ANALYSIS OF UNBALANCED FIXED-EFFECT NON- INTERACTIVE MODEL

ANALYSIS OF UNBALANCED FIXED-EFFECT NON- INTERACTIVE MODEL

ABSTRACT

This study examines the analysis of fixed-effect non-interactive unbalanced data by a method called Intra-Factor Design. And to derive this design for analysis, mathematically, the matrix version of the fixed-effect model, Yijk = µ + τi + βj + εijk, was used. This resulted to the definition and formation of many matrices such as the Information Matrix, L; Replication Vector, r; Incidence Matrix, N; Vector of adjusted factor A totals, q; Variance–Covariance Matrix, Q, which is the generalized inverse of the Information Matrix; and other Matrices. The Least Squares Method which gave birth to several normal equations was used to estimate for the parameters, τ and β mathematically. Then, an illustrative example was given to ascertain the workability of this Intra-Factor procedure in testing for the main effects under some stated hypothesis for significance. But, before testing for the variance component of the main effects on the illustrative data, it was necessary to first ascertain that the data is fixed-effect and that interaction is either absent or non-significant since our interest is on “Fixed-Effect Non-interactive Models”. Thereafter, the Analysis of Variance Components for Adjusted Factor A with Unadjusted Factor B effects was carried out. This gave the result that Adjusted Factor A effect, τ, was not significant; whereas, the Unadjusted Factor B effect, β, was significant. Also, the Analysis of Variance Components was performed for Unadjusted Factor A effect with Adjusted Factor B effect and it yielded similar result as that of Adjusted Factor A with Unadjusted Factor B effects. We therefore concluded that for a Fixed Effect, Non-interactive Unbalanced Data Analysis, the Method of Intra-Factor Design can be successfully employed.