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基于类别水平的多级计分认知诊断Q矩阵修正：相对拟合统计量视角

本站小编 Free考研考试/2022-01-01
汪大勋1, 高旭亮2, 蔡艳1, 涂冬波1()
1 江西师范大学心理学院, 南昌 330022
2 贵州师范大学心理学院, 贵阳 550000
收稿日期:2018-12-14出版日期:2020-01-25发布日期:2019-11-21
通讯作者:涂冬波E-mail:tudongbo@aliyun.com

基金资助:* 国家自然科学基金(31660278);国家自然科学基金(31760288);国家自然科学基金(31960186);江西省教育厅研究生创新基金(YC2018-B025);江西师范大学研究生境内外访学项目的资助

A method of Q-matrix validation for polytomous response cognitive diagnosis model based on relative fit statistics

WANG Daxun1, GAO Xuliang2, CAI Yan1, TU Dongbo1()
1 School of Psychology, Jiangxi Normal University, Nanchang 330022, China
2 School of Psychology, Guizhou Normal University, Guiyang 550000, China
Received:2018-12-14Online:2020-01-25Published:2019-11-21
Contact:TU Dongbo E-mail:tudongbo@aliyun.com






摘要/Abstract


摘要： 多级计分认知诊断模型的开发对认知诊断的发展具有重要作用, 但对于多级计分模型下的Q矩阵修正还有待研究。本研究尝试对多级计分认知诊断Q矩阵修正进行研究, 并聚焦更具诊断价值的基于项目类别水平的Q矩阵修正。将相对拟合统计量应用于多级计分认知诊断Q矩阵修正, 并与已有方法Stepwise方法( Ma & de la Torre, 2019)进行比较。研究表明：BIC方法对多级计分认知诊断模型的Q矩阵修正具有较高的模式判准率和属性判准率, 其对Q矩阵的恢复率也高于Stepwise方法, BIC方法修正后的Q矩阵与数据更加拟合; 在复杂模型中, 相对拟合指标BIC比AIC和-2LL表现更好, 在实践中, 使用者可以选择BIC法进行测验Q矩阵修正; Q矩阵修正效果受到被试人数的影响, 增加被试人数可以提高Q矩阵修正的正确率。总之, 本研究为多级计分认知诊断Q矩阵修正提供了重要的方法支持。


表1测验Q矩阵
题目 类别 A1 A2 A3 A4 A5 题目 类别 A1 A2 A3 A4 A5
1 1 1 0 0 0 0 11 1 1 1 0 0 0
1 2 0 1 0 0 0 11 2 0 0 0 0 1
2 1 0 0 1 0 0 12 1 1 1 1 0 0
2 2 0 0 0 1 0 12 2 0 0 0 1 1
3 1 0 0 0 0 1 13 1 1 1 0 0 0
3 2 1 0 0 0 0 13 2 0 0 1 1 1
4 1 0 0 0 0 1 14 1 1 0 1 0 0
4 2 0 0 0 1 0 14 2 0 0 0 1 0
5 1 0 0 1 0 0 14 3 0 0 0 0 1
5 2 0 1 0 0 0 15 1 0 0 0 0 1
6 1 1 0 0 0 0 15 2 0 0 1 1 0
6 2 0 1 1 0 0 15 3 0 1 0 0 0
7 1 0 0 1 0 0 16 1 1 0 0 0 0
7 2 0 0 0 1 1 16 2 0 1 0 0 0
8 1 0 0 0 0 1 16 3 0 0 1 1 0
8 2 1 1 0 0 0 17 1 1 0 0 0 0
9 1 0 0 0 1 1 18 1 0 1 0 0 0
9 2 0 0 1 0 0 19 1 0 0 1 0 0
10 1 0 1 0 1 0 20 1 0 0 0 1 0
10 2 1 0 0 0 0 21 1 0 0 0 0 1

