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Beyond Difference Scores: Unlocking Insights with Polynomial Regression in Studies on the Effects of Implicit-Explicit Congruency Cover

Beyond Difference Scores: Unlocking Insights with Polynomial Regression in Studies on the Effects of Implicit-Explicit Congruency

Open Access
|Apr 2024

Figures & Tables

pb-64-1-1246-g1.png
Figure 1

Six visualizations to explain RSA graphically.

Table 1

Means, standard deviations, and correlations with confidence intervals of all research variables after data imputation, N = 135.

VARIABLEMSD123456
1. Depression  4.223.77
2. Anxiety  5.485.02  .78**
[.71, .84]
3. Aggression  2.7922.42  .48**
[.34, .60]
  .57**
[.45, .68]
4. Explicit SE  21.205.06–.61**
[–.71, –.49]
–.57**
[–.68, –.45]
–.24**
[–.39, –.07]
5. Implicit SE  0.2800.37  .02
[–.15, .19]
  .09
[–.08, .26]
–.05
[–.22, .12]
  .01
[–.16, .18]
6. contDif–0.0010.41  .45**
[.30, .57]
  .47**
[.33, .59]
  .13
[–.04, .29]
–.70**
[–.78, –.61]
  .70**
[.61, .78]
7. CreemersDif  1.1100.87  .26**
[.09, .41]
  .29**
[.13, .44]
  .18*
[.01, .34]
–.15
[–.31, .02]
–.07
[–.24, .10]
  .05
[–.12, .22]

[i] Note: M and SD are used to represent mean and standard deviation, respectively.

Values in square brackets indicate the 95% confidence interval for each correlation. The confidence interval is a plausible range of population correlations that could have caused the sample correlation (Cumming, 2014).

* Indicates p < .05. ** Indicates p < .01.

Table 2

Frequency counts for the two categorical difference score variables: categorical difference (congruent, damaged and fragile SE), and the dummy variable used in Creemer’s method (damaged and fragile). N = 135.

CONGRUENTDAMAGEDFRAGILE
Categorical394749
Creemer’s dummyNA6768
Table 3

The continuous difference score (z-implicit – z-explicit)and it quadratic term as orthogonal predictors of standardized depression, anxiety, and aggression. In block one the main effect is modelled, in the second block the quadratic term is added.

DEPRESSIONANXIETYAGGRESSION
(1)(2)(3)(4)(5)(6)
Difference (implicit – explicit SE)0.339***
(0.055)
  5.482***
(0.847)
0.340***
(0.055)
5.498***
(0.843)
0.115*
(0.061)
1.851*
(0.978)
Difference2  3.045***
(0.847)
3.146***
(0.843)
2.085**
(0.978)
Intercept0.000
(0.076)
–0.000
(0.073)
0.000
(0.076)
0.000
(0.073)
0.000
(0.085)
0.000
(0.084)
R2.224  .293.226.299.026.058
Adjusted R2.218  .283.220.289.018.044

[i] Note: *p < 0.1; **p < 0.05; ***p < 0.01.

Table 4

The categorical difference score (z-implicit – z-explicit) as predictor of standardized depression, anxiety, and aggression. Fragile (SD < –0.5) and damaged (SD > 0.5) are entered as dummy variables with congruent self-esteem (0.5 SD) as the intercept.

DEPRESSIONANXIETYAGGRESSION
(1)(3)(5)
Damaged (I > E)  0.804***
(0.198)
  0.856***
(0.196)
  0.320
(0.214)
Fragile (E > I)–0.093
(0.196)
–0.075
(0.194)
  0.063
(0.212)
Intercept–0.241*
(0.144)
–0.265*
(0.142)
–0.131
(0.156)
R2  .166  .183  .019
Adjusted R2  .154  .170  .004

[i] Note: *p < 0.1; **p < 0.05; ***p < 0.01.

Table 5

Creemers method for handling difference scores; The absolute value of the difference is entered as a continuous predictor, and the direction of the difference as a dummy variable (z-implicit – z-explicit) with fragile when <0, and damaged when >0. The two variables are predictors of standardized depression, anxiety, and aggression.

