Nonlinear Interaction Components -- 2-group Example

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					Nonlinear Interaction Components -- 2-group Example

Here are data from a 2-group design in which participants                                                                                     90
were assigned to two different feedback conditions (1 =
intermittent feed, 2 = continuous feedback) and completed
an assigned number of practices with that type of feedback
before performance testing.
                                                                                                                                              80

Both of the groups show a quadratic component to their
practice-performance function.

Below are analyses of the relationship between #practice,                                                                                     70
feedback type and their interaction with performance -- with
                                                                                                                                                                                                                                   GRP




                                                                                                                         Mean PERF
and without the quadratic component.
                                                                                                                                                                                                                                         1.00

                                                                                                                                              60                                                                                         2.00
                                                                                                                                               2.00     3.00     4.00       5.00        6.00     7.00    8.00    9.00   10.00 11.00


                                                                                                                                                   PRACTICE




                                                                                                                                     Coding needed to run the linear model includes:

                                                                                                                                      Centering the quantitative practice (X) variable
                                                                                                                                       (mean = 6.5, std = 2.89)

                                                                                                                                      Dummy coding the grouping variable (here the highest-
                                                                                                                                       coded group – continuous feedback) was set as the
                                                                                                                                       comparison group)

                                                                                                                                      Interaction term computed as the product of the dummy
                                                                                                                                       code and the centered quantitative variable



                                                                                                                                     Additional coding needed for the quadratic model includes:

                                                                                                                                      Quadratic term computed as the square of the centered
                                                                                                                                       practice (X) variable (nonlinear main effect)

                                                                                                                                      Quadratic interaction term computed as the product of
                                                                                                                                       the dummy code and the quadratic term (nonlinear
                                                                                                                                       interaction)




Results from this model…

                                                        Model Summary                                                                                                              ANOVAc

                                                                                                                                                                   Sum of
                                                                                        Change Statistics                                 Model                    Squares         df          Mean Square     F        Sig.
                                 Adjusted        Std. Error of   R Square                                                                 1         Regression    3138.655               3       1046.218    156.091      .000 a
 Model      R       R Square     R Square       the Estimate      Change    F Change        df1         df2        Sig. F Change                    Residual       375.345              56           6.703
 1           .945 a     .893         .887            2.58894         .893    156.091              3           56            .000                    Total         3514.000              59
 2           .972 b     .945         .939            1.89998         .051      24.988             2           54            .000          2         Regression    3319.064               5         663.813   183.885      .000 b
   a. Predictors: (Constant), INT, DC, PRAC_C                                                                                                       Residual       194.936              54           3.610
   b. Predictors: (Constant), INT, DC, PRAC_C, PRAC_CSQ, INTSQ                                                                                      Total         3514.000              59
                                                                                                                                              a. Predictors: (Constant), INT, DC, PRAC_C
                                                                                                                                              b. Predictors: (Constant), INT, DC, PRAC_C, PRAC_CSQ, INTSQ
                                                                                                                                              c. Dependent Variable: PERF
                                        Coefficientsa

                            Unstandardized          Standardized
                               Coefficients          Coefficients
  Model                      B         Std. Error       Beta             t        Sig.
  1        (Constant)      75.700           .473                    160.153         .000
           DC               -7.400          .668            -.483    -11.070        .000
           PRAC_C            2.164          .165             .812     13.148        .000
           INT          -1.02E-15           .233             .000          .000    1.000
  2        (Constant)      77.669           .525                    147.989         .000
           DC             -11.337           .742            -.741    -15.275        .000
           PRAC_C            2.164          .121             .812     17.915        .000
           INT          -1.02E-15           .171             .000          .000    1.000
           PRAC_CSQ           -.239         .048            -.227      -4.999       .000
           INTSQ               .477         .068             .411       7.069       .000
      a. Dependent Variable: PERF




The full model is …

                                 Perf’ = b0 + b1*DC + b2*prac_c + b3*prac_csq + b4*int + b5*intsq

b0 – constant – expected performance for those in comparison group with the mean (0) amount of practice

b1 - the simple effect of feedback for the mean (0) amount of practice
    - expected direction and extent of change in performance for those in the target group, compared to those in the
         comparison group, holding all other predictors constant at the value 0

b2 - the simple linear effect of practice for those in the comparison group (continuous feedback)
    - expected direction and extent of change in performance for a 1-unit increase in practice holding all other predictors
         constant at 0

b3 - simple quadratic effect of practice for those in the comparison group (continuous feedback)
    - expected direction and extent of change in performance for a 1-unit change in performance, holding all other
         predictors constant at 0

b4 - linear interaction - how the linear effect of practice for the target (intermittent feedback) differs from the linear effect of
          practice for the comparison group (continuous feedback)
      - how the difference between target and comparison group performances changes for different
          amounts of practice
      - expected direction and extent of change in effect of one predictor for a 1-unit increase in the value of the other
          predictor, holding all other predictors constant at 0

b5 - quadratic interaction - how the quadratic effect of practice for the target (intermittent feedback) differs from the
          quadratic effect of practice for the comparison group (continuous feedback)
     - how how the difference between target and comparison group performances changes for
           different amounts of practice, for different amounts of practice
    - difference in expected direction and extent of change in effect of one predictor for a 1-unit increase in the value of
          the other predictor, holding all the other predictors constant, for a 1-unit change in practice

				
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posted:10/1/2012
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