表1测验Q矩阵
题目 类别 A1 A2 A3 A4 A5 题目 类别 A1 A2 A3 A4 A5
1 1 1 0 0 0 0 11 1 1 1 0 0 0
1 2 0 1 0 0 0 11 2 0 0 0 0 1
2 1 0 0 1 0 0 12 1 1 1 1 0 0
2 2 0 0 0 1 0 12 2 0 0 0 1 1
3 1 0 0 0 0 1 13 1 1 1 0 0 0
3 2 1 0 0 0 0 13 2 0 0 1 1 1
4 1 0 0 0 0 1 14 1 1 0 1 0 0
4 2 0 0 0 1 0 14 2 0 0 0 1 0
5 1 0 0 1 0 0 14 3 0 0 0 0 1
5 2 0 1 0 0 0 15 1 0 0 0 0 1
6 1 1 0 0 0 0 15 2 0 0 1 1 0
6 2 0 1 1 0 0 15 3 0 1 0 0 0
7 1 0 0 1 0 0 16 1 1 0 0 0 0
7 2 0 0 0 1 1 16 2 0 1 0 0 0
8 1 0 0 0 0 1 16 3 0 0 1 1 0
8 2 1 1 0 0 0 17 1 1 0 0 0 0
9 1 0 0 0 1 1 18 1 0 1 0 0 0
9 2 0 0 1 0 0 19 1 0 0 1 0 0
10 1 0 1 0 1 0 20 1 0 0 0 1 0
10 2 1 0 0 0 0 21 1 0 0 0 0 1


表2Q矩阵错误类型
Q Q矩阵错误模拟规则 调整的类别 调整的属性个数 备注
Q1 ${{q}_{jk}}=0\to {{q}_{jk}}=1$ $K_{jh}^{*}=1$的类别 5 属性冗余
Q2 ${{q}_{jk}}=1\to {{q}_{jk}}=0$ $K_{jh}^{*}>2$的类别 5 属性缺失
Q3 ${{q}_{jk}}=0\to {{q}_{jk}}=1,{{q}_{j{k}'}}=1\to {{q}_{j{k}'}}=0$ $K_{jh}^{*}>2$的类别 10 属性既冗余又缺失
Q4 ${{q}_{jk}}=0\to {{q}_{jk}}=1$
${{q}_{jk}}=1\to {{q}_{jk}}=0$${{q}_{jk}}=0\to {{q}_{jk}}=1\text{ }{{q}_{j{k}'}}=1\to {{q}_{j{k}'}}=0$		 分别为Q1、Q2和Q3的类别 20 Q1、Q2和Q3的组合
Q5 10%随机调整 随机 20 调整后$1<K_{jh}^{*}<3$
Q6 20%随机调整 随机 40 调整后$1<K_{jh}^{*}<3$

表2Q矩阵错误类型
Q Q矩阵错误模拟规则 调整的类别 调整的属性个数 备注
Q1 ${{q}_{jk}}=0\to {{q}_{jk}}=1$ $K_{jh}^{*}=1$的类别 5 属性冗余
Q2 ${{q}_{jk}}=1\to {{q}_{jk}}=0$ $K_{jh}^{*}>2$的类别 5 属性缺失
Q3 ${{q}_{jk}}=0\to {{q}_{jk}}=1,{{q}_{j{k}'}}=1\to {{q}_{j{k}'}}=0$ $K_{jh}^{*}>2$的类别 10 属性既冗余又缺失
Q4 ${{q}_{jk}}=0\to {{q}_{jk}}=1$
${{q}_{jk}}=1\to {{q}_{jk}}=0$${{q}_{jk}}=0\to {{q}_{jk}}=1\text{ }{{q}_{j{k}'}}=1\to {{q}_{j{k}'}}=0$		 分别为Q1、Q2和Q3的类别 20 Q1、Q2和Q3的组合
Q5 10%随机调整 随机 20 调整后$1<K_{jh}^{*}<3$
Q6 20%随机调整 随机 40 调整后$1<K_{jh}^{*}<3$


