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Consider the following factor equation for kth occasion: [numerical formula] where Z_k the N×n matrix of standard scores on the variables, F_k is the N×q matrix of factor scores, A_k is the n×q matrix of factor loadings, and U_k is the N×n matrix of unique scores. Under the appropriate assumptions, it is derived that [numerical formula] where R_\u003ckk\u0027\u003e is the matrix of inter variable correlations, S_\u003ckk\u0027\u003e is the matrix of inter factor scores correlations (or covariances), and Δ_\u003ckk\u0027\u003e is the matrix of inter unique score covariances, repectively, between kth and k\u0027th occasions. Various models can be formulated corresponding to the assumptions on A_k and S_\u003ckk\u0027\u003e. Main models and their assumptions are as follows: 1.1 General model: [numerical formula] 1.3 Longitudinal factor analysis model (Corballis, 1973): [numerical formula] where D_\u003ckk\u0027\u003e is the diagonal matrix. 1.4 Multimethod factor analysis model (Jackson, 1975): [numerical formula] 2.1 Common factor loading model: [numerical formula] 2.2 Invariant factor loading model (Hakstian, 1973): [numerical formula] 2.4 Quasi three-mode factor analysis model: [numerical formula] 2.6 Extended PARAFAC model: [numerical formula] 3.1 Common factor score model: [numerical formula] 4. Invariant Model: [numerical formula] Least squares alogorithm which minimizes the quantity, [numerical formula] where R^†_\u003ckk\u003e is defined as [numerical formula] is formulated for each model. 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3相データにおける因子変化の記述のための諸方法(I) : 因子分析型のモデル
https://doi.org/10.18999/bulfep.30.145
https://doi.org/10.18999/bulfep.30.145cac8ab13-2b10-49e0-9d74-f48403b6219c
名前 / ファイル | ライセンス | アクション |
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2006-01-06 | |||||
タイトル | ||||||
タイトル | 3相データにおける因子変化の記述のための諸方法(I) : 因子分析型のモデル | |||||
その他のタイトル | ||||||
その他のタイトル | METHOD FOR DESCRIPTION OF FACTOR CHANGE IN THREE-MODE DATA (I) : FACTOR ANALYTICAL MODELS | |||||
著者 |
村上, 隆
× 村上, 隆× MURAKAMI, Takashi |
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抄録 | ||||||
内容記述 | This paper presents and compares several factor analytic models, some of which are new, dealing with threemode data, especially longitudinal or multitrait-multimethod data. Consider the following factor equation for kth occasion: [numerical formula] where Z_k the N×n matrix of standard scores on the variables, F_k is the N×q matrix of factor scores, A_k is the n×q matrix of factor loadings, and U_k is the N×n matrix of unique scores. Under the appropriate assumptions, it is derived that [numerical formula] where R_<kk'> is the matrix of inter variable correlations, S_<kk'> is the matrix of inter factor scores correlations (or covariances), and Δ_<kk'> is the matrix of inter unique score covariances, repectively, between kth and k'th occasions. Various models can be formulated corresponding to the assumptions on A_k and S_<kk'>. Main models and their assumptions are as follows: 1.1 General model: [numerical formula] 1.3 Longitudinal factor analysis model (Corballis, 1973): [numerical formula] where D_<kk'> is the diagonal matrix. 1.4 Multimethod factor analysis model (Jackson, 1975): [numerical formula] 2.1 Common factor loading model: [numerical formula] 2.2 Invariant factor loading model (Hakstian, 1973): [numerical formula] 2.4 Quasi three-mode factor analysis model: [numerical formula] 2.6 Extended PARAFAC model: [numerical formula] 3.1 Common factor score model: [numerical formula] 4. Invariant Model: [numerical formula] Least squares alogorithm which minimizes the quantity, [numerical formula] where R^†_<kk> is defined as [numerical formula] is formulated for each model. Analysis of Kelly & Fiske's multitrait-multimethod matrix is attached as a numerical example, and the type of the factor change described by each model is discussed. | |||||
内容記述タイプ | Abstract | |||||
内容記述 | ||||||
内容記述 | 国立情報学研究所で電子化したコンテンツを使用している。 | |||||
内容記述タイプ | Other | |||||
出版者 | ||||||
出版者 | 名古屋大学教育学部 | |||||
言語 | ||||||
言語 | jpn | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | departmental bulletin paper | |||||
ID登録 | ||||||
ID登録 | 10.18999/bulfep.30.145 | |||||
ID登録タイプ | JaLC | |||||
ISSN(print) | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 03874796 | |||||
書誌情報 |
名古屋大學教育學部紀要. 教育心理学科 巻 30, p. 145-176, 発行日 1983-12-24 |
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フォーマット | ||||||
application/pdf | ||||||
著者版フラグ | ||||||
値 | publisher | |||||
URI | ||||||
識別子 | http://hdl.handle.net/2237/3646 | |||||
識別子タイプ | HDL |