CompExpDes - Computer Experiment Designs

In computer experiments space-filling designs are having great impact. Most popularly used space-filling designs are Uniform designs (UDs), Latin hypercube designs (LHDs) etc. For further references one can see Mckay (1979) <DOI:10.1080/00401706.1979.10489755> and Fang (1980) <https://cir.nii.ac.jp/crid/1570291225616774784>. In this package, we have provided algorithms for generate efficient LHDs and UDs. Here, generated LHDs are efficient as they possess lower value of Maxpro measure, Phi_p value and Maximum Absolute Correlation (MAC) value based on the weightage given to each criterion. On the other hand, the produced UDs are having good space-filling property as they always attain the lower bound of Discrete Discrepancy measure. Further, some useful functions added in this package for adding more value to this package.

Last updated 3 months ago

1.95 score 15 scripts 274 downloads

SudokuDesigns - Sudoku as an Experimental Design

Sudoku designs (Bailey et al., 2008<doi:10.1080/00029890.2008.11920542>) can be used as experimental designs which tackle one extra source of variation than conventional Latin square designs. Although Sudoku designs are similar to Latin square designs, only addition is the region concept. Some very important functions related to row-column designs as well as block designs along with basic functions are included in this package.

Last updated 3 months ago

1.68 score 24 scripts 234 downloads

TREDesigns - Ternary Residual Effect Designs

There are some experimental scenarios where each experimental unit receives a sequence of treatments across multiple periods, and treatment effects persist beyond the period of application. It focuses on the construction and calculation of the parametric value of the residual effect designs balanced for carryover effects, also referred to as crossover designs, change-over designs, or repeated measurements designs (Aggarwal and Jha, 2010<doi:10.1080/15598608.2010.10412013>). The primary objective of the package is to generate a new class of Balanced Ternary Residual Effect Designs (BTREDs), balanced for carryover effects tailored explicitly for situations where the number of periods is less than or equal to the number of treatments. In addition, the package provides four new classes of Partially Balanced Ternary Residual Effect Designs (PBTREDs), constructed using incomplete block designs, initial sequences, and rectangular association scheme. In addition, one extra function is included to help study the parametric properties of a given residual effect design.

Last updated 29 days ago

1.30 score 175 downloads

NBBDesigns - Neighbour Balanced Block Designs (NBBDesigns)

Neighbour-balanced designs ensure that no treatment is disadvantaged unfairly by its surroundings. The treatment allocation in these designs is such that every treatment appears equally often as a neighbour with every other treatment. Neighbour Balanced Designs are employed when there is a possibility of neighbour effects from treatments used in adjacent experimental units. In the literature, a vast number of such designs have been developed. This package generates some efficient neighbour balanced block designs which are balanced and partially variance balanced for estimating the contrast pertaining to direct and neighbour effects, as well as provides a function for analysing the data obtained from such trials (Azais, J.M., Bailey, R.A. and Monod, H. (1993). "A catalogue of efficient neighbour designs with border plots". Biometrics, 49, 1252-1261 ; Tomar, J. S., Jaggi, Seema and Varghese, Cini (2005)<DOI: 10.1080/0266476042000305177>. "On totally balanced block designs for competition effects"). This package contains functions named nbbd1(),nbbd2(),nbbd3(),pnbbd1() and pnbbd2() which generates neighbour balanced block designs within a specified range of number of treatment (v). It contains another function named anlys()for performing the analysis of data generated from such trials.

