hassediagrams: Hasse Diagram of the Layout Structure and Restricted Layout Structure

Description

Returns a Hasse diagram of the layout structure (Bate and Chatfield (2016)) doi:10.1080/00224065.2016.11918173 or the restricted layout structure (Bate and Chatfield (2016)) doi:10.1080/00224065.2016.11918174 of an experimental design.

Author(s)

Maintainer: Damianos Michaelides dm3g15@soton.ac.uk

Authors:

• Simon Bate simon.t.bate@gsk.com

• Marion Chatfield

See Also

Useful links:

• https://github.com/GSK-Biostatistics/hassediagrams

• Report bugs at https://github.com/GSK-Biostatistics/hassediagrams/issues

A cross-nested design for an analytical method investigation

Description

The reliability of an analytical method was assessed in an experiment consisting of three batches of material, analysed by four analysts, two at each site. Within each site, there were two chromatographic systems and two columns. For each batch/analyst/system/column combination, two preparations (dissolved samples) were made. From each preparation, two injections were performed.

Usage

data(analytical)

Format

A data frame of 192 observations on 8 variables/factors:

Site

Categoric factor with levels 1 and 2.

Analyst

Categoric factor with levels 1-4.

Run

Categoric factor with levels 1-16.

Prep

Categoric factor with levels 1-96.

Injection

Categoric factor with levels 1-192.

System

Categoric factor with levels 1-4.

Column

Categoric factor with levels 1-4.

Batch

Categoric factor with levels 1-3.

Source

Bate, S.T. and Chatfield, M.J. (2016). "Identifying the Structure of the Experimental Design". *Journal of Quality Technology* 48, pp. 343-364.

Examples

data("analytical")
analytical

A fractional factorial design for investigating asphalt concrete production

Description

This is fractional factorial design given in Anderson and McLean (1974) p.256 from an experiment to investigate the effect of controllable variables/factors on the quality of asphalt concrete production.

Usage

data(concrete)

Format

A half fraction factorial design of 16 runs on 6 variables/factors. The 6 variables/factors, each at two levels, included in the design are:

Aggregate gradation (AG)

Categoric factor with levels being fine and coarse.

Compaction temperature (CoT)

Numeric factor with low 250 and high 300.

Asphalt content (AC)

Numeric factor with low 5 and high 7.

Curing condition (CC)

Categoric factor with levels wrapped and unwrapped.

Curing temperature (CuT)

Numeric factor with low 45 and high 72.

Run

Categoric factor with levels 1-16.

Source

Anderson, V.L. and McLean, R.A. (1974). *Design of Experiments.* Marcel Dekker Inc.: New York.

Examples

data("concrete")
concrete

A crossover design for a dental study

Description

This is a crossover design (Study H) given in Newcombe et al. (1995) to study the effects of CHX rinses on 4 day plaque regrowth. The study consisted of 24 patients assessed over 3 treatment periods. The purpose of the study was to compare 2 CHX rinses with saline. The design is based on pairs of Latin squares balanced for carry over.

Usage

data(dental)

Format

A crossover design of 72 runs on 5 variables/factors. The 5 variables/factors included in the design are:

Sequence

Categoric factor with levels 1-6.

Subject

Categoric factor with levels 1-32.

Period

Categoric factor with levels 1-3.

Treatment

Categoric factor with levels CHX1, CHX2 and Saline.

Observation

Categoric factor with levels 1-72.

Source

Newcombe, R.G., Addy, M. and McKeown, S. (1995). "Residual effect of chlorhexidine gluconate in 4-day plaque regrowth crossover trials, and its implications for study design". *Journal of Periodontal Research*, 30, 5, pp. 319-324.

Examples

data("dental")
dental

Hasse diagram of the layout structure and restricted layout structure

Description

Returns a Hasse diagram of the 'layout structure' or the 'restricted layout structure' of an experimental design.

Details

The package consists of three main functions: hasselayout, itemlist, and hasserls. The first function generates the Hasse diagram of the layout structure of an experimental design. The latter two functions are used together to generate the Hasse diagram of the restricted layout structure of an experimental design.

Author(s)

Damianos Michaelides (Maintainer) <dm3g15@soton.ac.uk> Simon Bate <simon.t.bate@gsk.com> Marion Chatfield

References

Bate, S.T. and Chatfield, M.J. (2016a), Identifying the structure of the experimental design. Journal of Quality Technology, 48, 343-364.

Bate, S.T. and Chatfield, M.J. (2016b), Using the structure of the experimental design and the randomization to construct a mixed model. Journal of Quality Technology, 48, 365-387.

