducted on the A and B samples. The

explained error sum of squares for the final 20 iterations and the increase in error sum of squares

resulting from each fusion suggested a similar range of cluster solutions across both sample

halves (6 to 12 cluster solutions for the A sample and 7 to 10 clusters for the B sample).

Theoretical and statistical considerations suggested 7- and 8-cluster solutions as the best

candidates for both A and B samples. The 8-cluster solution yielded a cluster pair that did not

match, as indicated by an average squared Euclidean distance (ASED) between centroids of

greater than .50 for the 8th cluster pair, suggesting a poor match between cluster centroids for the

8th cluster. Comparing the 7-cluster k means solution yielded good matches across the A and B

samples for all cluster pairs. The ASEDs for the pairwise matches and the centroid graphs are

provided in the online supplement (Table S-1 and Figure S-1). With a maximum ASED of .208,

the correspondence between the cluster means for the 7-cluster solution across two different

samples provided strong evidence of the reliability of the cluster solutions.

       Comparing results across alternate methods. Ward’s method on the A sample indicated

an optimal number of clusters and k means on the B sample used the optimal number of clusters

suggested by the Ward’s analysis. Comparing cluster centroids indicated a high degree of

overlap using different samples, different programs, and different clustering techniques

(Maximum ASED = 0.182). Centroid graphs showing the correspondence between solutions

across methods are provided in supplemental Figure S-2.

       Amount of ESS explained. Another facet of the generalizability of a cluster solution

concerns the match between the data and the classification solution, and the degree to which a

solution accounts for the variability in the data. A 7-cluster solution accounted for about half of

the variability in motivation beliefs for each sample half (48.70% for the A sample and 48.84 for

the B sample using Ward’s and 54.53% (A) and 53.69 (B) using k means). This represents good
                                                              Patterns of Motivation Beliefs       49


correspondence between the classification system and the data and provides evidence of the

generalizability of the results.

        Using dropped items to establish validity of clusters. The validity of the cluster solution

was checked by testing for differences between clusters on theoretically-related constructs.

Patterns were compared using items that were dropped when forming the scales. Two subjective

task value items cross-loaded on interest, utility, and attainment and were dropped from the

scales. Patterns characterized by higher values on these scales should and did have the highest

means on these dropped items. A full factorial multivariate analysis of variance (MANOVA) was

conducted with cluster membership as a between-subjects factor. As expected, results indicated

that three patterns with the same high levels of interest, utility, and attainment value did not

differ from one another on these dropped items, F (2,757) = 1.49, p = .226. A second MANOVA

with posthoc tests performed with a Games-Howell correction indicated that the three high

patterns differed significantly in the expected direction from patterns characterized by lower

subjective task value, F (12,3670) = 51.20, p = .000 (F ratio is Wilk’s approximation).
                                                                      Patterns of Motivation Beliefs      50


Table S-1

 Distance between paired cluster k means centroids from A and B sample at Time 1

 Cluster Pair           Average Squared Euclidian Distance
 1                                 0.023
 2                                 0.030
 3                                 0.065
 4                                 0.075
 5                                 0.091
 6                                 0.100
 7                                 0.208
 Mean: 0.084            Maximum: 0.208 Minimum: 0.023


  Table S-2

 Missing data and imputation analysis for “A” (n=935) and “B” (n=935) samples

                                                                                      A            B
 Number of cases with complete data                                                    916          928
 Number of imputed cases                                                                13            3
 Number of cases where no twin was found                                                 1            0
 Number of cases with missing values in too many variables                               5            4
 Total Cases                                                                           935          935
 Note. Values were imputed for up to 2 of the 8 clustering variables when a twin was found that met the
 standard similarity criterion of .50, based on standardized values.
                                                                              Patterns of Motivation Beliefs         51




