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Title: | Design and Analysis of Experiments for Spatially Correlated Observations |
Other Titles: | Not Available |
Authors: | Seema Jaggi V.K. Gupta Rajender Parsad |
ICAR Data Use Licennce: | http://krishi.icar.gov.in/PDF/ICAR_Data_Use_Licence.pdf |
Author's Affiliated institute: | ICAR::Indian Agricultural Statistics Research Institute |
Published/ Complete Date: | 2008-10-31 |
Project Code: | Not Available |
Keywords: | Spatial Correlation Block designs |
Publisher: | ICAR-IASRI, Library Avenue, Pusa, New Delhi |
Citation: | Seema Jaggi, V.K. Gupta and Rajender Parsad (2008). Design and Analysis of Experiments for Spatially Correlated Observations. IASRI, New Delhi. I.A.S.R.I./P.R.-02/2008 |
Series/Report no.: | I.A.S.R.I./P.R.-02/2008; |
Abstract/Description: | Experimentation is an essential component of any scientific investigation with the primary aim of unbiased and efficient estimation of treatment contrasts. The experiments are therefore conducted using statistical design of experiments. One of the requirements in the analysis of data from comparative experiments is that the observations should be independent. However, there arise situations, especially in agricultural field experiments, that plots occurring close together within a block are likely to be more similar than the plots occurring far away from each other as the blocks are often formed using adjacent plots within a field. Thus, the observations from the experimental plots occurring close together within a block may be dependent and therefore, correlated. The observations may be correlated because of the layout of the plots, pest infections from neighbouring plots or some local factors which blocking cannot remove. Therefore, in order to draw statistically valid inferences about the treatment comparisons, we may need to consider the correlation structures within the blocks. When the observations are correlated, the choice of an efficient design depends on the covariance structure and the relative position of treatments in a block. Chapter 2 describes some methods of constructing block designs for these situations. The designs obtained are pairwise balanced and thus universally optimal. A list of these designs has also been presented. The effect of spatial correlation on the treatment effects has been illustrated through a data set from an agricultural field experiment conducted in RCB design. It is concluded that failure to account for spatially correlated errors in analysis may cause inefficient estimation of treatment significance. The model under a row-column setup, with observations correlated within a row, has been defined and the coefficient matrix of reduced normal equations for estimating treatments contrast for a correlated error structure has been derived in Chapter 3. Latin square design with v treatments in v rows and v columns has been studied under correlated error structure within a row. This design under AR(1) correlation structure is a partially variance balanced row-column design with two associate classes. Besides the observations within a block being correlated, the response from a plot to a particular treatment may be affected by the treatments in the neighbouring plots. Causes of neighbour effects may be due to spread of an applied treatment such as irrigation, fertilizer, pest control spray, from one plot to surrounding ones. Therefore, designs are to be developed for experiments under neighbour effects and dependent (correlated) observations. Two types of models have been considered based on how the neighbour effects of treatments are taken into account. The model with neighbour effect from only one side is one-sided neighbour model. This situation arises when there is prevailing wind from one side. The other model is two-sided neighbour model, where neighbour effects are from both, left and right, sides with different effects. The layout of the experiment for these models include border plots at end of every block. The treatment(s) applied on them are the ones from the trial. Observations for border units are not modeled. The joint information matrix for estimating direct and neighbour effects under spatially correlated observations has been obtained. A series of block design for estimating direct and one-sided neighbour effects of treatments in the presence of correlated observations has been obtained. Block design for estimating direct and two-sided neighbour effects of treatments in the presence of correlated observations has also been obtained. The designs developed for correlated observations are position dependent and lack within block randomization thereby sacrificing the basic principle of randomization. Also the designs require large number of blocks thereby increasing the total number of experimental units. To circumvent this problem, an alternative is to study the efficiency of optimal block designs with uncorrelated observations, in the presence of correlated observations. Balanced incomplete block (BIB) and partially balanced incomplete block (PBIB) designs are an important class of binary, proper incomplete block designs that are highly efficient for inferring on a complete set of orthonormalized treatment contrasts when the observations are uncorrelated. Robustness of these designs against correlated observations has been studied for NN and AR(1) correlation structures for different values of correlation coefficients in Chapter 5. A design is said to be robust for a specific correlation structure if the loss in A-efficiency of the design for different values of correlation coefficients is less than 10%. A list of BIB and PBIB designs, specifically Group Divisible (GD) for number of treatments v <=10 and cyclic designs giving A-efficiency for both the error structures has been prepared for different values of correlation coefficient. These designs are found to be quite robust and therefore can be used in the presence of correlation among observations. The robustness of complete block designs balanced for neighbour effects, that are otherwise efficient for zero correlation structure, is also studied for given correlation structure and a given value of correlation under one-sided and two-sided neighbour effects model. These designs perform satisfactorily under correlated error structure and can be used in case the observations are correlated. Related SAS codes have also been developed and given in different chapters. |
Description: | Not Available |
ISSN: | Not Available |
Type(s) of content: | Research Paper |
Sponsors: | Not Available |
Language: | English |
Name of Journal: | Not Available |
NAAS Rating: | Not Available |
Volume No.: | Not Available |
Page Number: | 1-107 |
Name of the Division/Regional Station: | Not Available |
Source, DOI or any other URL: | Not Available |
URI: | http://krishi.icar.gov.in/jspui/handle/123456789/6199 |
Appears in Collections: | AEdu-IASRI-Publication |
Files in This Item:
File | Description | Size | Format | |
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Final Report-DST-DAE FOR SPATIALLY CORRELATED OBSERVATION.pdf | 2.61 MB | Adobe PDF | View/Open |
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