Box, G.E.P., Hunter, J.S., and Hunter, W.G., (1978), Statistics for Experimenters. New York, Wiley.

Joshi, D.D. (1987), Linear Estimation and Design of Experiments. Wiley Eastern, New Delhi.

Williams, E.R., Matheson, A.C. and Harwood, C.E. (2002), Experimental design and analysis for tree improvement. 2nd edition. CSIRO, Melbourne, Australia.

See Also

For dataset details, see: - concrete - dental - human - analytical

Hasse diagram of the layout structure

Description

Returns a Hasse diagram of the layout structure of an experimental design

Usage

hasselayout(
  datadesign,
  randomfacsid = NULL,
  showLS = "Y",
  showpartialLS = "Y",
  showdfLS = "Y",
  check.confound.df = "Y",
  maxlevels.df = "Y",
  table.out = "N",
  pdf = "N",
  example = "example",
  outdir = NULL,
  hasse.font = "sans",
  produceBWPlot = "N",
  structural.colour = "grey",
  structural.width = 2,
  partial.colour = "orange",
  partial.width = 1.5,
  objects.colour = "mediumblue",
  df.colour = "red",
  larger.fontlabelmultiplier = 1,
  middle.fontlabelmultiplier = 1,
  smaller.fontlabelmultiplier = 1
)

Arguments

Details

The hasselayout function generates the Hasse diagram of the layout structure of the experimental design, as described in Bate and Chatfield (2016a). The diagram consists of a set of structural objects, corresponding to the factors and generalised factors, and the relationships between the structural objects (either crossed, nested, partially crossed or equivalent), as defined by the structure of the experimental design.

The function requires a dataframe containing only the variables corresponding to the experimental factors that define the experimental design (i.e., no response variables should be included).

In the dataframe the levels of the variables/factors must be uniquely identified and have a physical meaning, otherwise the function will not correctly identify the nesting/crossing of the variables/factors. For example, consider an experiment consisting of Factor A (with k levels) that nests Factor B (with q levels per level of Factor A). The levels of Factor B should be labelled 1 to k x q and not 1 to q (repeated k times).

Where present, two partially crossed factors are illustrated on the diagram with a dotted line connecting them. This feature can be excluded using the showpartialLS option.

The maximum number of possible levels of each generalised factor, along with the actual number present in the design and the "skeleton ANOVA" degrees of freedom, can be included in the structural object label on the Hasse diagram.

Using the randomfacsid argument the factors that correspond to random effects can be highlighted by underlining them on the Hasse diagram. The vector should be equal to the number of variables/factors in the design and consist of fixed (entry = 0) or random (entry = 1) values.

The hasselayout function evaluates the design in order to identify if there are any confounded degrees of freedom across the design. It is not recommended to perform this evaluation for large designs due to the potential high computational cost. This can be controlled using the check.confound.df = "N" option.

Value

The function hasselayout returns:

1. The Hasse diagram of the layout structure (if showLS="Y").

2. The layout structure table shows the relationships between the structural objects in the layout structure (if table.out="Y"). The individual entries in the table consist of blanks on the main diagonal and 0's, (0)'s or 1's elsewhere. If the factor (or generalised factor) corresponding to the ith row and the factor (or generalised factor) corresponding to the jth column are fully crossed, then a 0 is entered in the (i,j)th entry in the table. If these factors (or generalised factors) are partially crossed, or the ith row factor (or generalised factor) only has one level and nests the jth column factor (or generalised factor), then the (i,j)th entry is (0). If the ith row factor (or generalised factor) is nested within the jth column factor (or generalised factor), then a 1 is entered in the (i,j)th entry. If two factors (or generalised factors) are equivalent, then they share a single row and column in the table, where the row and column headers include both factor (or generalised factor) names, separated by an "=" sign.

3. If there are confounded degrees of freedom, a table of the structural objects and a description of the associated degrees of freedom is printed.

Author(s)

Damianos Michaelides, Simon Bate, and Marion Chatfield

References

Bate, S.T. and Chatfield, M.J. (2016a), Identifying the structure of the experimental design. Journal of Quality Technology, 48, 343-364.

Bate, S.T. and Chatfield, M.J. (2016b), Using the structure of the experimental design and the randomization to construct a mixed model. Journal of Quality Technology, 48, 365-387.

Box, G.E.P., Hunter, J.S., and Hunter, W.G., (1978), Statistics for Experimenters. Wiley.

Joshi, D.D. (1987), Linear Estimation and Design of Experiments. Wiley Eastern, New Delhi.

