Growth curve analysis of complete and incomplete longitudinal data

Growth curve analysis is reviewed for both complete and incomplete data structures. Specific attention is paid to the incomplete data model of Kleinbaum and its applicability to the mixed longitudinal study. Design considerations and efficiency for various incomplete longitudinal studies are also discussed.     

Linear Integer Programming Approach to Construction of Balanced Incomplete Block Designs

This article proposes a linear integer programming-based algorithm to construct balanced incomplete block designs. Working of the algorithm is illustrated with the help of an example. The algorithm is able to generate balanced incomplete block designs very fast in most of the cases. The performance of the proposed algorithm is compared with other algorithms proposed in the literature. It is demonstrated that the proposed algorithm is competitive with the existing algorithms.     

Regular E-Optimal Spring Balance Weighing Designs with Correlated Errors

The problems linked with an E-optimal spring balance weighing design with correlated errors are discussed. The topic is focus on the determining the maximal eigenvalue of the inverse of the information matrix of estimators. The constructing method of the E-optimal design, based on the incidence matrices of balanced incomplete block designs, is presented.     

On use of symmetrical balanced incomplete block design in construction of sampling design realising pre-assigned sets of inclusion probabilities of first two orders.

Gupta, Nigam and Kumar (1982) proposed a sampling scheme using certain combinatorial properties of balanced incomplete block design (BIBD) which realises first order inclusion probabilities proportional to measure of size(IPPS). Here their results have been extended by presenting samplng schemes realising pre-assigned sets of inclusion probabilities of first two orders.     

ON CONSTRUCTION OF GENERALIZED GROUP DIVISIBLE DESIGNS WITH TWO GROUPS

ABSTRACT

Many simple and general methods of construction, using α-resolvable balanced incomplete block designs, for generalized group divisible designs with two groups (GGDD(2)) are given. The E-optimality of all constructed designs is also discussed.     

Constructions of Nested Pairwise Efficiency and Variance Balanced Designs

ABSTRACT

Nested pairwise efficiency and variance balanced designs form a new class of block designs. In this article, two methods of constructing such designs from a symmetric balanced incomplete block design are proposed with some illustrations.     

Analysis of a design under the competing effects model with missing values

The analysis of doubly-balanced incomplete block designs (also known as 3-designs) with missing values using a competing effects model is discussed and illustrated with a numerical example.     

Mixture designs with orthogonal blocks

Constructions of blocked mixture designs are considered in situations where BLUEs of the block effect contrasts are orthogonal to the BLUEs of the regression coefficients. Orthogonal arrays (OA), Balanced Arrays (BAs), incidence matrices of balanced incomplete block designs (BIBDs), and partially balanced incomplete block designs (PBIBDs) are used. Designs with equal and unequal block sizes are considered. Also both cases where the constants involved in the orthogonality conditions depend and do not depend on the factors have been taken into account. Some standard (already available) designs can be obtained as particular cases of the designs proposed here.     

On the construction of group divisible incomplete block designs

In this paper a method of constructing group-divisible incomplete block designs has been suggested. A series of balanced incomplete block designs has also been obtained.     

The Construction of Optimal Imcomplete Block Designs When Observations Within a Block are Correlated

An algorithmic method is described for the construction of optimal incomplete block designs when a known correlation structure is assumed for observations from plots in the same block. The method is applicable to a wide class of designs and correlation structures. Some examples are given to illustrate the procedure.     

Balanced treatment incomplete block designs through integer programming

An algorithm is presented to construct balanced treatment incomplete block (BTIB) designs using a linear integer programming approach. Construction of BTIB designs using the proposed approach is illustrated with an example. A list of efficient BTIB designs for 2 ? v ? 12, v + 1 ? b ? 50, 2 ? k ? min(10, v), r ? 10, r₀ ? 20 is provided. The proposed algorithm is implemented as part of an R package.     

