Analysis and ratio of linear function of parameters in fixed effect three level nested design

The aims of this study are first to build the linear model of the fixed effect three level nested design. The model is not full column rank and has a constraint on its parameters; second is to transform the non full column rank model with a constraint into full column rank and unconstraint model by...

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Main Authors:	Usman, Mustofa, Malik, Ibnu, Warsono, Warsono, Elfaki, Faiz Ahmed Mohamed
Format:	Article
Language:	English English
Published:	Asian Research Publishing Network (ARPN) 2016
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/51057/ http://irep.iium.edu.my/51057/ http://irep.iium.edu.my/51057/1/51057_-_Analysis_and_ratio_of_linear_function_of_parameters_in_fixed_effect_three_level_nested_design.pdf http://irep.iium.edu.my/51057/4/51057_Analysis%20and%20ratio%20of%20linear_Scopus.pdf

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spelling	iium-510572017-01-16T06:46:36Z http://irep.iium.edu.my/51057/ Analysis and ratio of linear function of parameters in fixed effect three level nested design Usman, Mustofa Malik, Ibnu Warsono, Warsono Elfaki, Faiz Ahmed Mohamed QA Mathematics The aims of this study are first to build the linear model of the fixed effect three level nested design. The model is not full column rank and has a constraint on its parameters; second is to transform the non full column rank model with a constraint into full column rank and unconstraint model by using method of model reduction; and third is to derive statistics for testing various hypotheses by using Generalized Likelihood Ratio (GLR) test and to derive the ratio of linear function of parameters by using Fieller’s Theorem . Based on the full column rank and unconstraint model the analysis to be conducted is : to estimate the parameters, to derive statistics for testing various hypotheses and to derive confidence intervals of the ratio of the linear function of parameters. The estimation of parameters and the statistics for testing some hypotheses are unbiased. Based on the simulation results, it can be shown that the tests are unbiased and in line with the criteria given by Pearson and Please. The simulation results for the (1-α) confidence interval of the ratio of the linear function of parameters tau (τi), beta (βj(i)) and gamma (γk(ij)) are presented for different values of ρ’s and in all cases the values of ρ’s are contained in the 95% confidence intervals. Asian Research Publishing Network (ARPN) 2016-06-10 Article PeerReviewed application/pdf en http://irep.iium.edu.my/51057/1/51057_-_Analysis_and_ratio_of_linear_function_of_parameters_in_fixed_effect_three_level_nested_design.pdf application/pdf en http://irep.iium.edu.my/51057/4/51057_Analysis%20and%20ratio%20of%20linear_Scopus.pdf Usman, Mustofa and Malik, Ibnu and Warsono, Warsono and Elfaki, Faiz Ahmed Mohamed (2016) Analysis and ratio of linear function of parameters in fixed effect three level nested design. ARPN Journal of Engineering and Applied Sciences, 11 (11). pp. 7121-7129. ISSN 1819-6608 http://www.arpnjournals.com/jeas/archive.htm
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English English
topic	QA Mathematics
spellingShingle	QA Mathematics Usman, Mustofa Malik, Ibnu Warsono, Warsono Elfaki, Faiz Ahmed Mohamed Analysis and ratio of linear function of parameters in fixed effect three level nested design
description	The aims of this study are first to build the linear model of the fixed effect three level nested design. The model is not full column rank and has a constraint on its parameters; second is to transform the non full column rank model with a constraint into full column rank and unconstraint model by using method of model reduction; and third is to derive statistics for testing various hypotheses by using Generalized Likelihood Ratio (GLR) test and to derive the ratio of linear function of parameters by using Fieller’s Theorem . Based on the full column rank and unconstraint model the analysis to be conducted is : to estimate the parameters, to derive statistics for testing various hypotheses and to derive confidence intervals of the ratio of the linear function of parameters. The estimation of parameters and the statistics for testing some hypotheses are unbiased. Based on the simulation results, it can be shown that the tests are unbiased and in line with the criteria given by Pearson and Please. The simulation results for the (1-α) confidence interval of the ratio of the linear function of parameters tau (τi), beta (βj(i)) and gamma (γk(ij)) are presented for different values of ρ’s and in all cases the values of ρ’s are contained in the 95% confidence intervals.
format	Article
author	Usman, Mustofa Malik, Ibnu Warsono, Warsono Elfaki, Faiz Ahmed Mohamed
author_facet	Usman, Mustofa Malik, Ibnu Warsono, Warsono Elfaki, Faiz Ahmed Mohamed
author_sort	Usman, Mustofa
title	Analysis and ratio of linear function of parameters in fixed effect three level nested design
title_short	Analysis and ratio of linear function of parameters in fixed effect three level nested design
title_full	Analysis and ratio of linear function of parameters in fixed effect three level nested design
title_fullStr	Analysis and ratio of linear function of parameters in fixed effect three level nested design
title_full_unstemmed	Analysis and ratio of linear function of parameters in fixed effect three level nested design
title_sort	analysis and ratio of linear function of parameters in fixed effect three level nested design
publisher	Asian Research Publishing Network (ARPN)
publishDate	2016
url	http://irep.iium.edu.my/51057/ http://irep.iium.edu.my/51057/ http://irep.iium.edu.my/51057/1/51057_-_Analysis_and_ratio_of_linear_function_of_parameters_in_fixed_effect_three_level_nested_design.pdf http://irep.iium.edu.my/51057/4/51057_Analysis%20and%20ratio%20of%20linear_Scopus.pdf
first_indexed	2023-09-18T21:12:13Z
last_indexed	2023-09-18T21:12:13Z
_version_	1777411328645791744

Analysis and ratio of linear function of parameters in fixed effect three level nested design

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