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一种基于多阶认知诊断模型测评科学素养的方法

本站小编 Free考研考试/2022-01-01
詹沛达(), 于照辉, 李菲茗, 王立君
浙江师范大学教师教育学院, 金华 321004
收稿日期:2018-09-21出版日期:2019-06-25发布日期:2019-04-25
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(31600908);浙江省自然科学基金项目(LY16C090001);教育部人文社会科学研究青年基金项目(19YJC190025);浙江省教育科学规划重点课题资助(2019SB112)

Using a multi-order cognitive diagnosis model to assess scientific literacy

ZHAN Peida(), YU Zhaohui, LI Feiming, WANG Lijun
College of Teacher Education, Zhejiang Normal University, Jinhua 321004, China
Received:2018-09-21Online:2019-06-25Published:2019-04-25
Contact:ZHAN Peida E-mail:pdzhan@gmail.com






摘要/Abstract


摘要： 科学素养是指作为一名有反思意识的公民所具有的解决科学问题和运用科学理念的能力。为实现在认知诊断中对科学素养的测评, 本文基于PISA 2015科学素养测评框架首次提出科学素养包含的三阶潜在结构, 使用新提出的多阶认知诊断模型对PISA 2015科学测评数据进行分析, 并通过模拟研究探究新模型的心理测量学性能。结果表明：(1)新模型能够较好地分析包含三阶潜在结构的科学素养; (2)科学知识对科学素养的影响最大, 科学背景次之, 科学能力的影响最小; (3)全贝叶斯MCMC算法能够为新模型提供较精准的参数估计。



图1PISA 2015科学素养测评框架(来源：OECD (2016)第23页图2.2).
图1PISA 2015科学素养测评框架(来源：OECD (2016)第23页图2.2).



图2PISA 2015科学素养所包含的三阶潜在结构
图2PISA 2015科学素养所包含的三阶潜在结构



图3CDA中二阶潜在特质与属性间的关系示例图 注：θ为第二阶潜在特质; α为(第一阶)属性; K为总属性数量; I为总题目数量
图3CDA中二阶潜在特质与属性间的关系示例图 注：θ为第二阶潜在特质; α为(第一阶)属性; K为总属性数量; I为总题目数量



图4CDA中第三阶潜在特质与属性间的关系示例图. 注：θ(3)为第三阶潜在特质; θ(2)为第二阶潜在特质; α为(第一阶)属性; K为总属性数量; I为总题目数量。
图4CDA中第三阶潜在特质与属性间的关系示例图. 注：θ(3)为第三阶潜在特质; θ(2)为第二阶潜在特质; α为(第一阶)属性; K为总属性数量; I为总题目数量。


表1PISA 2015科学测验部分题目的Q矩阵
题目 θ(3)
θ1(2) θ2(2) θ3(2)
A1 A2 A3 A4 A5 A6 A7 A8 A9
DS269Q01 1 1 1
DS269Q03 1 1 1
CS269Q04 1 1 1
CS408Q01 1 1 1
DS408Q03 1 1 1
CS408Q04 1 1 1
CS408Q05 1 1 1
CS521Q02 1 1 1
CS521Q06 1 1 1
DS519Q01 1 1 1
CS519Q02 1 1 1
DS519Q03 1 1 1
CS527Q01 1 1 1
CS527Q03 1 1 1
CS527Q04 1 1 1
CS466Q01 1 1 1
CS466Q07 1 1 1
CS466Q05 1 1 1

表1PISA 2015科学测验部分题目的Q矩阵
题目 θ(3)
θ1(2) θ2(2) θ3(2)
A1 A2 A3 A4 A5 A6 A7 A8 A9
DS269Q01 1 1 1
DS269Q03 1 1 1
CS269Q04 1 1 1
CS408Q01 1 1 1
DS408Q03 1 1 1
CS408Q04 1 1 1
CS408Q05 1 1 1
CS521Q02 1 1 1
CS521Q06 1 1 1
DS519Q01 1 1 1
CS519Q02 1 1 1
DS519Q03 1 1 1
CS527Q01 1 1 1
CS527Q03 1 1 1
CS527Q04 1 1 1
CS466Q01 1 1 1
CS466Q07 1 1 1
CS466Q05 1 1 1


表2PISA 2015科学测验部分题目数据的模型-数据拟合指标值.
模型 -2LL AIC BIC DIC ppp
MO-DINA 19332 19389 19673 24775 0.738
HO-DINA 19345 19399 19668 24644 0.716
DINA 19415 19962 22687 24856 0.692

表2PISA 2015科学测验部分题目数据的模型-数据拟合指标值.
模型 -2LL AIC BIC DIC ppp
MO-DINA 19332 19389 19673 24775 0.738
HO-DINA 19345 19399 19668 24644 0.716
DINA 19415 19962 22687 24856 0.692


