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多维对数正态作答时间模型：对潜在加工速度多维性的探究

本站小编 Free考研考试/2022-01-01
詹沛达1(), Hong Jiao2, Kaiwen Man3
1浙江师范大学教师教育学院心理学系, 金华 321004
2Measurement, Statistics, and Evaluation, Department of Human Development and Quantitative Methodology, University of Maryland, College Park, Maryland, United States
3Educational Studies in Psychology, Research Methodology, and Counseling, The University of Alabama, Tuscaloosa, United States
收稿日期:2020-03-02出版日期:2020-09-25发布日期:2020-07-24
通讯作者:詹沛达E-mail:pdzhan@gmail.com

基金资助:* 国家自然科学基金青年基金项目(31900795)

The multidimensional log-normal response time model: An exploration of the multidimensionality of latent processing speed

ZHAN Peida1(), Hong JIAO2, Kaiwen MAN3
1Department of Psychology, College of Teacher Education, Zhejiang Normal University, Jinhua, 321004, China
2Measurement, Statistics, and Evaluation, Department of Human Development and Quantitative Methodology, University of Maryland, College Park, Maryland, United States
3Educational Studies in Psychology, Research Methodology, and Counseling, The University of Alabama, Tuscaloosa, United States
Received:2020-03-02Online:2020-09-25Published:2020-07-24
Contact:ZHAN Peida E-mail:pdzhan@gmail.com






摘要/Abstract


摘要： 在心理与教育测量中, 潜在加工速度反映学生运用潜在能力解决问题的效率。为在多维测验中探究潜在加工速度的多维性并实现参数估计, 本研究提出多维对数正态作答时间模型。实证数据分析及模拟研究结果表明：(1)潜在加工速度具有与潜在能力相匹配的多维结构; (2)新模型可精确估计个体水平的多维潜在加工速度及与作答时间有关的题目参数; (3)冗余指定潜在加工速度具有多维性带来的负面影响低于忽略其多维性所带来的。


表12012年PISA计算机化数学测验的Q矩阵
题目 θ1 θ2 θ3
CM015Q02D 1
CM015Q03D 1
CM020Q01 1
CM020Q02 1
CM020Q03 1
CM020Q04 1
CM038Q03T 1
CM038Q05 1
CM038Q06 1

表12012年PISA计算机化数学测验的Q矩阵
题目 θ1 θ2 θ3
CM015Q02D 1
CM015Q03D 1
CM020Q01 1
CM020Q02 1
CM020Q03 1
CM020Q04 1
CM038Q03T 1
CM038Q05 1
CM038Q06 1


表22012年PISA计算机化数学测验数据的探索性因素分析中的数据-模型拟合指标
Model χ2 df TLI CFI AIC BIC SRMR RMSEA [90% CI]
1-factor 462.79** 27 0.896 0.922 24592.15 24737.03 0.045 0.101 [0.093, 0.109]
2-factor 225.49** 19 0.930 0.963 24370.85 24558.65 0.032 0.083 [0.073, 0.093]
3-factor 32.66** 12 0.989 0.996 24192.02 24417.38 0.010 0.033 [0.020, 0.047]
4-factor 5.56 6 1.000 1.000 24176.92 24434.48 0.004 0.000 [0.000, 0.031]
5-factor 0.09 1 1.006 1.000 24181.44 24465.83 0.000 0.000 [0.000, 0.045]

表22012年PISA计算机化数学测验数据的探索性因素分析中的数据-模型拟合指标
Model χ2 df TLI CFI AIC BIC SRMR RMSEA [90% CI]
1-factor 462.79** 27 0.896 0.922 24592.15 24737.03 0.045 0.101 [0.093, 0.109]
2-factor 225.49** 19 0.930 0.963 24370.85 24558.65 0.032 0.083 [0.073, 0.093]
3-factor 32.66** 12 0.989 0.996 24192.02 24417.38 0.010 0.033 [0.020, 0.047]
4-factor 5.56 6 1.000 1.000 24176.92 24434.48 0.004 0.000 [0.000, 0.031]
5-factor 0.09 1 1.006 1.000 24181.44 24465.83 0.000 0.000 [0.000, 0.045]


表3三因素模型的旋转因素载荷矩阵
题目 因素1 因素2 因素3
CM015Q02D 0.695*
CM015Q03D 0.609*
CM020Q01 0.565*
CM020Q02 0.801*
CM020Q03 0.642*
CM020Q04 0.943*
CM038Q03T 0.502*
CM038Q05 0.985*
CM038Q06 0.621*

表3三因素模型的旋转因素载荷矩阵
题目 因素1 因素2 因素3
CM015Q02D 0.695*
CM015Q03D 0.609*
CM020Q01 0.565*
CM020Q02 0.801*
CM020Q03 0.642*
CM020Q04 0.943*
CM038Q03T 0.502*
CM038Q05 0.985*
CM038Q06 0.621*


