Date of Submission

7-28-1990

Date of Award

7-28-1991

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Mathematics

Department

Electronics and Communication Sciences Unit (ECSU-Kolkata)

Supervisor

Mukherjee, B. N. (ECSU-Kolkata; ISI)

Abstract (Summary of the Work)

In recent years, the teahniques of struotural analynie of covarianoe and correlation matrioes have frequently be en employed espeed ally in the s ooial and behavioural soieno es for analysing multivariate data. Analysis of covarlance structures (ACOVS) lea; generie tem describing a variety of statistioal procedures for testing and measuring the goodnese-of-fit of certain types of struotures postulated a priori for the cova- riance matrix by plaoing al temative restriotione on the para- neter natrioes of the general model" [Mukherjee, 1976, p. 132].The aoronyn AOOVS' standa for; analyeis of covarianoe atructurea; and waa firat proposed by Book (1960) as a method for studying the atruotural ad discriminal p ower of paychol.0- el cal tenta which are design ed on the basia of certain theories or assump ti ona. But its techniques are not necessarily the same as thoee involved in the atudy of structural relationships (of. Kendall and Stuart, 1967, p. 374). ACOVS is a kind of patterm analyais of covariance matricea rather than the pattema of responees in the raw data whioh are generally taken into ccmai- deration for c om figurational scoring (NoQuitty, 1956).Analysie of coveriance atruotures (ACOVS) 1s nainly aimed at estimating and teeting a set of hypotheaes of a specific pattern of relatione anong a set of meanured or manifeot variablen( MVe) and latent veriables (LVs), both depend ent and indep endent. In ACOVS, given an hypotheai Bed nodel d efined in terme of fixed and free paraneters, and given a sample covari- ance matrix, S, for the MVe, one oan solve for estimates of the free parameters of the mod el. The nost ocunon approach for fitting the hypotheeised model to data ie to obtain naximue 11kelihood (M) estimaten of paraneters and an aoocmp anying likelihood ratio ohi-equare test of the null hypothesis. A vari ety of o ther informatd on can be obtained regarding goodnees- of-fit of the mod el (Ben tl er and Bonett, 1980; Jörekog and sörbom, 1988; Mulaik, James, Alstine, Bennett, Lind and Stilwell, 1989). The en tire procese of formulating the hypoth esized struc tural model, the specificati an of the free and fixed para- meters of the deduoed covard ance matrix, the estimation and testing of the nod el aa wel1 an an operati on of sequem tially modi fying the model so ns to improve its fit and/or pareimony 1e called analyeie of oovariance etruo tures (ACOVS).ACOVS han been quite useful in dealing with simultanecue equa ti on modele which arise very frequently in social and eo cmo- mie scienes. A set of regrennion equations is said to oouprise a simul taneous equation nod el if one or more of the expl anatory variables in one or more of the equatione ie itself the dependent (end ogenoua) variable an0ooiated with another equation in the full syatem. Sueh modele have aleo boun referred to structural equation systems,dependence analysis, pah or casual analysis with the latent variables (Everitt,1984).

Comments

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28842918

Control Number

ISILib-TH275

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

Download

Included in

Mathematics Commons

Share

COinS