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TESTING OF VARIANCE COMPONENTS FOR CONTINUOUS DATA FROM NESTED UNBALANCED DESIGNS

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Title TESTING OF VARIANCE COMPONENTS FOR CONTINUOUS DATA FROM NESTED UNBALANCED DESIGNS
Not Available
 
Creator Ankita
Susheel Kumar Sarkar
Anil Kumar
Sanjeev Panwar
Shashi Shekhar
Rajan Kumar
 
Subject Unbalanced data
Variance components
Nested design
Effect size
Approximate tests
 
Description In case of random effects models for balanced
designs, the analysis is simple and no problem is
encountered in testing the variance components since
the sums of squares are independent, sums of squares
are chi-square variates, ratio of variance components
follow standard F-distribution and hence exact testing
is possible. When a random effects model is considered
in unbalanced designs, analysis of variance technique
rarely produce exact tests for testing the hypothesis.
Under the conventional normality assumptions, except
for the error component, the analysis of variance fails
to decompose the total sums of squares into
independently distributed sums of squares. Also, sums
of squares are neither chi-square variates nor multiple
of chi-square variate. The sums of squares are not
independent either. Another standardized measure that
quantifies the difference between means and
relationship between independent and the dependent
variable is effect-size measure. Two generally used
statistics for computing effect-size are eta and omega squared statistics. But, these statistics do not yield
correct estimate of effect-size that are comparable
across different designs [Bakeman (2005)]. In that
scenario, generalized eta and omega statistics given by
Olejnik and Algina (2003) can be used. There was a
conversation on two-way factorial ANOVA with mixed
effects and interactions [Nelder (1977, 1982, 1994,
2008)]. The major assessments about the two-way
factorial ANOVA model is no substantial rationale for
the imposed constraints on random interactions and a
lack of clear interpretation of its variance components,
especially for the main random effects in respect of
the response [Nelder (1977), Wolfinger and Stroup
(2000), Lencina et al. (2007)]. As a result, the usual
model is more widely used nowadays. The unbalanced
mixed ANOVA models are often analyzed under the
linear mixed models (LMM) framework using the
restricted maximum likelihood (REML) or generalized
least squares approaches [Littell (2002), Stroup (2013),
Jiang (2017)]. Kaur and Garg (2020) attempted for
Computer aided construction of rectangular PBIB designs. Gupta and Sharma (2020) constructed a set
of balanced incomplete block designs (BIBD) against
the loss of two blocks where loss of some observations
lie in between at most two common treatments. Gupta
(2021) worked on nested partially balanced incomplete
block designs and its analysis. Singh et al. (2021)
presented mixture designs generated using orthogonal
arrays.
In this study, the one way random effects model
for unbalanced nested design in which we have given
the model, hypothesis to be tested, sums of squares
and testing procedure for the hypothesis along with
analysis of variance table. In the next section, we have
explained model, hypothesis testing, sums of squares,
hypothesis testing procedure and analysis of variance
table for two way unbalanced nested design. Since in
two way unbalanced case the means squares are
generally not independent and are not distributed as
chi-square variates, exact testing is not available for
the main class variance component. We have obtained
the expected size of approximate tests and the actual
size for both conventional and approximate tests. Then
with the help of a simulated data we found out the
numerical for actual size of the conventional test and
the actual and expected size of the approximate tests
for some assumed values of the variance components.
Under unbalanced design, testing of variance ratios are generally neither independent nor distributed as chi-
square variates and does not follow standard F-distribution. In this case, exact testing of variance ratios is not available in the
literature. Procedure for unbalanced data (generally not independent and are not distributed as chi-square variates) has been
developed for testing the variance components in one way and two way unbalanced nested designs.
Not Available
 
Date 2022-06-29T07:52:51Z
2022-06-29T07:52:51Z
2022-04-14
 
Type Research Paper
 
Identifier Ankita, Susheel Kumar Sarkar, Anil Kumar, Sanjeev Panwar, Shashi Shekhar and Rajan Kumar (2022). Testing of Variance Components for Continuous Data from Nested Unbalanced Designs. International Journal of Agricultural and Statistical Sciences. DocID: https://connectjournals.com/03899.2022.18.391
0973-1903
http://krishi.icar.gov.in/jspui/handle/123456789/73509
 
Language English
 
Relation Not Available;
 
Publisher International Journal of Agricultural and Statistical Sciences