Approximate and exact distributions of rank tests for balanced incomplete block designs

Judges rank k out of t objects according to m replic ations of abasic balanced incomplete block design with bblocks. In Alvo and Cabilio(1991),it is shown that the Durbin test, which is the usual test in this situation, can be written in terms of Spearman correlations between the blocks, and using a Kendall correlation, they generated a new statistic for this situation.This Kendall tau based statistic has a richer support than the Durbin statistic, and is at least as efficient.In the present paper,exact and simulation based tables are generated for both statistics, and various approximations to these null distributions are considered and compared.     

Kernel-based density estimation using censored,truncated or grouped data

Censoring, truncation and grouping represent different but related forms of incompleteness. Methods of producing kernel functions on the incomplete observations are proposed. They involve substituting for or averaging over the incomplete observations. Consistency of the procedures in terms of:the criterion of integrated mean squared error is established and optimal choice of smoothing parameter is achieved.     

Comparisons of parameter and hypothesis definitions in a general linear model

In the context of the general linear model E(Y)=Xβ possibly subject to restrictions Rβ=r two secondary parameters may be well defined by Θ_i=G_iE(Y)-Θ_oi=C_i β-Θ_oi,i=1,2, and corresponding nonconstant hypotheses, H_i:Θ_i=0. The following possible relations are defined: Θ₁: is dependent upon /equivalent to/identical to Θ₂:H₁is a subhypothesis of/is identical to H₂. Necessary and sufficient conditions, involving straightforward matrix computations, are presented for each relation. Comparisons of secondary parameters and hypotheses are illustrated with an incomplete, unbalanced 3 × 4 factorial design from Searle in which, using a constrained version of Searle's model, parameters and hypotheses in the incomplete, unbalanced design are shown to be indentical to parameters one would define if complete balanced data were available. Techniques for computing simplified definitions are illustrated.     

Joint-regression Analysis for Incomplete Two-way Tables

Joint-regression analysis of incomplete two-way tables of genotype-by-environment data is usually carried out using the iterative method of Digby (1979). However, the nonlinear analysis method of Ng & Grunwald (1997) can also be used. The speed of convergence for the Ng & Grunwald method compares favourably with that of Digby, and more importantly the method gives valid inference and hence should be preferred.     

Application of minque procedure to block designs

Method of minimum norm quadratic unbiased estimation (MINQUE) is applied to incomplete block designs. Simple formulae are derived for a class of designs which includes the balanced designs.     

Optimal two-level conjoint designs with constant attributes in the profile sets

We propose a simple strategy to construct D-, A-, G- and V-optimal two-level designs for rating-based conjoint studies with large numbers of attributes. In order to simplify the rating task, the designs hold one or more attributes at a constant level in each profile set. Our approach combines orthogonal designs and binary incomplete block designs with equal replication. The designs are variance-balanced meaning that they yield an equal amount of information on each of the part-worths.     

The estimation of R 2 and adjusted R 2 in incomplete data sets using multiple imputation

The coefficient of determination, known also as the R ², is a common measure in regression analysis. Many scientists use the R ² and the adjusted R ² on a regular basis. In most cases, the researchers treat the coefficient of determination as an index of ‘usefulness’ or ‘goodness of fit,’ and in some cases, they even treat it as a model selection tool. In cases in which the data is incomplete, most researchers and common statistical software will use complete case analysis in order to estimate the R ², a procedure that might lead to biased results. In this paper, I introduce the use of multiple imputation for the estimation of R ² and adjusted R ² in incomplete data sets. I illustrate my methodology using a biomedical example.     

Analysis of multiple sets of incomplete rankings

The L statistic is extended to allow incomplete or partial rankings within groups. As a special case of these extensions, tests for ofered alternatives analogous to the page test are provided for other than complete rankings. A two group illustration is provided by an alternative analysis of the Bradley and Terry taste-testing experiment on pork-roasts.     

A new approximation to the incomplete beta function

A new approximation to the incomplete beta function is proposed. This approximation compares favourably well with the Mudholkar-Chaubey (1976) approximation and it is infact superior for equal degrees of freedom. Moreover’ it is simpler to evaluate.