表42012年PISA计算机化数学测验数据分析中模型-数据拟合指标
分析模型 -2LL DIC WAIC ppp
MLRTM 19305 22505 22055 0.633
ULRTM 21310 22890 22770 0.597

表42012年PISA计算机化数学测验数据分析中模型-数据拟合指标
分析模型 -2LL DIC WAIC ppp
MLRTM 19305 22505 22055 0.633
ULRTM 21310 22890 22770 0.597


表52012年PISA计算机化数学测验数据分析中多维潜在加工速度的方差-协方差矩阵估计值
Στ τ1 τ2 τ3
τ1 0.301 (0.016)
[0.270, 0.334]		 0.751 0.767
τ2 0.185 (0.010)
[0.167, 0.204]		 0.202 (0.010)
[0.184, 0.220]		 0.855
τ3 0.227 (0.012)
[0.206, 0.250]		 0.208 (0.009)
[0.190, 0.226]		 0.292 (0.013)
[0.266, 0.317]

表52012年PISA计算机化数学测验数据分析中多维潜在加工速度的方差-协方差矩阵估计值
Στ τ1 τ2 τ3
τ1 0.301 (0.016)
[0.270, 0.334]		 0.751 0.767
τ2 0.185 (0.010)
[0.167, 0.204]		 0.202 (0.010)
[0.184, 0.220]		 0.855
τ3 0.227 (0.012)
[0.206, 0.250]		 0.208 (0.009)
[0.190, 0.226]		 0.292 (0.013)
[0.266, 0.317]



图12012年PISA计算机化数学测验数据分析中前20名被试潜在加工速度估计值 注：ULRTM = 单维对数正态作答时间模型; MLRTM = 多维对数正态作答时间模型; τ = 潜在加工速度
图12012年PISA计算机化数学测验数据分析中前20名被试潜在加工速度估计值 注：ULRTM = 单维对数正态作答时间模型; MLRTM = 多维对数正态作答时间模型; τ = 潜在加工速度


表62012年PISA计算机化数学测验数据分析中题目参数估计值
题目 ULRTM MLRTM
ξ ω ξ ω
M SE 95% CI M SE 95% CI M SE 95% CI M SE 95% CI
1 4.470 0.020 [4.432, 4.508] 1.617 0.031 [1.558, 1.678] 4.469 0.020 [4.433, 4.510] 1.845 0.045 [1.760, 1.936]
2 4.630 0.019 [4.592, 4.667] 1.697 0.032 [1.635, 1.762] 4.629 0.019 [4.594, 4.668] 1.976 0.051 [1.874, 2.076]
3 4.778 0.016 [4.750, 4.811] 2.423 0.050 [2.327, 2.519] 4.778 0.015 [4.747, 4.807] 2.505 0.055 [2.397, 2.612]
4 3.860 0.018 [3.825, 3.895] 1.866 0.036 [1.793, 1.934] 3.859 0.017 [3.825, 3.894] 1.915 0.038 [1.841, 1.991]
5 4.258 0.016 [4.226, 4.291] 2.186 0.044 [2.104, 2.274] 4.258 0.016 [4.224, 4.287] 2.202 0.047 [2.112, 2.295]
6 3.739 0.017 [3.707, 3.774] 2.031 0.040 [1.958, 2.116] 3.739 0.017 [3.706, 3.771] 2.097 0.043 [2.012, 2.179]
7 4.190 0.016 [4.158, 4.220] 2.314 0.047 [2.221, 2.406] 4.189 0.017 [4.156, 4.222] 2.516 0.063 [2.393, 2.638]
8 4.522 0.018 [4.487, 4.557] 1.879 0.036 [1.809, 1.950] 4.522 0.018 [4.488, 4.558] 2.091 0.047 [1.995, 2.180]
9 4.377 0.020 [4.338, 4.417] 1.600 0.031 [1.533, 1.656] 4.379 0.021 [4.339, 4.420] 1.701 0.036 [1.632, 1.771]
μξ 4.316 0.202 [3.901, 4.701] 4.315 0.199 [3.914, 4.708]
σξ2 0.367 0.217 [0.103, 0.751] 0.366 0.219 [0.113, 0.763]