 5.0                                                       5.0
 4.5                                                       4.5
 4.0                                                       4.0
 3.5                                                       3.5
                                                      A7                                                        A2
 3.0                                                       3.0
                                                      B5                                                        B7
 2.5                                                       2.5
 2.0                                                       2.0
 1.5                                                       1.5
 1.0                                                       1.0
       INT   UTIL   ATTN COST MAP   PAP   PAV   EFF              INT   UTIL   ATTN COST MAP   PAP   PAV   EFF




 5.0                                                       5.5
 4.5                                                       5.0
                                                           4.5
 4.0
                                                           4.0
 3.5
                                                      A1   3.5                                                  A6
 3.0
                                                      B6   3.0                                                  B1
 2.5                                                       2.5
 2.0                                                       2.0
 1.5                                                       1.5

 1.0                                                       1.0
       INT   UTIL   ATTN COST MAP   PAP   PAV   EFF              INT   UTIL   ATTN COST MAP   PAP   PAV   EFF




 5.0                                                       5.0
 4.5                                                       4.5
 4.0                                                       4.0
 3.5                                                       3.5
                                                      A3                                                        A5
 3.0                                                       3.0
                                                      B2                                                        B4
 2.5                                                       2.5

 2.0                                                       2.0

 1.5                                                       1.5

 1.0                                                       1.0
       INT   UTIL   ATTN COST MAP   PAP   PAV   EFF              INT   UTIL   ATTN COST MAP   PAP   PAV   EFF




 5.0
 4.5
 4.0
 3.5
                                                      A4
 3.0
                                                      B3
 2.5
 2.0
 1.5
 1.0
       INT   UTIL   ATTN COST MAP   PAP   PAV   EFF




Figure S-1. Centroid matches for 7-cluster solutions for A and B samples at Time 1.

Note. Int = interest value; util = utility value; attn = attainment value; cost = cost value; map =

mastery approach goals; pap = performance approach goals; pav = performance avoid goals; eff

= competence beliefs (efficacy).
                                                                                                            Patterns of Motivation Beliefs               52



 5.0                                                                                     5.0

 4.5                                                                                     4.5

 4.0                                                                                     4.0

 3.5                                                                                     3.5
                                                                             CA7                                                                   CA6
 3.0                                                                                     3.0
                                                                             CB4                                                                   CB6
 2.5                                                                                     2.5

 2.0                                                                                     2.0

 1.5                                                                                     1.5

 1.0                                                                                     1.0
       int   util    attn    cost     map    pap     pav         eff                           int   util   attn   cost   map   pap   pav   eff



 5.0                                                                                     5.0

 4.5                                                                                     4.5

 4.0                                                                                     4.0

 3.5                                                                                     3.5
                                                                                   CA4                                                             CA5
 3.0                                                                                     3.0
                                                                                   CB5                                                             CB3
 2.5                                                                                     2.5

 2.0                                                                                     2.0
 1.5                                                                                     1.5

 1.0                                                                                     1.0
       int    util    attn     cost    map     pap         pav         eff                     int   util   attn   cost   map   pap   pav   eff




 5.0                                                                                     5.0

 4.5                                                                                     4.5

 4.0                                                                                     4.0

 3.5                                                                                     3.5
                                                                                   CA3                                                             CB2
 3.0                                                                                     3.0
                                                                                   CB7                                                             CA1
 2.5                                                                                     2.5

                                                                                         2.0
 2.0
                                                                                         1.5
 1.5
                                                                                         1.0
 1.0
                                                                                               int   util   attn   cost   map   pap   pav    eff
       int    util    attn     cost    map     pap         pav         eff




 5.0

 4.5

 4.0

 3.5
                                                                                   CB1
 3.0
                                                                                   CA2
 2.5

 2.0

 1.5

 1.0
       int    util    attn     cost    map     pap         pav         eff




Figure S-2. Centroid matches for 7-cluster Time 1 solutions across methods and samples.

Note. Int = interest value; util = utility value; attn = attainment value; cost = cost value; map =

mastery approach goals; pap = performance approach goals; pav = performance avoid goals; eff

= competence beliefs (efficacy).

								
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