Hypothesis Testing of the Q-matrix

Abstract The recent surge of interests in cognitive assessment has led to the development of cognitive diagnosis models. Central to many such models is a specification of the Q-matrix, which relates items to latent attributes that have natural interpretations. In practice, the Q-matrix is usually co...
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Autor*in:	Gu, Yuqi [verfasserIn] Liu, Jingchen [verfasserIn] Xu, Gongjun [verfasserIn] Ying, Zhiliang [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	-matrix diagnostic classification models hypothesis testing

Übergeordnetes Werk:	Enthalten in: Psychometrika - New York : Springer-Verl., 1936, 83(2018), 3 vom: 11. Juli, Seite 515-537
Übergeordnetes Werk:	volume:83 ; year:2018 ; number:3 ; day:11 ; month:07 ; pages:515-537

Links:	Volltext

DOI / URN:	10.1007/s11336-018-9629-6

Katalog-ID:	SPR018768156

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520			\|a Abstract The recent surge of interests in cognitive assessment has led to the development of cognitive diagnosis models. Central to many such models is a specification of the Q-matrix, which relates items to latent attributes that have natural interpretations. In practice, the Q-matrix is usually constructed subjectively by the test designers. This could lead to misspecification, which could result in lack of fit of the underlying statistical model. To test possible misspecification of the Q-matrix, traditional goodness of fit tests, such as the Chi-square test and the likelihood ratio test, may not be applied straightforwardly due to the large number of possible response patterns. To address this problem, this paper proposes a new statistical method to test the goodness fit of the Q-matrix, by constructing test statistics that measure the consistency between a provisional Q-matrix and the observed data for a general family of cognitive diagnosis models. Limiting distributions of the test statistics are derived under the null hypothesis that can be used for obtaining the test p-values. Simulation studies as well as a real data example are presented to demonstrate the usefulness of the proposed method.
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allfields	10.1007/s11336-018-9629-6 doi (DE-627)SPR018768156 (SPR)s11336-018-9629-6-e DE-627 ger DE-627 rakwb eng 150 ASE 77.03 bkl Gu, Yuqi verfasserin aut Hypothesis Testing of the Q-matrix 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The recent surge of interests in cognitive assessment has led to the development of cognitive diagnosis models. Central to many such models is a specification of the Q-matrix, which relates items to latent attributes that have natural interpretations. In practice, the Q-matrix is usually constructed subjectively by the test designers. This could lead to misspecification, which could result in lack of fit of the underlying statistical model. To test possible misspecification of the Q-matrix, traditional goodness of fit tests, such as the Chi-square test and the likelihood ratio test, may not be applied straightforwardly due to the large number of possible response patterns. To address this problem, this paper proposes a new statistical method to test the goodness fit of the Q-matrix, by constructing test statistics that measure the consistency between a provisional Q-matrix and the observed data for a general family of cognitive diagnosis models. Limiting distributions of the test statistics are derived under the null hypothesis that can be used for obtaining the test p-values. Simulation studies as well as a real data example are presented to demonstrate the usefulness of the proposed method. -matrix (dpeaa)DE-He213 diagnostic classification models (dpeaa)DE-He213 hypothesis testing (dpeaa)DE-He213 Liu, Jingchen verfasserin aut Xu, Gongjun verfasserin aut Ying, Zhiliang verfasserin aut Enthalten in Psychometrika New York : Springer-Verl., 1936 83(2018), 3 vom: 11. Juli, Seite 515-537 (DE-627)487892054 (DE-600)2188500-X 1860-0980 nnns volume:83 year:2018 number:3 day:11 month:07 pages:515-537 https://dx.doi.org/10.1007/s11336-018-9629-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 77.03 ASE AR 83 2018 3 11 07 515-537
