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   2011, Vol. 43 Issue (10) : 1219-1228     DOI:
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Appropriate Standardized Estimates of Latent Interaction Models without the Mean Structure
WU Yan;WEN Zhong-Lin;HAU Kit-Tai;Herbert W. MARSH
(1 Department of Applied Psychology, Guangdong University of Foreign Studies, Guangzhou 510420, China)
(2 Center for Studies of Psychological Application, South China Normal University, Guangzhou 510631, China)
(3 Department of Educational Psychology, The Chinese University of Hong Kong, Hong Kong, China)
(4 Department of Education, Oxford University, Oxford, OX2 6PY, UK)
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Abstract  There are two important lines of progress in the recent research on latent interaction modeling. First, the appropriate ‘standardized’ parameter estimates have been proposed and formulated using parameter estimates routinely available from existing SEM software packages (see, e.g., Wen, Marsh, & Hau, 2010). Second, it has been found that the mean structure is not necessary in the structural equation models of latent interaction, as the parameters of the main and interaction effects remain theoretically unchanged both with and without the mean structure (see, e.g., Lin, Wen, Marsh, & Lin, 2010).
Although the appropriate standardized parameter estimates have been established under the framework of the traditional latent interaction models with the mean structure, it is unknown whether the same concepts and the formulae for standardized parameter estimates remain applicable under the framework of the simplified latent interaction models without the mean structure. To answer this question, we deduced the appropriate standardized form of the structural equation for latent interaction models, and formulated the appropriate standardized estimations of main and interaction effects without the mean structure in the models.
Furthermore, through a simulation study, we compared two estimation methods—maximum likelihood (ML) versus generalized least squares (GLS), and two strategies for forming the product indicators—matched-pair product indicators versus all possible cross product indicators. Results showed that matched-pair product indicators had an advantage over all possible cross product indicators, and that ML estimates were preferable to GLS estimates when calculating the appropriate standardized estimates of main and interaction effects. It is therefore recommended that matched-pair product indicators should be adopted. The ML method is the preferred choice in estimating the latent interaction.
Keywords latent variable      interaction effect      structural equation model      product indicator      estimation approach     
Corresponding Authors: WEN Zhong-Lin   
Issue Date: 30 October 2011
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WU Yan
WEN Zhong-Lin
HAU Kit-Tai
Herbert W. MARSH
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WU Yan,WEN Zhong-Lin,HAU Kit-Tai, et al. Appropriate Standardized Estimates of Latent Interaction Models without the Mean Structure[J]. , 2011, 43(10): 1219-1228.
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http://journal.psych.ac.cn/xlxb/EN/      OR     http://journal.psych.ac.cn/xlxb/EN/Y2011/V43/I10/1219
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