表3BIC方法和Stepwise方法在seq-DINA模型中200次实验的平均结果
Q-matrix N PMR AMR FPR TPR RMSEA
Stepwise BIC Stepwise BIC Stepwise BIC Stepwise BIC QW QStepwise QBIC
Q1 500 0.795 0.788 0.957 0.963 0.118 0.157 0.958 0.965 0.017 0.015 0.007
1000 0.879 0.863 0.975 0.977 0.065 0.074 0.975 0.978 0.018 0.009 0.005
2000 0.918 0.911 0.984 0.986 0.048 0.049 0.985 0.986 0.019 0.005 0.003
Q2 500 0.763 0.790 0.953 0.962 0.367 0.021 0.958 0.962 0.017 0.016 0.007
1000 0.826 0.856 0.967 0.975 0.257 0.004 0.971 0.975 0.016 0.011 0.005
2000 0.865 0.903 0.976 0.984 0.219 0.002 0.980 0.984 0.017 0.008 0.003
Q3 500 0.758 0.786 0.952 0.962 0.339 0.126 0.963 0.966 0.033 0.016 0.006
1000 0.815 0.861 0.964 0.976 0.251 0.089 0.972 0.979 0.034 0.010 0.005
2000 0.856 0.910 0.974 0.985 0.180 0.065 0.980 0.987 0.035 0.009 0.004
Q4 500 0.680 0.776 0.938 0.961 0.363 0.110 0.962 0.966 0.041 0.020 0.007
1000 0.721 0.853 0.950 0.975 0.288 0.064 0.968 0.978 0.041 0.015 0.005
2000 0.745 0.905 0.956 0.984 0.251 0.040 0.972 0.986 0.042 0.013 0.003
Q5 500 0.760 0.777 0.951 0.959 0.112 0.068 0.956 0.961 0.075 0.020 0.008
1000 0.835 0.851 0.968 0.975 0.082 0.041 0.972 0.976 0.073 0.011 0.004
2000 0.874 0.903 0.975 0.984 0.065 0.022 0.978 0.984 0.076 0.013 0.004
Q6 500 0.629 0.687 0.924 0.933 0.184 0.105 0.943 0.940 0.100 0.035 0.015
1000 0.656 0.744 0.931 0.942 0.173 0.097 0.949 0.949 0.102 0.038 0.017
2000 0.687 0.793 0.935 0.953 0.163 0.081 0.951 0.959 0.102 0.037 0.010

表3BIC方法和Stepwise方法在seq-DINA模型中200次实验的平均结果
Q-matrix N PMR AMR FPR TPR RMSEA
Stepwise BIC Stepwise BIC Stepwise BIC Stepwise BIC QW QStepwise QBIC
Q1 500 0.795 0.788 0.957 0.963 0.118 0.157 0.958 0.965 0.017 0.015 0.007
1000 0.879 0.863 0.975 0.977 0.065 0.074 0.975 0.978 0.018 0.009 0.005
2000 0.918 0.911 0.984 0.986 0.048 0.049 0.985 0.986 0.019 0.005 0.003
Q2 500 0.763 0.790 0.953 0.962 0.367 0.021 0.958 0.962 0.017 0.016 0.007
1000 0.826 0.856 0.967 0.975 0.257 0.004 0.971 0.975 0.016 0.011 0.005
2000 0.865 0.903 0.976 0.984 0.219 0.002 0.980 0.984 0.017 0.008 0.003
Q3 500 0.758 0.786 0.952 0.962 0.339 0.126 0.963 0.966 0.033 0.016 0.006
1000 0.815 0.861 0.964 0.976 0.251 0.089 0.972 0.979 0.034 0.010 0.005
2000 0.856 0.910 0.974 0.985 0.180 0.065 0.980 0.987 0.035 0.009 0.004
Q4 500 0.680 0.776 0.938 0.961 0.363 0.110 0.962 0.966 0.041 0.020 0.007
1000 0.721 0.853 0.950 0.975 0.288 0.064 0.968 0.978 0.041 0.015 0.005
2000 0.745 0.905 0.956 0.984 0.251 0.040 0.972 0.986 0.042 0.013 0.003
Q5 500 0.760 0.777 0.951 0.959 0.112 0.068 0.956 0.961 0.075 0.020 0.008
1000 0.835 0.851 0.968 0.975 0.082 0.041 0.972 0.976 0.073 0.011 0.004
2000 0.874 0.903 0.975 0.984 0.065 0.022 0.978 0.984 0.076 0.013 0.004
Q6 500 0.629 0.687 0.924 0.933 0.184 0.105 0.943 0.940 0.100 0.035 0.015
1000 0.656 0.744 0.931 0.942 0.173 0.097 0.949 0.949 0.102 0.038 0.017
2000 0.687 0.793 0.935 0.953 0.163 0.081 0.951 0.959 0.102 0.037 0.010