Last updated 1 years ago

1.20 score 16 scripts 263 downloads

MixedLevelRSDs - Mixed Level Response Surface Designs

Response Surface Designs (RSDs) involving factors not all at same levels are called Mixed Level RSDs (or Asymmetric RSDs). In many practical situations, RSDs with asymmetric levels will be more suitable as it explores more regions in the design space. (J.S. Mehta and M.N. Das (1968) <doi:10.2307/1267046>. "Asymmetric rotatable designs and orthogonal transformations").This package contains function named ATORDs_I() for generating asymmetric third order rotatable designs (ATORDs) based on third order designs given by Das and Narasimham (1962). Function ATORDs_II() generates asymmetric third order rotatable designs developed using t-design of unequal set sizes, which are smaller in size as compared to design generated by function ATORDs_I(). In general, third order rotatable designs can be classified into two classes viz., designs that are suitable for sequential experimentation and designs for non-sequential experimentation. The sequential experimentation approach involves conducting the trials step by step whereas, in the non-sequential experimentation approach, the entire runs are executed in one go (M. N. Das and V. Narasimham (1962) <doi:10.1214/AOMS/1177704374>. "Construction of Rotatable Designs through Balanced Incomplete Block Designs"). ATORDs_I() and ATORDs_II() functions generate non-sequential asymmetric third order designs. Function named SeqTORD() generates symmetric sequential third order design in blocks and also gives G-efficiency of the given design. Function named Asymseq() generates asymmetric sequential third order designs in blocks (M. Hemavathi, Eldho Varghese, Shashi Shekhar and Seema Jaggi (2020) <doi:10.1080/02664763.2020.1864817>. "Sequential asymmetric third order rotatable designs (SATORDs)"). In response surface design, situations may arise in which some of the factors are qualitative in nature (Jyoti Divecha and Bharat Tarapara (2017) <doi:10.1080/08982112.2016.1217338>. "Small, balanced, efficient, optimal, and near rotatable response surface designs for factorial experiments asymmetrical in some quantitative, qualitative factors"). The Function named QualRSD() generates second order design with qualitative factors along with their D-efficiency and G-efficiency. The function named RotatabilityQ() calculates a measure of rotatability (measure Q, 0 <= Q <= 1) given by Draper and Pukelshiem(1990) for given a design based on a second order model, (Norman R. Draper and Friedrich Pukelsheim(1990) <doi:10.1080/00401706.1990.10484635>. "Another look at rotatability").

Last updated 2 years ago

1.11 score 13 scripts 222 downloads

AsymmetricSORDs - Asymmetric Second Order Rotatable Designs (AsymmetricSORDs)

Response surface designs (RSDs) are widely used for Response Surface Methodology (RSM) based optimization studies, which aid in exploring the relationship between a group of explanatory variables and one or more response variable(s) (G.E.P. Box and K.B. Wilson (1951), "On the experimental attainment of optimum conditions" ; M. Hemavathi, Shashi Shekhar, Eldho Varghese, Seema Jaggi, Bikas Sinha & Nripes Kumar Mandal (2022) <DOI: 10.1080/03610926.2021.1944213>."Theoretical developments in response surface designs: an informative review and further thoughts".). Second order rotatable designs are the most prominent and popular class of designs used for process and product optimization trials but it is suitable for situations when all the number of levels for each factor is the same. In many practical situations, RSDs with asymmetric levels (J.S. Mehta and M.N. Das (1968). "Asymmetric rotatable designs and orthogonal transformations" ; M. Hemavathi, Eldho Varghese, Shashi Shekhar & Seema Jaggi (2020) <DOI: 10.1080/02664763.2020.1864817>. "Sequential asymmetric third order rotatable designs (SATORDs)" .) are more suitable as these designs explore more regions in the design space.This package contains functions named Asords() ,CCD_coded(), CCD_original(), SORD_coded() and SORD_original() for generating asymmetric/symmetric RSDs along with the randomized layout. It also contains another function named Pred.var() for generating the variance of predicted response as well as the moment matrix based on a second order model.

Last updated 3 years ago

1.11 score 13 scripts 261 downloads

TORDs - Third Order Rotatable Designs (TORDs)

Third order response surface designs (M. Hemavathi, Shashi Shekhar, Eldho Varghese, Seema Jaggi, Bikas Sinha & Nripes Kumar Mandal (2022) <DOI:10.1080/03610926.2021.1944213>."Theoretical developments in response surface designs: an informative review and further thoughts") are classified into two types viz., designs which are suitable for sequential experimentation and designs for non-sequential experimentation (M. Hemavathi, Eldho Varghese, Shashi Shekhar & Seema Jaggi (2022)<DOI:10.1080/02664763.2020.1864817>." Sequential asymmetric third order rotatable designs (SATORDs)"). The sequential experimentation approach involves conducting the trials step by step whereas, in the non-sequential experimentation approach, the entire runs are executed in one go.This package contains functions named STORDs() and NSTORDs() for generating sequential/non-sequential TORDs given in Das, M. N., and V. L. Narasimham (1962). <DOI:10.1214/aoms/1177704374>. "Construction of rotatable designs through balanced incomplete block designs" along with the randomized layout. It also contains another function named Pred3.var() for generating the variance of predicted response as well as the moment matrix based on a third order response surface model.

Last updated 3 years ago

1.04 score 11 scripts 118 downloads

MEDesigns - Mating Environmental Designs

In breeding experiments, mating environmental (ME) designs are very popular as mating designs are directly implemented in the field environment using block or row-column designs. Here, three functions are given related to three new methods which will generate mating diallel cross designs (Hinkelmann and Kempthorne, 1963<doi:10.2307/2333899>) or mating environmental (ME) designs along with design parameters, C matrix, eigenvalues (EVs), degree of fractionations (DF) and canonical efficiency factor (CEF). Another one function is added to check the properties of a given ME diallel cross design.

