Model Fit Comparison

Figure S2.1. Fit of the linear model to the data.

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Figure S2.2. Fit of the quadratic model to the data.

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Quadratic Model

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

Table S2.1. Linear and quadratic effects of social time.
    Happiness
    B CI p
(Intercept)   0.00 -0.02 – 0.02 1.00
Linear   0.07 0.05 – 0.09 <.001
Quadratic   -0.03 -0.05 – -0.02 <.001
Observations  10360
R2 / adj. R2  .006 / .006

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Figure S2.3. Linear, quadratic, and piecemeal relationship.

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Diagnostics

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Assumptions

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Table S2.2. Omnibus diagnostic statistics for the quadratic model.
Value p-value Decision
Global Stat 1.2e+03 0.00 Assumptions NOT satisfied!
Skewness 1.1e+03 0.00 Assumptions NOT satisfied!
Kurtosis 9.2e+01 0.00 Assumptions NOT satisfied!
Link Function 7.9e-02 0.78 Assumptions acceptable.
Heteroscedasticity 1.8e-01 0.67 Assumptions acceptable.

Notes. Tests are directional test statistic
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Figure S2.4. Essential diagnostic plots for the quadratic model.

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Influential Cases.

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Figure S2.5. Most influential cases by leverage (x-axis), std. residual (y-axis), and Cook’s distance (circle size).

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Table S2.3. Most influential cases by leverage, studentized residual, and Cook’s distance.
StudRes Hat CookD
1003 -3.6 0.00 0.01
6547 -3.1 0.05 0.19
6701 1.5 0.08 0.07

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Replottig: Influential Cases Removed

Figure S2.6. Linear, quadratic, and piecemeal relationship with the most influential cases removed.

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Figure S2.7. Is the re-specificied model still a good fit to the data?

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Assumptions Reexamined

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Table S2.4. Omnibus diagnostic statistics for the quadratic model after removing influential cases.
Value p-value Decision
Global Stat 1183.75 0.00 Assumptions NOT satisfied!
Skewness 1094.24 0.00 Assumptions NOT satisfied!
Kurtosis 88.94 0.00 Assumptions NOT satisfied!
Link Function 0.45 0.50 Assumptions acceptable.
Heteroscedasticity 0.12 0.73 Assumptions acceptable.

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Table S2.5. Model comparison with and without influential cases.
    All Observations   Without Influential
    B CI p   B CI p
(Intercept)   0.00 -0.02 – 0.02 1.00   -0.00 -0.02 – 0.02 1.00
Linear   0.07 0.05 – 0.09 <.001   0.07 0.05 – 0.09 <.001
Quadratic   -0.03 -0.05 – -0.02 <.001   -0.03 -0.05 – -0.01 .003
Observations  10360  10357
R2 / adj. R2  .006 / .006  .006 / .006