表4BIC方法和Stepwise方法在seq-RRUM模型中200次实验的平均结果
Q-matrix N PMR AMR FPR TPR RMSEA
Stepwise BIC Stepwise BIC Stepwise BIC Stepwise BIC QW QStepwise QBIC
Q1 500 0.750 0.841 0.952 0.975 0.083 0.022 0.952 0.975 0.006 0.007 0.006
1000 0.823 0.884 0.968 0.982 0.037 0.041 0.968 0.983 0.005 0.005 0.005
2000 0.864 0.915 0.976 0.987 0.029 0.020 0.977 0.987 0.004 0.005 0.004
Q2 500 0.746 0.839 0.953 0.975 0.332 0.199 0.958 0.978 0.027 0.008 0.007
1000 0.819 0.890 0.968 0.983 0.264 0.153 0.972 0.986 0.026 0.006 0.005
2000 0.843 0.919 0.974 0.988 0.252 0.117 0.978 0.990 0.026 0.005 0.003
Q3 500 0.734 0.847 0.949 0.976 0.300 0.121 0.959 0.980 0.022 0.008 0.006
1000 0.794 0.877 0.963 0.981 0.241 0.086 0.971 0.983 0.023 0.006 0.005
2000 0.843 0.914 0.973 0.987 0.171 0.057 0.979 0.989 0.023 0.005 0.003
Q4 500 0.714 0.832 0.946 0.974 0.275 0.123 0.963 0.981 0.030 0.008 0.007
1000 0.770 0.881 0.959 0.982 0.215 0.085 0.973 0.987 0.031 0.006 0.005
2000 0.796 0.917 0.966 0.987 0.195 0.058 0.978 0.991 0.032 0.005 0.003
Q5 500 0.751 0.841 0.952 0.975 0.098 0.047 0.956 0.976 0.039 0.008 0.006
1000 0.807 0.880 0.965 0.982 0.073 0.038 0.968 0.983 0.035 0.005 0.005
2000 0.849 0.914 0.974 0.987 0.053 0.021 0.976 0.987 0.039 0.005 0.004
Q6 500 0.686 0.817 0.941 0.968 0.134 0.063 0.953 0.973 0.063 0.014 0.008
1000 0.726 0.848 0.948 0.973 0.127 0.058 0.960 0.978 0.070 0.012 0.007
2000 0.748 0.896 0.953 0.982 0.120 0.032 0.966 0.984 0.063 0.009 0.004

表4BIC方法和Stepwise方法在seq-RRUM模型中200次实验的平均结果
Q-matrix N PMR AMR FPR TPR RMSEA
Stepwise BIC Stepwise BIC Stepwise BIC Stepwise BIC QW QStepwise QBIC
Q1 500 0.750 0.841 0.952 0.975 0.083 0.022 0.952 0.975 0.006 0.007 0.006
1000 0.823 0.884 0.968 0.982 0.037 0.041 0.968 0.983 0.005 0.005 0.005
2000 0.864 0.915 0.976 0.987 0.029 0.020 0.977 0.987 0.004 0.005 0.004
Q2 500 0.746 0.839 0.953 0.975 0.332 0.199 0.958 0.978 0.027 0.008 0.007
1000 0.819 0.890 0.968 0.983 0.264 0.153 0.972 0.986 0.026 0.006 0.005
2000 0.843 0.919 0.974 0.988 0.252 0.117 0.978 0.990 0.026 0.005 0.003
Q3 500 0.734 0.847 0.949 0.976 0.300 0.121 0.959 0.980 0.022 0.008 0.006
1000 0.794 0.877 0.963 0.981 0.241 0.086 0.971 0.983 0.023 0.006 0.005
2000 0.843 0.914 0.973 0.987 0.171 0.057 0.979 0.989 0.023 0.005 0.003
Q4 500 0.714 0.832 0.946 0.974 0.275 0.123 0.963 0.981 0.030 0.008 0.007
1000 0.770 0.881 0.959 0.982 0.215 0.085 0.973 0.987 0.031 0.006 0.005
2000 0.796 0.917 0.966 0.987 0.195 0.058 0.978 0.991 0.032 0.005 0.003
Q5 500 0.751 0.841 0.952 0.975 0.098 0.047 0.956 0.976 0.039 0.008 0.006
1000 0.807 0.880 0.965 0.982 0.073 0.038 0.968 0.983 0.035 0.005 0.005
2000 0.849 0.914 0.974 0.987 0.053 0.021 0.976 0.987 0.039 0.005 0.004
Q6 500 0.686 0.817 0.941 0.968 0.134 0.063 0.953 0.973 0.063 0.014 0.008
1000 0.726 0.848 0.948 0.973 0.127 0.058 0.960 0.978 0.070 0.012 0.007
2000 0.748 0.896 0.953 0.982 0.120 0.032 0.966 0.984 0.063 0.009 0.004


