# Nonlinear Interaction Components -- 2-group Example

Document Sample

```					Nonlinear Interaction Components -- 2-group Example

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
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

 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

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 0 posted: 10/1/2012 language: English pages: 2