DEPRESSIONANXIETYAGGRESSION
(1)(2)(3)(4)(5)(6)
Size of SE Discrepancy  0.346***
(0.090)
  0.629***
(0.089)
  0.362***
(0.114)
  0.619***
(0.843)
  0.221**
(0.099)
  0.294**
(0.133)
Direction SE Discrepancy 1 = Fragile (0 = Damaged)–0.726***
(0.153)
–0.018
(0.240)
–0.766***
(0.151)
–0.124
(0.238)
–0.264
(0.169)
–0.081
(0.277)
Size * Direction–0.644***
(0.173)
–0.584***
(0.172)
–0.166
(0.200)
Intercept–0.020
(0.146)
–0.329**
(0.162)
–0.017
(0.144)
–0.298*
(0.161)
–0.112
(0.161)
–0.192
(0.187)
R2  .218  .293  .241  .303  .053  .058
Adjusted R2  .206  .277  .230  .287  .038  .036

[i] Note: *p < 0.1; **p < 0.05; ***p < 0.01.

Table 6

Polynomial regression of orthogonal factors based on the standardized predictors explicit and implicit self-esteem as predictors of standardized depression, anxiety and aggression. For each dependent variable three models are shown; the first contains only main effects, the second adds polynomial terms, and the final, third model adds an interaction term.

DEPENDENT VARIABLE:
DEPRESSIONANXIETYAGGRESSION
(1)(2)(3)(4)(5)(6)(7)(8)(9)
Explicit self-esteem–0.660***
(0.065)
–7.660***
(0.741)
–7.638***
(0.731)
–0.591***
(0.070)
–6.625***
(0.799)
–6.863***
(0.785)
–0.266**
(0.083)
–3.169***
(0.974)
–3.149***
(0.969)
Implicit self-esteem  0.019
(0.065)
  0.167
(0.739)
  0.310
(0.733)
  0.089
(0.070)
  1.254
(0.801)
  1.173
(0.787)
–0.037
(0.084)
–0.426
(0.972)
–0.291
(0.971)
Explicit self-esteem2  2.149***
(0.739)
  2.232***
(0.731)
  1.634
(0.799)
  1.854**
(0.785)
–0.009
(0.972)
  0.069
(0.968)
Implicit self-esteem2  0.387  0.420  1.254  0.711  1.297  1.328
Explicit self-esteem * Implicit self-esteem–0.135**
(0.064)
–0.170**
(0.069)
–0.127
(0.085)
Intercept  0.000
(0.065)
  0.000
(0.064)
  0.003
(0.063)
  0.000
(0.070)
  0.001
(0.069)
  0.004
(0.067)
–0.000
(0.084)
–0.000
(0.084)
  0.003
(0.083)
R2  0.435  0.471  0.488  0.355  0.380  0.410  0.073  0.085  0.101
Adjusted R2  0.426  0.454  0.468  0.345  0.366  0.387  0.059  0.057  0.066

[i] Note: *p < 0.1; **p < 0.05; ***p < 0.01.

pb-64-1-1246-g2.png
Figure 2

Response surface plot representing the regression equation for the relationship between explicit and implicit self-esteem on depression.

pb-64-1-1246-g3.png
Figure 3

Response surface plot representing the regression equation for the relationship between explicit and implicit self-esteem on anxiety.

pb-64-1-1246-g4.png
Figure 4

Response surface plot representing the regression equation for the relationship between explicit and implicit self-esteem on aggression.

DOI: https://doi.org/10.5334/pb.1246 | Journal eISSN: 0033-2879
Language: English
Submitted on: Jul 21, 2023
Accepted on: Feb 6, 2024
Published on: Apr 5, 2024
Published by: Ubiquity Press
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2024 Liselotte Visser, Ron Pat-el, Johan Lataster, Jacques Van Lankveld, Nele Jacobs, published by Ubiquity Press
This work is licensed under the Creative Commons Attribution 4.0 License.