表5BIC方法和Stepwise方法在seq-GDINA模型中200次实验的平均结果
Q-matrix N PMR AMR FPR TPR RMSEA
Stepwise BIC Stepwise BIC Stepwise BIC Stepwise BIC QW QStepwise QBIC
Q1 500 0.795 0.861 0.961 0.979 0.075 0.006 0.962 0.979 0.007 0.007 0.007
1000 0.875 0.913 0.978 0.987 0.032 0.004 0.978 0.987 0.005 0.006 0.005
2000 0.919 0.950 0.986 0.993 0.020 0.001 0.986 0.993 0.004 0.005 0.004
Q2 500 0.799 0.864 0.964 0.980 0.209 0.211 0.967 0.983 0.029 0.008 0.009
1000 0.877 0.916 0.979 0.988 0.108 0.110 0.980 0.990 0.030 0.006 0.006
2000 0.915 0.948 0.986 0.993 0.093 0.067 0.987 0.994 0.030 0.004 0.004
Q3 500 0.794 0.867 0.961 0.980 0.236 0.125 0.969 0.984 0.022 0.007 0.008
1000 0.854 0.910 0.974 0.987 0.170 0.069 0.979 0.989 0.025 0.006 0.006
2000 0.904 0.949 0.984 0.993 0.106 0.038 0.988 0.994 0.025 0.005 0.003
Q4 500 0.775 0.863 0.958 0.979 0.193 0.106 0.970 0.985 0.033 0.009 0.008
1000 0.840 0.912 0.972 0.987 0.136 0.062 0.981 0.991 0.033 0.007 0.006
2000 0.884 0.945 0.981 0.992 0.112 0.040 0.989 0.994 0.034 0.005 0.004
Q5 500 0.786 0.866 0.959 0.980 0.086 0.040 0.962 0.981 0.034 0.009 0.009
1000 0.859 0.911 0.975 0.987 0.053 0.023 0.977 0.988 0.036 0.006 0.006
2000 0.912 0.949 0.985 0.993 0.031 0.011 0.987 0.993 0.041 0.005 0.004
Q6 500 0.731 0.838 0.948 0.973 0.122 0.059 0.960 0.978 0.061 0.015 0.009
1000 0.784 0.885 0.959 0.980 0.104 0.039 0.970 0.983 0.066 0.010 0.007
2000 0.913 0.948 0.985 0.992 0.037 0.015 0.987 0.993 0.041 0.004 0.004