Williams, E.R., Matheson, A.C. and Harwood, C.E. (2002), Experimental design and analysis for tree improvement. 2nd edition. CSIRO, Melbourne, Australia.

Examples

## Examples using the package build-in data concrete, dental, human, analytical.

## A fractional factorial design for investigating asphalt concrete production
hasselayout(datadesign=concrete, larger.fontlabelmultiplier=1.6, 
            smaller.fontlabelmultiplier=1.3, table.out="Y")

## A crossover design for a dental study
hasselayout(datadesign=dental, randomfacsid = c(0,1,0,0,0), 
            larger.fontlabelmultiplier = 1.6)

## A block design for an experiment assessing human-computer interaction
hasselayout(datadesign=human, randomfacsid = c(1,1,0,0,0,0,1), 
            larger.fontlabelmultiplier=1.4)

## A cross-nested design for an analytical method investigation
hasselayout(datadesign=analytical, randomfacsid = c(0,0,1,1,1,0,0,0), 
            showpartialLS="N", check.confound.df="N", 
            larger.fontlabelmultiplier=1, 
            smaller.fontlabelmultiplier=1.6)


## Examples using data from the dae package (conditionally loaded)

if (requireNamespace("dae", quietly = TRUE)) {
  
  ## Data for a balanced incomplete block experiment, Joshi (1987)
  
  data(BIBDWheat.dat, package = "dae")
  # remove the response from the dataset
  BIBDWheat <- BIBDWheat.dat[, -4]
  hasselayout(datadesign=BIBDWheat, example = "BIBDWheat")
  
  
  ## Data for an un-replicated 2^4 factorial experiment to investigate a chemical process
  ## from Table 10.6 of Box, Hunter and Hunter (1978)
  
  data(Fac4Proc.dat, package = "dae")
  # remove the response from the dataset
  Fac4Proc <- Fac4Proc.dat[, -6]
  hasselayout(datadesign=Fac4Proc, example = "Fac4Proc", showpartialLS="N", 
              smaller.fontlabelmultiplier=2)
  
 
 ## Data for an experiment with rows and columns from p.144 of 
 ## Williams, Matheson and Harwood (2002)

 data(Casuarina.dat, package = "dae")
 # remove the response from the dataset
 Casuarina <- Casuarina.dat[, -7]
 # create unique factor level labels
 Casuarina$Row <- paste(Casuarina$Reps, Casuarina$Rows)
 Casuarina$Col <- paste(Casuarina$Reps, Casuarina$Columns)
 Casuarina <- Casuarina[, -c(2,3)]
 hasselayout(datadesign=Casuarina, randomfacsid=c(1,0,1,0,0,0), 
             example="Casuarina", check.confound.df="N", 
             showpartialLS="N")
  
} else {
  message("Examples using data from the 'dae' package 
           require 'dae' to be installed.")
}

Hasse diagram of the restricted layout structure

Description

Returns a Hasse diagram of the restricted layout structure of an experimental design

Usage

hasserls(
  object,
  randomisation.objects,
  random.arrows = NULL,
  showRLS = "Y",
  showpartialRLS = "Y",
  showdfRLS = "Y",
  showrandRLS = "Y",
  check.confound.df = "Y",
  maxlevels.df = "Y",
  table.out = "N",
  equation.out = "N",
  pdf = "N",
  example = "example",
  outdir = NULL,
  hasse.font = "sans",
  produceBWPlot = "N",
  structural.colour = "grey",
  structural.width = 2,
  partial.colour = "orange",
  partial.width = 1.5,
  objects.colour = "mediumblue",
  df.colour = "red",
  arrow.colour = "mediumblue",
  arrow.width = 1.5,
  arrow.pos = 7.5,
  larger.fontlabelmultiplier = 1,
  middle.fontlabelmultiplier = 1,
  smaller.fontlabelmultiplier = 1
)

Arguments

Details

The hasserls function generates the Hasse diagram of the restricted layout structure. The Hasse diagram consists of a set of randomisation objects, corresponding to the factors and generalised factors, and the relationships between the objects (either crossed, nested, partially crossed or equivalent), as defined by the structure of the experimental design and the randomisation performed, see Bate and Chatfield (2016b).

The function requires an object of class "rls" containing the structural objects in the layout structure.

Where present, two partially crossed factors are illustrated on the diagram with a dotted line connecting them. This feature can be excluded using the showpartialRLS option.

The maximum number of possible levels of each generalised factor, along with the actual number present in the design and the "skeleton ANOVA" degrees of freedom, can be included in the randomisation object label on the Hasse diagram.

The randomisation arrows that illustrate the randomisation performed can be included on the Hasse diagram.

