Result from fitted Y* response function for TEST 1 analysis (first row), and from the different eye movement parameters (LMM analysis), for TEST 2.
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The second column reports the model selected for the specific parameter under analysis (see below for the symbol legend). The subsequent columns report the regression coefficients (β) and p-values (p) of the fixed factors (flight time T, ball arrival height Z) and their interaction term (when significant). The sixth column reports the AIC values computed including the random factor (AIClmm) and without it (AIClm). If AIClmm lm the inclusion of the random factor (i.e. subject) is justified, indicating that the particular eye movement parameter varies across subjects. The seventh column reports the marginal and the condition R2 coefficient of the regression. Finally the two rightmost columns show the significance of the by-subject adjustment of the slope relatively to both the T factor (ps1), and the Z factor (ps2), and the correlation between the two random parameters (intercept and slope for each factor).*: p_value **: p_value***: p_value§ (GLMM)Model type Yij* = β0 + βTtj + βzzj + εij + μi;† (LMM) Model type (LMM) vij = β0 + βTtj + βzzj + S0i +εij;†† (LMM) Model type: vij = β0 + βTtj + βzzj + γtjzj + S0i +εij;††† (LMM) Model type: vij = β0 + (βT + Sli)tj + βzzj + S0i + εij;†††† (LMM) Model type: vij = β0 + βTtj + (βz + S2i)zj + S0i +εij;‡ (LM) Model type: vij = β0 + βTtj + βzzj + γtjzj + εijResult from fitted Y* response function for TEST 1 analysis (first row), and from the different eye movement parameters (LMM analysis), for TEST 2.
第二列列出了所分析的特定参数所选用的模型（符号说明详见下文）。后续各列分别报告了固定因子（飞行时长T、球到达高度Z）及其交互项（若显著）的回归系数（β）与p值（p）。第六列报告了纳入随机因子时的AIC值（AIClmm）与未纳入随机因子时的AIC值（AIClm）。若AIClmm < AIClm，则纳入随机因子（即被试个体）的设定合理，表明该特定眼动参数存在个体间差异。第七列报告了回归模型的边际R²与条件R²系数。最后最右侧两列分别展示了针对飞行时长T因子（ps1）与球到达高度Z因子（ps2）的被试间斜率调整显著性，以及两类随机参数（各因子的截距与斜率）间的相关性。*: p值；**: p值；***: p值；§（广义线性混合模型（Generalized Linear Mixed Model, GLMM））模型形式：Y<sub>ij</sub>* = β₀ + β<sub>T</sub>t<sub>j</sub> + β<sub>z</sub>z<sub>j</sub> + ε<sub>ij</sub> + μ<sub>i</sub>；†（线性混合模型（Linear Mixed Model, LMM））模型形式：v<sub>ij</sub> = β₀ + β<sub>T</sub>t<sub>j</sub> + β<sub>z</sub>z<sub>j</sub> + S<sub>0i</sub> + ε<sub>ij</sub>；††（线性混合模型（Linear Mixed Model, LMM））模型形式：v<sub>ij</sub> = β₀ + β<sub>T</sub>t<sub>j</sub> + β<sub>z</sub>z<sub>j</sub> + γt<sub>j</sub>z<sub>j</sub> + S<sub>0i</sub> + ε<sub>ij</sub>；†††（线性混合模型（Linear Mixed Model, LMM））模型形式：v<sub>ij</sub> = β₀ + (β<sub>T</sub> + S<sub>1i</sub>)t<sub>j</sub> + β<sub>z</sub>z<sub>j</sub> + S<sub>0i</sub> + ε<sub>ij</sub>；††††（线性混合模型（Linear Mixed Model, LMM））模型形式：v<sub>ij</sub> = β₀ + β<sub>T</sub>t<sub>j</sub> + (β<sub>z</sub> + S<sub>2i</sub>)z<sub>j</sub> + S<sub>0i</sub> + ε<sub>ij</sub>；‡（线性模型（Linear Model, LM））模型形式：v<sub>ij</sub> = β₀ + β<sub>T</sub>t<sub>j</sub> + β<sub>z</sub>z<sub>j</sub> + γt<sub>j</sub>z<sub>j</sub> + ε<sub>ij</sub>。本结果来自TEST 1分析的拟合Y*响应函数（第一行），以及TEST 2中不同眼动参数的线性混合模型（Linear Mixed Model, LMM）分析结果。
