Model Fit Comparison

Figure S3a.1. Fit of the linear model to the data.

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Figure S3a.2. Fit of the quadratic model to the data.

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Quadratic Model

\(y =a+ bx + cx^{2}\), where y is Mood and x is Social Time.

Table S3a.1. Linear and quadratic effects of social time.
    Mood
    B CI p
(Intercept)   -0.00 -0.13 – 0.13 1.00
Linear   0.40 0.27 – 0.54 <.001
Quadratic   -0.26 -0.39 – -0.12 <.001
Observations  168
R2 / adj. R2  .230 / .221

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Figure S3a.3. Linear, quadratic, and piecemeal relationship (all observations).

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Diagnostics

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Assumptions

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Table S3a.2. Omnibus diagnostic statistics for the quadratic model.
Value p-value Decision
Global Stat 19.2 0.001 Assumptions NOT satisfied!
Skewness 1.7 0.194 Assumptions acceptable.
Kurtosis 6.4 0.011 Assumptions NOT satisfied!
Link Function 2.2 0.141 Assumptions acceptable.
Heteroscedasticity 8.9 0.003 Assumptions NOT satisfied!

Notes. Tests are directional test statistic
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Figure S3a.4. Omnibus diagnostic statistics for the quadratic model.

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Influential Cases.

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Figure S3a.5. Most influential cases by leverage (x-axis), std. residual (y-axis), and Cook’s distance (circle size).

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Table S3a.3. Most influential cases by leverage, studentized residual, and Cook’s distance.
StudRes Hat CookD
30 -0.72 0.13 0.03
164 -3.79 0.06 0.29

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Replottig: Influential Cases Removed

Figure S3a.6. Linear, quadratic, and piecemeal relationship with the most influential cases removed.

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Figure S3a.7. Is the re-specificied model still a good fit to the data?

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Assumptions Reexamined

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Table S3a.4. Omnibus diagnostic statistics for the quadratic model after removing influential cases.
Value p-value Decision
Global Stat 7.08 0.132 Assumptions acceptable.
Skewness 0.15 0.700 Assumptions acceptable.
Kurtosis 1.89 0.169 Assumptions acceptable.
Link Function 0.72 0.397 Assumptions acceptable.
Heteroscedasticity 4.32 0.038 Assumptions NOT satisfied!

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Table S3a.5. Model comparison with and without influential cases.
    All Observations   Without Influential
    B CI p   B CI p
(Intercept)   -0.00 -0.13 – 0.13 1.00   -0.00 -0.14 – 0.14 1.00
Linear   0.40 0.27 – 0.54 <.001   0.40 0.26 – 0.54 <.001
Quadratic   -0.26 -0.39 – -0.12 <.001   -0.19 -0.33 – -0.05 .008
Observations  168  166
R2 / adj. R2  .230 / .221  .196 / .186