Last updated 3 months ago

1.00 score 8 scripts 235 downloads

OPTeCD - Optimal Partial Tetra-Allele Cross Designs

Tetra-allele cross often referred as four-way cross or double cross or four-line cross are those type of mating designs in which every cross is obtained by mating amongst four inbred lines. A tetra-allele cross can be obtained by crossing the resultant of two unrelated diallel crosses. A common triallel cross involving four inbred lines A, B, C and D can be symbolically represented as (A X B) X (C X D) or (A, B, C, D) or (A B C D) etc. Tetra-allele cross can be broadly categorized as Complete Tetra-allele Cross (CTaC) and Partial Tetra-allele Crosses (PTaC). Rawlings and Cockerham (1962)<doi:10.2307/2527461> firstly introduced and gave the method of analysis for tetra-allele cross hybrids using the analysis method of single cross hybrids under the assumption of no linkage. The set of all possible four-way mating between several genotypes (individuals, clones, homozygous lines, etc.) leads to a CTaC. If there are N number of inbred lines involved in a CTaC, the the total number of crosses, T = N*(N-1)*(N-2)*(N-3)/8. When more number of lines are to be considered, the total number of crosses in CTaC also increases. Thus, it is almost impossible for the investigator to carry out the experimentation with limited available resource material. This situation lies in taking a fraction of CTaC with certain underlying properties, known as PTaC.

Last updated 3 months ago

1.00 score 483 downloads

HadIBDs - Incomplete Block Designs using Hadamard Matrix (HadIBDs)

Hadamard matrix based statistical designs are of immense importance as the resultant designs carry various desirable characterizing properties. Constructing Partially Balanced Incomplete Block Designs (PBIBds) using Kronecker product of incidence matrices of Balanced Incomplete Block (BIB) and Partially Balanced Incomplete Block (PBIB) designs is much evident from literature. Here, we have constructed Incomplete Block Designs (IBDs) based on Hadamard matrices and Kronecker product of Hadamard matrices.

Last updated 6 months ago

1.00 score 3 scripts 252 downloads

GETdesigns - Generalized Extended Triangular Designs ('GETdesigns')

Since their introduction by Bose and Nair (1939) <https://www.jstor.org/stable/40383923>, partially balanced incomplete block (PBIB) designs remain an important class of incomplete block designs. The concept of association scheme was used by Bose and Shimamoto (1952) <doi:10.1080/01621459.1952.10501161> for the classification of these designs. The constraint of resources always motivates the experimenter to advance towards PBIB designs, more specifically to higher associate class PBIB designs from balanced incomplete block designs. It is interesting to note that many times higher associate PBIB designs perform better than their counterpart lower associate PBIB designs for the same set of parameters v, b, r, k and lambda_i (i=1,2...m). This package contains functions named GETD() for generating m-associate (m>=2) class PBIB designs along with parameters (v, b, r, k and lambda_i, i = 1, 2,…,m) based on Generalized Triangular (GT) Association Scheme. It also calculates the Information matrix, Average variance factor and canonical efficiency factor of the generated design. These designs, besides having good efficiency, require smaller number of replications and smallest possible concurrence of treatment pairs.

Last updated 11 months ago

1.00 score 3 scripts 289 downloads

GRCdesigns - Generalized Row-Column Designs

When the number of treatments is large with limited experimental resources then Row-Column(RC) designs with multiple units per cell can be used. These designs are called Generalized Row-Column (GRC) designs and are defined as designs with v treatments in p rows and q columns such that the intersection of each row and column (cell) consists of k experimental units. For example (Bailey & Monod (2001)<doi:10.1111/1467-9469.00235>), to conduct an experiment for comparing 4 treatments using 4 plants with leaves at 2 different heights row-column design with two units per cell can be used. A GRC design is said to be structurally complete if corresponding to the intersection of each row and column, there appears at least two treatments. A GRC design is said to be structurally incomplete if corresponding to the intersection of any row and column, there is at least one cell which does not contain any treatment.