spelling	10.1007/s11336-018-9629-6 doi (DE-627)SPR018768156 (SPR)s11336-018-9629-6-e DE-627 ger DE-627 rakwb eng 150 ASE 77.03 bkl Gu, Yuqi verfasserin aut Hypothesis Testing of the Q-matrix 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The recent surge of interests in cognitive assessment has led to the development of cognitive diagnosis models. Central to many such models is a specification of the Q-matrix, which relates items to latent attributes that have natural interpretations. In practice, the Q-matrix is usually constructed subjectively by the test designers. This could lead to misspecification, which could result in lack of fit of the underlying statistical model. To test possible misspecification of the Q-matrix, traditional goodness of fit tests, such as the Chi-square test and the likelihood ratio test, may not be applied straightforwardly due to the large number of possible response patterns. To address this problem, this paper proposes a new statistical method to test the goodness fit of the Q-matrix, by constructing test statistics that measure the consistency between a provisional Q-matrix and the observed data for a general family of cognitive diagnosis models. Limiting distributions of the test statistics are derived under the null hypothesis that can be used for obtaining the test p-values. Simulation studies as well as a real data example are presented to demonstrate the usefulness of the proposed method. -matrix (dpeaa)DE-He213 diagnostic classification models (dpeaa)DE-He213 hypothesis testing (dpeaa)DE-He213 Liu, Jingchen verfasserin aut Xu, Gongjun verfasserin aut Ying, Zhiliang verfasserin aut Enthalten in Psychometrika New York : Springer-Verl., 1936 83(2018), 3 vom: 11. Juli, Seite 515-537 (DE-627)487892054 (DE-600)2188500-X 1860-0980 nnns volume:83 year:2018 number:3 day:11 month:07 pages:515-537 https://dx.doi.org/10.1007/s11336-018-9629-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 77.03 ASE AR 83 2018 3 11 07 515-537
allfields_unstemmed	10.1007/s11336-018-9629-6 doi (DE-627)SPR018768156 (SPR)s11336-018-9629-6-e DE-627 ger DE-627 rakwb eng 150 ASE 77.03 bkl Gu, Yuqi verfasserin aut Hypothesis Testing of the Q-matrix 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The recent surge of interests in cognitive assessment has led to the development of cognitive diagnosis models. Central to many such models is a specification of the Q-matrix, which relates items to latent attributes that have natural interpretations. In practice, the Q-matrix is usually constructed subjectively by the test designers. This could lead to misspecification, which could result in lack of fit of the underlying statistical model. To test possible misspecification of the Q-matrix, traditional goodness of fit tests, such as the Chi-square test and the likelihood ratio test, may not be applied straightforwardly due to the large number of possible response patterns. To address this problem, this paper proposes a new statistical method to test the goodness fit of the Q-matrix, by constructing test statistics that measure the consistency between a provisional Q-matrix and the observed data for a general family of cognitive diagnosis models. Limiting distributions of the test statistics are derived under the null hypothesis that can be used for obtaining the test p-values. Simulation studies as well as a real data example are presented to demonstrate the usefulness of the proposed method. -matrix (dpeaa)DE-He213 diagnostic classification models (dpeaa)DE-He213 hypothesis testing (dpeaa)DE-He213 Liu, Jingchen verfasserin aut Xu, Gongjun verfasserin aut Ying, Zhiliang verfasserin aut Enthalten in Psychometrika New York : Springer-Verl., 1936 83(2018), 3 vom: 11. Juli, Seite 515-537 (DE-627)487892054 (DE-600)2188500-X 1860-0980 nnns volume:83 year:2018 number:3 day:11 month:07 pages:515-537 https://dx.doi.org/10.1007/s11336-018-9629-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 77.03 ASE AR 83 2018 3 11 07 515-537
allfieldsGer	10.1007/s11336-018-9629-6 doi (DE-627)SPR018768156 (SPR)s11336-018-9629-6-e DE-627 ger DE-627 rakwb eng 150 ASE 77.03 bkl Gu, Yuqi verfasserin aut Hypothesis Testing of the Q-matrix 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The recent surge of interests in cognitive assessment has led to the development of cognitive diagnosis models. Central to many such models is a specification of the Q-matrix, which relates items to latent attributes that have natural interpretations. In practice, the Q-matrix is usually constructed subjectively by the test designers. This could lead to misspecification, which could result in lack of fit of the underlying statistical model. To test possible misspecification of the Q-matrix, traditional goodness of fit tests, such as the Chi-square test and the likelihood ratio test, may not be applied straightforwardly due to the large number of possible