表3PISA 2015科学测验部分题目的参数估计值.
题目 gi si 95% CI (gi) 95% CI (si) IDIi
DS269Q01 0.325 0.119 [0.263, 0.386] [0.082, 0.158] 0.556
DS269Q03 0.459 0.070 [0.397, 0.521] [0.042, 0.102] 0.471
CS269Q04 0.237 0.351 [0.190, 0.289] [0.304, 0.398] 0.412
CS408Q01 0.434 0.181 [0.373, 0.489] [0.142, 0.222] 0.385
DS408Q03 0.033 0.810 [0.015, 0.058] [0.776, 0.843] 0.157
CS408Q04 0.429 0.261 [0.374, 0.487] [0.219, 0.300] 0.310
CS408Q05 0.295 0.213 [0.220, 0.357] [0.160, 0.266] 0.492
CS521Q02 0.548 0.133 [0.494, 0.602] [0.097, 0.170] 0.319
CS521Q06 0.849 0.008 [0.809, 0.883] [0.002, 0.017] 0.143
DS519Q01 0.106 0.524 [0.047, 0.163] [0.457, 0.582] 0.370
CS519Q02 0.281 0.304 [0.231, 0.332] [0.256, 0.353] 0.415
DS519Q03 0.323 0.228 [0.212, 0.404] [0.174, 0.282] 0.449
CS527Q01 0.033 0.788 [0.012, 0.055] [0.742, 0.831] 0.179
CS527Q03 0.393 0.330 [0.343, 0.442] [0.289, 0.371] 0.277
CS527Q04 0.281 0.373 [0.203, 0.343] [0.316, 0.423] 0.346
CS466Q01 0.448 0.182 [0.378, 0.514] [0.140, 0.226] 0.370
CS466Q07 0.649 0.050 [0.543, 0.726] [0.026, 0.080] 0.301
CS466Q05 0.342 0.243 [0.284, 0.398] [0.184, 0.300] 0.415

表3PISA 2015科学测验部分题目的参数估计值.
题目 gi si 95% CI (gi) 95% CI (si) IDIi
DS269Q01 0.325 0.119 [0.263, 0.386] [0.082, 0.158] 0.556
DS269Q03 0.459 0.070 [0.397, 0.521] [0.042, 0.102] 0.471
CS269Q04 0.237 0.351 [0.190, 0.289] [0.304, 0.398] 0.412
CS408Q01 0.434 0.181 [0.373, 0.489] [0.142, 0.222] 0.385
DS408Q03 0.033 0.810 [0.015, 0.058] [0.776, 0.843] 0.157
CS408Q04 0.429 0.261 [0.374, 0.487] [0.219, 0.300] 0.310
CS408Q05 0.295 0.213 [0.220, 0.357] [0.160, 0.266] 0.492
CS521Q02 0.548 0.133 [0.494, 0.602] [0.097, 0.170] 0.319
CS521Q06 0.849 0.008 [0.809, 0.883] [0.002, 0.017] 0.143
DS519Q01 0.106 0.524 [0.047, 0.163] [0.457, 0.582] 0.370
CS519Q02 0.281 0.304 [0.231, 0.332] [0.256, 0.353] 0.415
DS519Q03 0.323 0.228 [0.212, 0.404] [0.174, 0.282] 0.449
CS527Q01 0.033 0.788 [0.012, 0.055] [0.742, 0.831] 0.179
CS527Q03 0.393 0.330 [0.343, 0.442] [0.289, 0.371] 0.277
CS527Q04 0.281 0.373 [0.203, 0.343] [0.316, 0.423] 0.346
CS466Q01 0.448 0.182 [0.378, 0.514] [0.140, 0.226] 0.370
CS466Q07 0.649 0.050 [0.543, 0.726] [0.026, 0.080] 0.301
CS466Q05 0.342 0.243 [0.284, 0.398] [0.184, 0.300] 0.415


表4PISA 2015科学测验部分题目的题目均值向量和方差协方差矩阵估计值.
参数 后验均值 95% CI 相关系数
Σ σβ2 1.773 [0.873, 3.571] 1.000
ρβδσβσδ -1.833 [-3.719, -0.856] -0.890
σδ2 2.394 [1.145, 4.778] 1.000
μ μβ -0.783 [-1.408, -0.154]
μδ -1.212 [-1.924, -0.493]

表4PISA 2015科学测验部分题目的题目均值向量和方差协方差矩阵估计值.
参数 后验均值 95% CI 相关系数
Σ σβ2 1.773 [0.873, 3.571] 1.000
ρβδσβσδ -1.833 [-3.719, -0.856] -0.890
σδ2 2.394 [1.145, 4.778] 1.000
μ μβ -0.783 [-1.408, -0.154]
μδ -1.212 [-1.924, -0.493]



图5PISA 2015科学测验中潜在结构参数估计值(基于MO-DINA模型). 注：括号内为95%贝叶斯可信区间.
图5PISA 2015科学测验中潜在结构参数估计值(基于MO-DINA模型). 注：括号内为95%贝叶斯可信区间.