表5BIC方法和Stepwise方法在seq-GDINA模型中200次实验的平均结果
Q-matrix N PMR AMR FPR TPR RMSEA
Stepwise BIC Stepwise BIC Stepwise BIC Stepwise BIC QW QStepwise QBIC
Q1 500 0.795 0.861 0.961 0.979 0.075 0.006 0.962 0.979 0.007 0.007 0.007
1000 0.875 0.913 0.978 0.987 0.032 0.004 0.978 0.987 0.005 0.006 0.005
2000 0.919 0.950 0.986 0.993 0.020 0.001 0.986 0.993 0.004 0.005 0.004
Q2 500 0.799 0.864 0.964 0.980 0.209 0.211 0.967 0.983 0.029 0.008 0.009
1000 0.877 0.916 0.979 0.988 0.108 0.110 0.980 0.990 0.030 0.006 0.006
2000 0.915 0.948 0.986 0.993 0.093 0.067 0.987 0.994 0.030 0.004 0.004
Q3 500 0.794 0.867 0.961 0.980 0.236 0.125 0.969 0.984 0.022 0.007 0.008
1000 0.854 0.910 0.974 0.987 0.170 0.069 0.979 0.989 0.025 0.006 0.006
2000 0.904 0.949 0.984 0.993 0.106 0.038 0.988 0.994 0.025 0.005 0.003
Q4 500 0.775 0.863 0.958 0.979 0.193 0.106 0.970 0.985 0.033 0.009 0.008
1000 0.840 0.912 0.972 0.987 0.136 0.062 0.981 0.991 0.033 0.007 0.006
2000 0.884 0.945 0.981 0.992 0.112 0.040 0.989 0.994 0.034 0.005 0.004
Q5 500 0.786 0.866 0.959 0.980 0.086 0.040 0.962 0.981 0.034 0.009 0.009
1000 0.859 0.911 0.975 0.987 0.053 0.023 0.977 0.988 0.036 0.006 0.006
2000 0.912 0.949 0.985 0.993 0.031 0.011 0.987 0.993 0.041 0.005 0.004
Q6 500 0.731 0.838 0.948 0.973 0.122 0.059 0.960 0.978 0.061 0.015 0.009
1000 0.784 0.885 0.959 0.980 0.104 0.039 0.970 0.983 0.066 0.010 0.007
2000 0.913 0.948 0.985 0.992 0.037 0.015 0.987 0.993 0.041 0.004 0.004


表6TIMSS 2011(8年级)数据Q矩阵及修正结果
Item Code 类别 A1 A2 A3 A4 A5 A6 A7
1 M042041 1 0 1 0 0 0 0 0
2 M042024 1 0 1 0 0 0 0 0
3 M042016 1 1 0 0 0 0 0 1*#
4 M042002 1 1 0 0 0 0 0 0
5 M042198A 1 0 0 1 0 0 0 0*#
6 M042198B 1 0 0 1 0 0 0 0
7 M042198C 1 0 0 1 0 0* 0 0
8 M042077 1 1 0 0 1 0 0 0
9 M042235 1 0 0 0 1 0* 0 0
10 M042150 1 0 0 0 0 1 0 0
11 M042300Z 1 0 0 0 0 0 1 1
11 M042300Z 2 0 0 0 0 1 0 0
12 M042169A 1 0* 0 0 0 0 0 1
13 M042169B 1 0 0 0 0 0 0 1
14 M042169C 1 0* 0 0 0 0 0 1
15 M032352 1 1 0 1*# 0 0 0 1*
16 M032725 1 0 1* 0 0 0 0*# 0
17 M032738 1 0 0 0 1 0 0 0
18 M032295 1 0 0 0 1 0 0 0
19 M032331 1 0 0 0 0 1 1 0
20 M032679 1 0 0 0 0 1 1* 0
21 M032047 1 1 0 0 1*# 0 0 0
22 M032398 1 0* 0 0 0 1 0 0
23 M032424 1 0 0*# 0 1 0 0 0

表6TIMSS 2011(8年级)数据Q矩阵及修正结果
Item Code 类别 A1 A2 A3 A4 A5 A6 A7
1 M042041 1 0 1 0 0 0 0 0
2 M042024 1 0 1 0 0 0 0 0
3 M042016 1 1 0 0 0 0 0 1*#
4 M042002 1 1 0 0 0 0 0 0
5 M042198A 1 0 0 1 0 0 0 0*#
6 M042198B 1 0 0 1 0 0 0 0
7 M042198C 1 0 0 1 0 0* 0 0
8 M042077 1 1 0 0 1 0 0 0
9 M042235 1 0 0 0 1 0* 0 0
10 M042150 1 0 0 0 0 1 0 0
11 M042300Z 1 0 0 0 0 0 1 1
11 M042300Z 2 0 0 0 0 1 0 0
12 M042169A 1 0* 0 0 0 0 0 1
13 M042169B 1 0 0 0 0 0 0 1
14 M042169C 1 0* 0 0 0 0 0 1
15 M032352 1 1 0 1*# 0 0 0 1*
16 M032725 1 0 1* 0 0 0 0*# 0
17 M032738 1 0 0 0 1 0 0 0
18 M032295 1 0 0 0 1 0 0 0
19 M032331 1 0 0 0 0 1 1 0
20 M032679 1 0 0 0 0 1 1* 0
21 M032047 1 1 0 0 1*# 0 0 0
22 M032398 1 0* 0 0 0 1 0 0
23 M032424 1 0 0*# 0 1 0 0 0


