Structural equation modeling (SEM) of categorical and mixed-data using the novel Gifi transformations and information complexity (ICOMP) criterion

HOWE, Eylem Deniz; KATRAGADDA, Suman; BOZDOGAN, Hamparsum

Structural equation modeling (SEM) of categorical and mixed-data using the novel Gifi transformations and information complexity (ICOMP) criterion

Eylem Deniz HOWE, (Mimar Sinan Üniversitesi, Güzel Sanatlar Fakültesi, Fen Edebiyat Fakültesi, İstatistik Bölümü, İstanbul, Türkiye)

Hamparsum BOZDOGAN, (Department of Statistics, Operations and Management Science, The University of Tennessee, Knoxville, USA)

Suman KATRAGADDA (Express-Scripts Company, St Louis, USA)

İstanbul Üniversitesi İşletme Fakültesi Dergisi

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Yıl: 2011 Cilt: 40 Sayı: 1 Sayfa Aralığı: 86 - 123 Metin Dili: Türkçe İndeks Tarihi: 29-07-2022

Structural equation modeling (SEM) of categorical and mixed-data using the novel Gifi transformations and information complexity (ICOMP) criterion

Öz:

Bu çalışmada Yapısal Eşitlik Modelleri’nde (YEM) kategorik, ikili veya karma veri setlerinin analizine ilişkin var olan problemleri çözmek için özgün bir alternatif yaklaşım olarak Gifi yöntemi önerilmiştir. Gifi yönteminde, kategorik değişkenleri nicel hale dönüştürmek için optimal ölçekleme yöntemi kullanılır. Nicelleştirme sürecinde gözlenen değişkendeki bilgi, dönüştürülmüş değişkende aynen korunur. Yani Gifi yöntemi, kategorik değişkenlerin ölçek özelliklerini bozmadan kategorik veriyi sürekli veriye dönüştürür ve bu dönüştürme işleminde herhangi bir bilgi kaybı söz konusu olmaz. Ölçek özellikleri, dönüştürülmüş doğrusal olmayan sürekli Gifi veri uzayında saklanır. Bu nedenle dönüştürme işleminden geriye dönüş mümkündür. Bu işlem, literatürde halen uygulanmakta olan rasgele belirlenmiş başlangıç değerlerini göz ardı eden Gifi sisteme özgün bir özelliktir. Gifi dönüşümünden sonra, çoklu normal dağılım varsayımına dayalı YEM kullanılarak dönüştürülmüş veri seti analiz edilmiştir. Böyle bir yaklaşım YEM’de, kategorik veriler için göz ardı edilen çok değişkenli normal dağılım varsayımını sağlamaktadır. Akaike’nin [1] Akaike Bilgi Kriteri (AIC), Bozdoğan’ın [2] Tutarlı Akaike Bilgi Kriteri (CAIC) ve Bozdoğan’ın [3-7] Bilgi Karmaşıklığı Kriteri (ICOMP) gibi bilgiye dayalı model seçim kriterleri YEM’de uyumun bir ölçümü olarak uygulanmaktadır. Minimum kriter değerini veren model, rakip modeller arasında veriye en iyi uyumlu model olarak seçilir. Bu çalışmada yaşam kalitesinin ölçüldüğü gerçek bir kategorik veri seti kullanılmıştır. Bu veri setine Gifi dönüşüm uygulayarak önerilen yaklaşımın çok yönlülüğü ve esnekliği gösterilmiştir. Ayrıca dönüştürülmüş veri seti üzerinden farklı YEM için model seçim kriter değerleri elde edilmiş ve minimum kriter değerini veren en iyi model belirlenmiştir.

Anahtar Kelime:

Kategorik ve karma veri setlerinin yapısal eşitlik modellemesinde (YEM) Gifi yaklaşımı kullanımı ve bilgi karmaşıklığı kriteri (ICOMP)

Öz:

This paper introduces and develops a novel and computationally feasible alternative approach to the analysis of categorical, dichotomous, and mixed data sets in structural equation models (SEMs) to overcome currently existing problems. Our approach is based on the Gifi system. The Gifi system uses the optimal scaling methodology to quantify the observed categorical variables. In the quantification process, information in the observed variable is retained in the quantified variable. That is, the Gifi system transforms categorical data to continuous data without destroying the scale properties of the categorical variables. The scaling is thus preserved in the transformed nonlinear continuous Gifi data space. Hence the transformation is invertible. This is one of the unique characteristics of the Gifi system which avoids the arbitrary thresholding specification that is currently practiced and used in the literature. After the Gifi transformation, we analyze the transformed data set using SEM based on the multinormal distributional assumption. Such an approach legitimizes the distributional assumption of multivariate normality in SEM. Information-theoretic model selection criteria such as Akaike’s [1] AIC, Bozdogan’s [2] Consistent AIC, called CAIC, and the information-theoretic measure of complexity ICOMP criterion of Bozdogan [3-7] are introduced and develop as measures of fit in SEMs. The model with the minimum values of the criteria is selected as the best fitting model among a portfolio of candidate models. We provide a real benchmark numerical example using SEM on a categorical data set which measures the quality of life (QOL) to illustrate the versatility and flexibility of our approach using the Gifi transformations on this data set and fit five alternative SEM models by scoring the model selection criteria.

Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

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APA	HOWE E, BOZDOGAN H, KATRAGADDA S (2011). Structural equation modeling (SEM) of categorical and mixed-data using the novel Gifi transformations and information complexity (ICOMP) criterion. , 86 - 123.
Chicago	HOWE Eylem Deniz,BOZDOGAN Hamparsum,KATRAGADDA Suman Structural equation modeling (SEM) of categorical and mixed-data using the novel Gifi transformations and information complexity (ICOMP) criterion. (2011): 86 - 123.
MLA	HOWE Eylem Deniz,BOZDOGAN Hamparsum,KATRAGADDA Suman Structural equation modeling (SEM) of categorical and mixed-data using the novel Gifi transformations and information complexity (ICOMP) criterion. , 2011, ss.86 - 123.
AMA	HOWE E,BOZDOGAN H,KATRAGADDA S Structural equation modeling (SEM) of categorical and mixed-data using the novel Gifi transformations and information complexity (ICOMP) criterion. . 2011; 86 - 123.
Vancouver	HOWE E,BOZDOGAN H,KATRAGADDA S Structural equation modeling (SEM) of categorical and mixed-data using the novel Gifi transformations and information complexity (ICOMP) criterion. . 2011; 86 - 123.
IEEE	HOWE E,BOZDOGAN H,KATRAGADDA S "Structural equation modeling (SEM) of categorical and mixed-data using the novel Gifi transformations and information complexity (ICOMP) criterion." , ss.86 - 123, 2011.
ISNAD	HOWE, Eylem Deniz vd. "Structural equation modeling (SEM) of categorical and mixed-data using the novel Gifi transformations and information complexity (ICOMP) criterion". (2011), 86-123.

APA	HOWE E, BOZDOGAN H, KATRAGADDA S (2011). Structural equation modeling (SEM) of categorical and mixed-data using the novel Gifi transformations and information complexity (ICOMP) criterion. İstanbul Üniversitesi İşletme Fakültesi Dergisi, 40(1), 86 - 123.
Chicago	HOWE Eylem Deniz,BOZDOGAN Hamparsum,KATRAGADDA Suman Structural equation modeling (SEM) of categorical and mixed-data using the novel Gifi transformations and information complexity (ICOMP) criterion. İstanbul Üniversitesi İşletme Fakültesi Dergisi 40, no.1 (2011): 86 - 123.
MLA	HOWE Eylem Deniz,BOZDOGAN Hamparsum,KATRAGADDA Suman Structural equation modeling (SEM) of categorical and mixed-data using the novel Gifi transformations and information complexity (ICOMP) criterion. İstanbul Üniversitesi İşletme Fakültesi Dergisi, vol.40, no.1, 2011, ss.86 - 123.
AMA	HOWE E,BOZDOGAN H,KATRAGADDA S Structural equation modeling (SEM) of categorical and mixed-data using the novel Gifi transformations and information complexity (ICOMP) criterion. İstanbul Üniversitesi İşletme Fakültesi Dergisi. 2011; 40(1): 86 - 123.
Vancouver	HOWE E,BOZDOGAN H,KATRAGADDA S Structural equation modeling (SEM) of categorical and mixed-data using the novel Gifi transformations and information complexity (ICOMP) criterion. İstanbul Üniversitesi İşletme Fakültesi Dergisi. 2011; 40(1): 86 - 123.
IEEE	HOWE E,BOZDOGAN H,KATRAGADDA S "Structural equation modeling (SEM) of categorical and mixed-data using the novel Gifi transformations and information complexity (ICOMP) criterion." İstanbul Üniversitesi İşletme Fakültesi Dergisi, 40, ss.86 - 123, 2011.
ISNAD	HOWE, Eylem Deniz vd. "Structural equation modeling (SEM) of categorical and mixed-data using the novel Gifi transformations and information complexity (ICOMP) criterion". İstanbul Üniversitesi İşletme Fakültesi Dergisi 40/1 (2011), 86-123.