表62012年PISA计算机化数学测验数据分析中题目参数估计值
题目 ULRTM MLRTM
ξ ω ξ ω
M SE 95% CI M SE 95% CI M SE 95% CI M SE 95% CI
1 4.470 0.020 [4.432, 4.508] 1.617 0.031 [1.558, 1.678] 4.469 0.020 [4.433, 4.510] 1.845 0.045 [1.760, 1.936]
2 4.630 0.019 [4.592, 4.667] 1.697 0.032 [1.635, 1.762] 4.629 0.019 [4.594, 4.668] 1.976 0.051 [1.874, 2.076]
3 4.778 0.016 [4.750, 4.811] 2.423 0.050 [2.327, 2.519] 4.778 0.015 [4.747, 4.807] 2.505 0.055 [2.397, 2.612]
4 3.860 0.018 [3.825, 3.895] 1.866 0.036 [1.793, 1.934] 3.859 0.017 [3.825, 3.894] 1.915 0.038 [1.841, 1.991]
5 4.258 0.016 [4.226, 4.291] 2.186 0.044 [2.104, 2.274] 4.258 0.016 [4.224, 4.287] 2.202 0.047 [2.112, 2.295]
6 3.739 0.017 [3.707, 3.774] 2.031 0.040 [1.958, 2.116] 3.739 0.017 [3.706, 3.771] 2.097 0.043 [2.012, 2.179]
7 4.190 0.016 [4.158, 4.220] 2.314 0.047 [2.221, 2.406] 4.189 0.017 [4.156, 4.222] 2.516 0.063 [2.393, 2.638]
8 4.522 0.018 [4.487, 4.557] 1.879 0.036 [1.809, 1.950] 4.522 0.018 [4.488, 4.558] 2.091 0.047 [1.995, 2.180]
9 4.377 0.020 [4.338, 4.417] 1.600 0.031 [1.533, 1.656] 4.379 0.021 [4.339, 4.420] 1.701 0.036 [1.632, 1.771]
μξ 4.316 0.202 [3.901, 4.701] 4.315 0.199 [3.914, 4.708]
σξ2 0.367 0.217 [0.103, 0.751] 0.366 0.219 [0.113, 0.763]



图2模拟研究1中K × I的Q′矩阵 注: 灰色为1、白色为0分别使用MLRTM和ULRTM去拟合生成数据。对于每组数据, 马尔可夫链数、迭代数和预热数等均与实证研究中保持一致。采用bias和RMSE来评估参数估计返真性; 另外, 也计算了各参数估计值与其真值之间的相关系数(Cor)。
图2模拟研究1中K × I的Q′矩阵 注: 灰色为1、白色为0分别使用MLRTM和ULRTM去拟合生成数据。对于每组数据, 马尔可夫链数、迭代数和预热数等均与实证研究中保持一致。采用bias和RMSE来评估参数估计返真性; 另外, 也计算了各参数估计值与其真值之间的相关系数(Cor)。



图3模拟研究1中题目参数返真性(题目水平) 注：U = 单维对数正态作答时间模型; M = 多维对数正态作答时间模型; RMSE = 均方根误差.
图3模拟研究1中题目参数返真性(题目水平) 注：U = 单维对数正态作答时间模型; M = 多维对数正态作答时间模型; RMSE = 均方根误差.


表7模拟研究1中被试参数返真性的总结
Parameter MA_bias M_RMSE Cor
τ1 0.016 0.147 0.956
τ2 0.017 0.147 0.955
τ3 0.016 0.144 0.957
τ4 0.017 0.143 0.958

表7模拟研究1中被试参数返真性的总结
Parameter MA_bias M_RMSE Cor
τ1 0.016 0.147 0.956
τ2 0.017 0.147 0.955
τ3 0.016 0.144 0.957
τ4 0.017 0.143 0.958


表8模拟研究1中被试参数的方差协方差矩阵返真性
Στ τ1 τ2 τ3 τ4
τ1 0.00003 (0.00000)
τ2 0.00023 (0.00003) 0.00069 (-0.00010)
τ3 0.00031 (0.00004) 0.00015 (0.00002) 0.00015 (0.00002)
τ4 0.00015 (0.00002) 0.00041 (-0.00006) 0.00020 (0.00003) 0.00079 (-0.00011)

表8模拟研究1中被试参数的方差协方差矩阵返真性
Στ τ1 τ2 τ3 τ4
τ1 0.00003 (0.00000)
τ2 0.00023 (0.00003) 0.00069 (-0.00010)
τ3 0.00031 (0.00004) 0.00015 (0.00002) 0.00015 (0.00002)
τ4 0.00015 (0.00002) 0.00041 (-0.00006) 0.00020 (0.00003) 0.00079 (-0.00011)



图4模拟研究2中题目参数返真性(题目水平) 注：U = 单维对数正态作答时间模型; M = 多维对数正态作答时间模型; RMSE = 均方根误差.
图4模拟研究2中题目参数返真性(题目水平) 注：U = 单维对数正态作答时间模型; M = 多维对数正态作答时间模型; RMSE = 均方根误差.


表9模拟研究2中被试参数返真性
分析模型 参数 MA_bias M_RMSE Cor
ULRTM τ 0.013 0.088 0.985
MLRTM τ1 0.023 0.197 0.974
τ2 0.026 0.226 0.973
τ3 0.027 0.235 0.971
τ4 0.023 0.199 0.974

表9模拟研究2中被试参数返真性
分析模型 参数 MA_bias M_RMSE Cor
ULRTM τ 0.013 0.088 0.985
MLRTM τ1 0.023 0.197 0.974
τ2 0.026 0.226 0.973
τ3 0.027 0.235 0.971
τ4 0.023 0.199 0.974







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