response patterns. To address this problem, this paper proposes a new statistical method to test the goodness fit of the Q-matrix, by constructing test statistics that measure the consistency between a provisional Q-matrix and the observed data for a general family of cognitive diagnosis models. Limiting distributions of the test statistics are derived under the null hypothesis that can be used for obtaining the test p-values. Simulation studies as well as a real data example are presented to demonstrate the usefulness of the proposed method. -matrix (dpeaa)DE-He213 diagnostic classification models (dpeaa)DE-He213 hypothesis testing (dpeaa)DE-He213 Liu, Jingchen verfasserin aut Xu, Gongjun verfasserin aut Ying, Zhiliang verfasserin aut Enthalten in Psychometrika New York : Springer-Verl., 1936 83(2018), 3 vom: 11. Juli, Seite 515-537 (DE-627)487892054 (DE-600)2188500-X 1860-0980 nnns volume:83 year:2018 number:3 day:11 month:07 pages:515-537 https://dx.doi.org/10.1007/s11336-018-9629-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 77.03 ASE AR 83 2018 3 11 07 515-537
allfieldsSound	10.1007/s11336-018-9629-6 doi (DE-627)SPR018768156 (SPR)s11336-018-9629-6-e DE-627 ger DE-627 rakwb eng 150 ASE 77.03 bkl Gu, Yuqi verfasserin aut Hypothesis Testing of the Q-matrix 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The recent surge of interests in cognitive assessment has led to the development of cognitive diagnosis models. Central to many such models is a specification of the Q-matrix, which relates items to latent attributes that have natural interpretations. In practice, the Q-matrix is usually constructed subjectively by the test designers. This could lead to misspecification, which could result in lack of fit of the underlying statistical model. To test possible misspecification of the Q-matrix, traditional goodness of fit tests, such as the Chi-square test and the likelihood ratio test, may not be applied straightforwardly due to the large number of possible response patterns. To address this problem, this paper proposes a new statistical method to test the goodness fit of the Q-matrix, by constructing test statistics that measure the consistency between a provisional Q-matrix and the observed data for a general family of cognitive diagnosis models. Limiting distributions of the test statistics are derived under the null hypothesis that can be used for obtaining the test p-values. Simulation studies as well as a real data example are presented to demonstrate the usefulness of the proposed method. -matrix (dpeaa)DE-He213 diagnostic classification models (dpeaa)DE-He213 hypothesis testing (dpeaa)DE-He213 Liu, Jingchen verfasserin aut Xu, Gongjun verfasserin aut Ying, Zhiliang verfasserin aut Enthalten in Psychometrika New York : Springer-Verl., 1936 83(2018), 3 vom: 11. Juli, Seite 515-537 (DE-627)487892054 (DE-600)2188500-X 1860-0980 nnns volume:83 year:2018 number:3 day:11 month:07 pages:515-537 https://dx.doi.org/10.1007/s11336-018-9629-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 77.03 ASE AR 83 2018 3 11 07 515-537
language	English
source	Enthalten in Psychometrika 83(2018), 3 vom: 11. Juli, Seite 515-537 volume:83 year:2018 number:3 day:11 month:07 pages:515-537
sourceStr	Enthalten in Psychometrika 83(2018), 3 vom: 11. Juli, Seite 515-537 volume:83 year:2018 number:3 day:11 month:07 pages:515-537
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	-matrix diagnostic classification models hypothesis testing
dewey-raw	150
isfreeaccess_bool	false
container_title	Psychometrika
authorswithroles_txt_mv	Gu, Yuqi @@aut@@ Liu, Jingchen @@aut@@ Xu, Gongjun @@aut@@ Ying, Zhiliang @@aut@@
publishDateDaySort_date	2018-07-11T00:00:00Z
hierarchy_top_id	487892054
dewey-sort	3150
id	SPR018768156
language_de	englisch
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author	Gu, Yuqi
spellingShingle	Gu, Yuqi ddc 150 bkl 77.03 misc -matrix misc diagnostic classification models misc hypothesis testing Hypothesis Testing of the Q-matrix
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title	Hypothesis Testing of the Q-matrix
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title_sort	hypothesis testing of the q-matrix
title_auth	Hypothesis Testing of the Q-matrix