表5PISA 2015科学测验部分题目数据的诊断结果示例(基于MO-DINA模型).
被试 α θ1(2) θ2(2) θ3(2) θ(3)
2 111111111 0.582 [-0.863, 2.194] 0.661 [-0.586, 2.174] 0.656 [-0.572, 2.175] 0.664 [-0.581, 2.194]
5 010001000 -0.873 [-2.317, 0.537] -0.940 [-2.290, 0.276] -0.910 [-2.307, 0.357] -0.939 [-2.302, 0.263]
7 010000000 -0.919 [-2.429, 0.541] -1.022 [-2.432, 0.198] -1.028 [-2.445, 0.211] -1.027 [-2.453, 0.183]
23 111111111 0.202 [-1.182, 1.950] 0.283 [-1.057, 1.961] 0.338 [-0.999, 1.959] 0.294 [-1.035, 1.968]
54 010101000 -0.831 [-2.414, 0.620] -0.880 [-2.319, 0.461] -0.870 [-2.368, 0.525] -0.886 [-2.341, 0.426]
86 111101110 -0.404 [-2.082, 1.368] -0.462 [-2.054, 1.314] -0.468 [-2.034, 1.293] -0.467 [-2.062, 1.300]

表5PISA 2015科学测验部分题目数据的诊断结果示例(基于MO-DINA模型).
被试 α θ1(2) θ2(2) θ3(2) θ(3)
2 111111111 0.582 [-0.863, 2.194] 0.661 [-0.586, 2.174] 0.656 [-0.572, 2.175] 0.664 [-0.581, 2.194]
5 010001000 -0.873 [-2.317, 0.537] -0.940 [-2.290, 0.276] -0.910 [-2.307, 0.357] -0.939 [-2.302, 0.263]
7 010000000 -0.919 [-2.429, 0.541] -1.022 [-2.432, 0.198] -1.028 [-2.445, 0.211] -1.027 [-2.453, 0.183]
23 111111111 0.202 [-1.182, 1.950] 0.283 [-1.057, 1.961] 0.338 [-0.999, 1.959] 0.294 [-1.035, 1.968]
54 010101000 -0.831 [-2.414, 0.620] -0.880 [-2.319, 0.461] -0.870 [-2.368, 0.525] -0.886 [-2.341, 0.426]
86 111101110 -0.404 [-2.082, 1.368] -0.462 [-2.054, 1.314] -0.468 [-2.034, 1.293] -0.467 [-2.062, 1.300]



图6模拟研究中的K × I的Q’ 矩阵. 灰色表示“1”, 白色表示“0”.
图6模拟研究中的K × I的Q’ 矩阵. 灰色表示“1”, 白色表示“0”.



图7模拟研究中题目参数的返真性. 注: bias = 偏差; RMSE = 均方根误差.
图7模拟研究中题目参数的返真性. 注: bias = 偏差; RMSE = 均方根误差.



图8模拟研究中属性参数的属性正确判准率(ACCR).
图8模拟研究中属性参数的属性正确判准率(ACCR).


表6模拟研究中高阶潜在特质参数的返真性.
参数 tbias RMSE Cor
平均绝对值 标准差 最小值 最大值 平均值 标准差 最小值 最大值
θ(3) 0.100 0.124 -0.380 0.368 0.686 0.090 0.408 0.983 0.721
θ1(2) 0.100 0.125 -0.378 0.352 0.689 0.092 0.385 0.983 0.719
θ2(2) 0.104 0.126 -0.372 0.351 0.683 0.089 0.416 0.947 0.726
θ3(2) 0.104 0.130 -0.481 0.381 0.690 0.095 0.358 1.050 0.715

表6模拟研究中高阶潜在特质参数的返真性.
参数 tbias RMSE Cor
平均绝对值 标准差 最小值 最大值 平均值 标准差 最小值 最大值
θ(3) 0.100 0.124 -0.380 0.368 0.686 0.090 0.408 0.983 0.721
θ1(2) 0.100 0.125 -0.378 0.352 0.689 0.092 0.385 0.983 0.719
θ2(2) 0.104 0.126 -0.372 0.351 0.683 0.089 0.416 0.947 0.726
θ3(2) 0.104 0.130 -0.481 0.381 0.690 0.095 0.358 1.050 0.715


表7模拟研究中潜在结构参数的返真性
参数 bias RMSE Cor
平均绝对值 标准差 最小值 最大值 平均值 标准差 最小值 最大值
λ0k 0.042 0.048 -0.066 0.072 0.189 0.062 0.129 0.305 0.982
λ1km 0.116 0.051 0.015 0.172 0.346 0.057 0.245 0.429 0.982
γ1(2) -0.031 0.053
γ2(2) -0.012 0.076
γ3(2) -0.012 0.076

表7模拟研究中潜在结构参数的返真性
参数 bias RMSE Cor
平均绝对值 标准差 最小值 最大值 平均值 标准差 最小值 最大值
λ0k 0.042 0.048 -0.066 0.072 0.189 0.062 0.129 0.305 0.982
λ1km 0.116 0.051 0.015 0.172 0.346 0.057 0.245 0.429 0.982
γ1(2) -0.031 0.053
γ2(2) -0.012 0.076
γ3(2) -0.012 0.076







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