表7TIMSS 2011(8年级)数据不同方法Q矩阵修正一致率
Q Qoriginal QBIC QStepwise
Qoriginal 1
QBIC 0.92 1
QStepwise 0.96 0.95 1

表7TIMSS 2011(8年级)数据不同方法Q矩阵修正一致率
Q Qoriginal QBIC QStepwise
Qoriginal 1
QBIC 0.92 1
QStepwise 0.96 0.95 1


表8TIMSS 2011 (8年级)数据原有Q矩阵和两种方法修正后Q矩阵的拟合指标
Q 相对拟合指标 绝对拟合指标
-2*LL AIC BIC M2检验 RMSEA SRMSR
M2 df p
Qoriginal 18888.23 19274.23 20165.39 123.51 83 0.003 0.026 0.059
QBIC 18624.73 19014.73 19915.13 89.02 81 0.254 0.012 0.044
QStepwise 18757.88 19139.88 20021.88 89.90 85 0.337 0.009 0.050

表8TIMSS 2011 (8年级)数据原有Q矩阵和两种方法修正后Q矩阵的拟合指标
Q 相对拟合指标 绝对拟合指标
-2*LL AIC BIC M2检验 RMSEA SRMSR
M2 df p
Qoriginal 18888.23 19274.23 20165.39 123.51 83 0.003 0.026 0.059
QBIC 18624.73 19014.73 19915.13 89.02 81 0.254 0.012 0.044
QStepwise 18757.88 19139.88 20021.88 89.90 85 0.337 0.009 0.050


表9TIMSS 2007(4年级)数据Q矩阵及修正结果
Item Code 类别 A1 A2 A3 A4 A5 A6 A7 A8
1 M041052 1 1 1 0 0 0 0 0 0
2 M041281 1 0 1 1* 0 1* 0 0 0
3 M041275 1 1 0 0 0 0 1 0 1*
3 M041275 2 1* 0 0 0 0 1 0 1*
4 M031303 1 0 1 1 0 0 0 0 0
5 M031309 1 0 1 1 0 0 0 0 0
6 M031245 1 0 1 0 1 0 0 0 0
7 M031242A 1 0 1 1 0 1 0 0 0
7 M031242B 2 0 0 0 0 0 0 1 0
8 M031242C 1 0 1* 1* 0 1 0 1* 0
9 M031247 1 0 1* 1 1 0 0 0 0
9 M031247 2 0 1 1 1 0 0 0 0
10 M031173 1 0* 1* 1 0 0 0 0 0
11 M031172 1 1* 1* 0 0 0 1* 0 1

表9TIMSS 2007(4年级)数据Q矩阵及修正结果
Item Code 类别 A1 A2 A3 A4 A5 A6 A7 A8
1 M041052 1 1 1 0 0 0 0 0 0
2 M041281 1 0 1 1* 0 1* 0 0 0
3 M041275 1 1 0 0 0 0 1 0 1*
3 M041275 2 1* 0 0 0 0 1 0 1*
4 M031303 1 0 1 1 0 0 0 0 0
5 M031309 1 0 1 1 0 0 0 0 0
6 M031245 1 0 1 0 1 0 0 0 0
7 M031242A 1 0 1 1 0 1 0 0 0
7 M031242B 2 0 0 0 0 0 0 1 0
8 M031242C 1 0 1* 1* 0 1 0 1* 0
9 M031247 1 0 1* 1 1 0 0 0 0
9 M031247 2 0 1 1 1 0 0 0 0
10 M031173 1 0* 1* 1 0 0 0 0 0
11 M031172 1 1* 1* 0 0 0 1* 0 1







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