Last updated 1 years ago

1.00 score 1 scripts 253 downloads

Tri.Hierarchical.IBDs - Tri-Hierarchical IBDs (Tri- Hierarchical Incomplete Block Designs)

Tri-hierarchical incomplete block design is defined as an arrangement of v treatments each replicated r times in a three system of blocks if, each block of the first system contains m_1 blocks of second system and each block of the second system contains m_2 blocks of the third system. Ignoring the first and second system of blocks, it leaves an incomplete block design with b_3 blocks of size k_3i units; ignoring first and third system of blocks, it leaves an incomplete block design with b_2 blocks each of size k_2i units and ignoring the second and third system of blocks, it leaves an incomplete block design with b_1 blocks each of size k_1 units. For dealing with experimental circumstances where there are three nested sources of variation, a tri-hierarchical incomplete block design can be adopted. Tri - hierarchical incomplete block designs can find application potential in obtaining mating-environmental designs for breeding trials. To know more about nested block designs one can refer Preece (1967) <doi:10.1093/biomet/54.3-4.479>. This package includes series1(), series2(), series3() and series4() functions. This package generates tri-hierarchical designs with six component designs under certain parameter restrictions.

Last updated 2 years ago

1.00 score 9 scripts 202 downloads

rsdNE - Response Surface Designs with Neighbour Effects (rsdNE)

Response surface designs with neighbour effects are suitable for experimental situations where it is expected that the treatment combination administered to one experimental unit may affect the response on neighboring units as well as the response on the unit to which it is applied. Integrating these effects in the response surface model improves the experiment's precision (Jaggi, S., Sarika and Sharma, V.K. (2010)<http://krishi.icar.gov.in/jspui/handle/123456789/4364>; Verma A., Jaggi S., Varghese, E.,Varghese, C.,Bhowmik, A., Datta, A. and Hemavathi M. (2021)<DOI: 10.1080/03610918.2021.1890123>). This package includes sym(), asym1(), asym2() functions that generates response surface designs which are rotatable under a polynomial model of a given order without interaction term incorporating neighbour effects.

Last updated 2 years ago

1.00 score 5 scripts 198 downloads

PBtDesigns - Partially Balanced t-Designs (PBtDesigns)

The t-designs represent a generalized class of balanced incomplete block designs in which the number of blocks in which any t-tuple of treatments (t >= 2) occur together is a constant. When the focus of an experiment lies in grading and selecting treatment subgroups, t-designs would be preferred over the conventional ones, as they have the additional advantage of t-tuple balance. t-designs can be advantageously used in identifying the best crop-livestock combination for a particular location in Integrated Farming Systems that will help in generating maximum profit. But as the number of components increases, the number of possible t-component combinations will also increase. Most often, combinations derived from specific components are only practically feasible, for example, in a specific locality, farmers may not be interested in keeping a pig or goat and hence combinations involving these may not be of any use in that locality. In such situations partially balanced t-designs with few selected combinations appearing in a constant number of blocks (while others not at all appearing) may be useful (Sayantani Karmakar, Cini Varghese, Seema Jaggi & Mohd Harun (2021)<doi:10.1080/03610918.2021.2008436>). Further, every location may not have the resources to form equally sized homogeneous blocks. Partially balanced t-designs with unequal block sizes (Damaraju Raghavarao & Bei Zhou (1998)<doi:10.1080/03610929808832657>. Sayantani Karmakar, Cini Varghese, Seema Jaggi & Mohd Harun (2022)." Partially Balanced t-designs with unequal block sizes") prove to be more suitable for such situations.This package generates three series of partially balanced t-designs namely Series 1, Series 2 and Series 3. Series 1 and Series 2 are designs having equal block sizes and with treatment structures 4(t + 1) and a prime number, respectively. Series 3 consists of designs with unequal block sizes and with treatment structure n(n-1)/2. This package is based on the function named PBtD() for generating partially balanced t-designs along with their parameters, information matrices, average variance factors and canonical efficiency factors.

Last updated 2 years ago

1.00 score 3 scripts 236 downloads

PolycrossDesigns - Polycross Designs ("PolycrossDesigns")

A polycross is the pollination by natural hybridization of a group of genotypes, generally selected, grown in isolation from other compatible genotypes in such a way to promote random open pollination. A particular practical application of the polycross method occurs in the production of a synthetic variety resulting from cross-pollinated plants. Laying out these experiments in appropriate designs, known as polycross designs, would not only save experimental resources but also gather more information from the experiment. Different experimental situations may arise in polycross nurseries which may be requiring different polycross designs (Varghese et. al. (2015) <doi:10.1080/02664763.2015.1043860>. " Experimental designs for open pollination in polycross trials"). This package contains a function named PD() which generates nine types of polycross designs suitable for various experimental situations.

Last updated 2 years ago

1.00 score 3 scripts 280 downloads