The hasserls function evaluates the design in order to identify if there are any confounded degrees of freedom across the design. It is not recommended to perform this evaluation for large designs, due to the potential high computational cost. This can be controlled using the check.confound.df = "N" option.

Objects that contain Unicode characters, e.g., u2192 or u2297 must be handled by Unicode friendly font families. Common font families that work with Unicode characters are: for Windows: Cambria, Embrima, Segoe UI Symbol, Arial Unicode MS, and for macOS: AppleMyungjo, .SF Compact Rounded, Arial Unicode MS, .SF Compact, .SF NS Rounded. The aforementioned fonts may not not be available in your R session. The available system fonts can be printed by systemfonts::system_fonts()$family. System available fonts can be imported by running showtext::font_import() or extrafont::font_import(). To check which fonts have been successfully imported, run showtext::fonts() or extrafont::fonts(). The Arial Unicode MS font can be downloaded from online sources. The Noto Sans Math font can be installed using sysfonts::font_add_google("Noto Sans Math").

Value

The function hasserls returns: 1. The Hasse diagram of the restricted layout structure (if showRLS = "Y").

2. The restricted layout structure table shows the relationships between the randomisation objects in the restricted layout structure (if table.out="Y"). The individual entries in the table consist of blanks on the main diagonal and 0’s, (0)’s or 1’s elsewhere. If the factor (or generalised factor) corresponding to the ith row and the factor (or generalised factor) corresponding to the jth column are fully crossed, then a 0 is entered in the (i,j)th entry in the table. If these factors (or generalised factors) are partially crossed, or the ith row factor (or generalised factor) only has one level and nests the jth column factor (or generalised factor), then the (i,j)th entry is (0). If the ith row factor (or generalised factor) is nested within the jth column factor (or generalised factor), then a 1 is entered in the (i,j)th entry. If two factors (or generalised factor) are equivalent, then they share a single row and column in the table, where the row and column headers include both factor (or generalised factor) names, separated by an "=" sign.

3. An equation that suggests the mixed model to be fitted (if equation.out="Y").

4. If there are confounded degrees of freedom, a table of the structural objects and a description of the associated degrees of freedom is printed.

Author(s)

Damianos Michaelides, Simon Bate, and Marion Chatfield

References

Bate, S.T. and Chatfield, M.J. (2016a), Identifying the structure of the experimental design. Journal of Quality Technology, 48, 343-364.

Bate, S.T. and Chatfield, M.J. (2016b), Using the structure of the experimental design and the randomization to construct a mixed model. Journal of Quality Technology, 48, 365-387.

Box, G.E.P., Hunter, J.S., and Hunter, W.G., (1978), Statistics for Experimenters. Wiley.

Joshi, D.D. (1987), Linear Estimation and Design of Experiments. Wiley Eastern, New Delhi.

Williams, E.R., Matheson, A.C. and Harwood, C.E. (2002), Experimental design and analysis for tree improvement. 2nd edition. CSIRO, Melbourne, Australia.

Examples

## NOTE TO USERS:
## Some examples below need Unicode symbols (e.g., "u2297 and "u2192"
## with a backslash, for the Kronecker and arrow symbols respectively),
## but we use ASCII fallbacks such as "x" and "->" in the code to ensure
## compatibility across systems.
## To render proper Unicode symbols in diagrams, update the labels manually
## i.e., x to \ u2297 to get the Kronecker symbol and -> to \ u2192 to get the
## arrow symbol, and set a Unicode-friendly font via the hasse.font argument.
## See the hasse.font argument and Details section in ?hasserls for guidance.

## Example: Asphalt concrete production (fractional factorial design)
concrete_objects <- itemlist(datadesign = concrete)
concrete_rls <- concrete_objects$TransferObject
concrete_rls[, 2] <- concrete_rls[, 1]
concrete_rls[27, 2] <- "AC^AG^CC^CoT^CuT -> Run"  
hasserls(object = concrete_objects,
         randomisation.objects = concrete_rls,
         larger.fontlabelmultiplier = 1.6,
         smaller.fontlabelmultiplier = 1.3,
         table.out = "Y", arrow.pos = 8,
         hasse.font = "sans")

## Example: Crossover dental study
dental_objects <- itemlist(datadesign = dental, randomfacsid = c(0,1,0,0,0))
dental_rand_arrows <- matrix(c(3, 5, 4, 7), ncol = 2, byrow = TRUE)
dental_rls <- dental_objects$TransferObject
dental_rls[c(1:5,7,8), 2] <- c("Mean", "Period", "Sequence",
                               "Treatment", "Subject[Sequence]",
                               "Period x Sequence",
                               "Observation")
hasserls(object = dental_objects,
         randomisation.objects = dental_rls,
         random.arrows = dental_rand_arrows,
         larger.fontlabelmultiplier = 1.6,
         table.out = "Y", equation.out = "Y",
         arrow.pos = 15, hasse.font = "sans")