abstract	Abstract The recent surge of interests in cognitive assessment has led to the development of cognitive diagnosis models. Central to many such models is a specification of the Q-matrix, which relates items to latent attributes that have natural interpretations. In practice, the Q-matrix is usually constructed subjectively by the test designers. This could lead to misspecification, which could result in lack of fit of the underlying statistical model. To test possible misspecification of the Q-matrix, traditional goodness of fit tests, such as the Chi-square test and the likelihood ratio test, may not be applied straightforwardly due to the large number of possible response patterns. To address this problem, this paper proposes a new statistical method to test the goodness fit of the Q-matrix, by constructing test statistics that measure the consistency between a provisional Q-matrix and the observed data for a general family of cognitive diagnosis models. Limiting distributions of the test statistics are derived under the null hypothesis that can be used for obtaining the test p-values. Simulation studies as well as a real data example are presented to demonstrate the usefulness of the proposed method.
abstractGer	Abstract The recent surge of interests in cognitive assessment has led to the development of cognitive diagnosis models. Central to many such models is a specification of the Q-matrix, which relates items to latent attributes that have natural interpretations. In practice, the Q-matrix is usually constructed subjectively by the test designers. This could lead to misspecification, which could result in lack of fit of the underlying statistical model. To test possible misspecification of the Q-matrix, traditional goodness of fit tests, such as the Chi-square test and the likelihood ratio test, may not be applied straightforwardly due to the large number of possible response patterns. To address this problem, this paper proposes a new statistical method to test the goodness fit of the Q-matrix, by constructing test statistics that measure the consistency between a provisional Q-matrix and the observed data for a general family of cognitive diagnosis models. Limiting distributions of the test statistics are derived under the null hypothesis that can be used for obtaining the test p-values. Simulation studies as well as a real data example are presented to demonstrate the usefulness of the proposed method.
abstract_unstemmed	Abstract The recent surge of interests in cognitive assessment has led to the development of cognitive diagnosis models. Central to many such models is a specification of the Q-matrix, which relates items to latent attributes that have natural interpretations. In practice, the Q-matrix is usually constructed subjectively by the test designers. This could lead to misspecification, which could result in lack of fit of the underlying statistical model. To test possible misspecification of the Q-matrix, traditional goodness of fit tests, such as the Chi-square test and the likelihood ratio test, may not be applied straightforwardly due to the large number of possible response patterns. To address this problem, this paper proposes a new statistical method to test the goodness fit of the Q-matrix, by constructing test statistics that measure the consistency between a provisional Q-matrix and the observed data for a general family of cognitive diagnosis models. Limiting distributions of the test statistics are derived under the null hypothesis that can be used for obtaining the test p-values. Simulation studies as well as a real data example are presented to demonstrate the usefulness of the proposed method.
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title_short	Hypothesis Testing of the Q-matrix
url	https://dx.doi.org/10.1007/s11336-018-9629-6
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author2	Liu, Jingchen Xu, Gongjun Ying, Zhiliang
author2Str	Liu, Jingchen Xu, Gongjun Ying, Zhiliang
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doi_str	10.1007/s11336-018-9629-6
up_date	2024-07-03T22:05:12.271Z
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code="a">GBV_ILN_4325</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4326</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4328</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4333</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4334</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4335</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4338</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4393</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">77.03</subfield><subfield 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score	7.4003716

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Hypothesis Testing of the Q-matrix

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