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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/51057/1/51057_-_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 my.iium.irep.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 REM 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
institution Universiti Islam Antarabangsa Malaysia
building IIUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider International Islamic University Malaysia
content_source IIUM Repository (IREP)
url_provider http://irep.iium.edu.my/
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/51057/1/51057_-_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
http://irep.iium.edu.my/51057/
http://www.arpnjournals.com/jeas/archive.htm
_version_ 1643613867958337536
score 13.211869

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