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Table 3.

Fixed Effects for the Two Separate Mixed Effects Models based on Cross-Sectional Time Series Analysis for dArousal and dValence

Fixed effects in modelCoefficientSEtCorrelation between model and data
dArousal Time 3.593e-05 6.221e-06 5.78 .35 
AOAV1 -8.765e-01 4.675e-01 1.88 
AOAV2 -1.099e+00 4.675e-01 2.35 
dUnderstanding -1.341e-02 2.330e-03 5.76 
Lag 1 dUnderstanding -9.089e-03 2.409e-03 3.77 
Lag 1 dArousal 3.378e-02 4.273e-02 0.79 
Lag 2 dUnderstanding -1.178e-02 2.338e-03 5.034 
Lag 2 dArousal -1.314e-01 2.725e-03 48.21 
Lag 3 dArousal -5.269e-02 2.652e-03 19.87 
 Lag 4 dArousal -3.488e-02 2.621e-03 13.31  
dValence dUnderstanding -0.008486 0.002192 3.87 .40 
Lag 2 dUnderstanding -0.011708 0.002286 5.12 
Lag 2 dValence -0.087825 0.008661 10.14 
Lag 3 dUnderstanding -0.005418 0.002373 2.28 
Lag 3 dValence -0.088710 0.002776 31.96 
Lag 4 dUnderstanding -0.003972 0.002307 1.72 
Lag 4 dValence -0.044222 0.002603 16.99 
Fixed effects in modelCoefficientSEtCorrelation between model and data
dArousal Time 3.593e-05 6.221e-06 5.78 .35 
AOAV1 -8.765e-01 4.675e-01 1.88 
AOAV2 -1.099e+00 4.675e-01 2.35 
dUnderstanding -1.341e-02 2.330e-03 5.76 
Lag 1 dUnderstanding -9.089e-03 2.409e-03 3.77 
Lag 1 dArousal 3.378e-02 4.273e-02 0.79 
Lag 2 dUnderstanding -1.178e-02 2.338e-03 5.034 
Lag 2 dArousal -1.314e-01 2.725e-03 48.21 
Lag 3 dArousal -5.269e-02 2.652e-03 19.87 
 Lag 4 dArousal -3.488e-02 2.621e-03 13.31  
dValence dUnderstanding -0.008486 0.002192 3.87 .40 
Lag 2 dUnderstanding -0.011708 0.002286 5.12 
Lag 2 dValence -0.087825 0.008661 10.14 
Lag 3 dUnderstanding -0.005418 0.002373 2.28 
Lag 3 dValence -0.088710 0.002776 31.96 
Lag 4 dUnderstanding -0.003972 0.002307 1.72 
Lag 4 dValence -0.044222 0.002603 16.99 

Note. For each model, the (absolute) Values or Coefficients that are more than twice as large as the associated SE (ratio shown in the t column) are again conservatively read as statistically significant at p < .05 level, and higher t values attain low p values. All but two of the shown predictors are significant, and those two are either required comparison levels or provided substantial benefit to the overall model (such that its quality was worsened by removal). In these time series data, the number of data points is relatively large, strengthening these interpretations. Then most importantly, the coefficients (i.e., effect sizes) of the statistically significant predictors can be considered in relation to the scales on which the modeled values are expressed (e.g., the Likert ranges). Random effects (not shown) were included in the dArousal model for piece (intercepts) and by-participant random slopes for the effect of Lag 1 dArousal. By-participant random slopes for the effect of Lag 1 dValence, Lag 2 dValence were included in the dValence model. AOAV1 = audio-only condition; AOAV2 = audio-visual condition. Besides autoregression, the lagged fixed effects represent the influence of the endogenous (self-reported) variable time series on the modeled dArousal or dValence time series with a delay of 1-4 samples (lags) between the two time series. Smaller lags reflect a closer temporal alignment between two time series (lag 0 being a perfect temporal alignment, indicated for example as dUnderstanding). In autoregression, or lagging one time series against itself (e.g., d Valence and lag 1 dValence), often the predictive effect of the lagged time series on the present value time series decreases as lags increase, but since each coefficient ultimately impacts on almost entirely the same sequence of values (bar the omitted lags), a rough impression of the overall effect of a predictor, such as dArousal, can be obtained by summing the coefficients of its lags. A positive/negative coefficient suggests that the particular fixed effect increases/decreases dArousal or dValence.

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