## Example: Human-computer interaction study
human_objects <- itemlist(datadesign = human,
                          randomfacsid = c(1,1,0,0,0,0,1))
human_rand_arrows <- matrix(c(3, 12, 6, 13), ncol = 2, byrow = TRUE)
human_rls <- human_objects$TransferObject
human_rls[, 2] <- c("Mean", "Day", "Method", "Period", "Room", "Sequence",
                    "NULL", "Subject | Subject -> Day x Sequence",  
                    "NULL", "NULL", "NULL", "Day x Room",
                    "Period x Room", "NULL",
                    "Test = Day^Method^Period^Room^Sequence")
hasserls(object = human_objects,
         randomisation.objects = human_rls,
         random.arrows = human_rand_arrows,
         larger.fontlabelmultiplier = 1.4,
         hasse.font = "sans")

## Example: Analytical method (cross-nested design)
analytical_objects <- itemlist(datadesign = analytical,
                               randomfacsid = c(0,0,1,1,1,0,0,0))
analytical_rand_arrows <- matrix(c(2, 19, 19, 20), ncol = 2, byrow = TRUE)
analytical_rls <- analytical_objects$TransferObject
analytical_rls[, 2] <- c("Mean", "Batch", "Site",
                         "Analyst[Site]", "Column[Site]",
                         "System[Site]", "NULL",
                         "{Analyst^Column}[Site]",
                         "{Analyst^System}[Site]", "NULL",
                         "{Column^System}[Site]",
                         "NULL", "NULL",
                         "{Analyst^Column^System}[Site] -> Run",  
                         "NULL", "NULL", "NULL", "NULL",
                         "Preparation[Run]", "Injection[Run]")
hasserls(object = analytical_objects,
         randomisation.objects = analytical_rls,
         random.arrows = analytical_rand_arrows,
         showpartialRLS = "N", check.confound.df = "N",
         larger.fontlabelmultiplier = 1,
         smaller.fontlabelmultiplier = 1.6,
         hasse.font = "sans")

## Conditionally run examples requiring 'dae'
if (requireNamespace("dae", quietly = TRUE)) {
  data(BIBDWheat.dat, package = "dae")
  BIBDWheat <- BIBDWheat.dat[, -4]
  BIBDWheat$Plots <- 1:30
  BIBDWheat_objects <- itemlist(datadesign = BIBDWheat)
  IBDWheat_rand_arrows <- matrix(c(3, 4), ncol = 2, byrow = TRUE)
  IBDWheat_rls <- BIBDWheat_objects$TransferObject
  IBDWheat_rls[1:4, 2] <- c("Mean", "Blocks", "Varieties", "Plot[Block]")
  hasserls(object = BIBDWheat_objects,
           randomisation.objects = IBDWheat_rls,
           random.arrows = IBDWheat_rand_arrows,
           equation.out = "Y")

  data(Fac4Proc.dat, package = "dae")
  Fac4Proc <- Fac4Proc.dat[, -6]
  Fac4Proc_objects <- itemlist(datadesign = Fac4Proc)
  Fac4Proc_rls <- Fac4Proc_objects$TransferObject
  Fac4Proc_rls[, 2] <- Fac4Proc_rls[, 1]
  Fac4Proc_rls[16, 2] <- "Catal^Conc^Press^Temp -> Run"  
  hasserls(object = Fac4Proc_objects,
           randomisation.objects = Fac4Proc_rls,
           showpartialRLS = "N", table.out = "Y",
           smaller.fontlabelmultiplier = 2,
           hasse.font = "sans")

  data(Casuarina.dat, package = "dae")
  Casuarina <- Casuarina.dat[, -7]
  Casuarina$Row <- paste(Casuarina$Reps, Casuarina$Rows)
  Casuarina$Col <- paste(Casuarina$Reps, Casuarina$Columns)
  Casuarina <- Casuarina[, -c(2, 3)]
  Casuarina_objects <- itemlist(datadesign = Casuarina,
                                randomfacsid = c(1,0,1,0,0,0))
  Casuarina_rand_objects <- c(1:6, 9, 13)
  Casuarina_rand_arrows <- matrix(c(3, 5, 4, 13), ncol = 2, byrow = TRUE)
  Casuarina_rls <- Casuarina_objects$TransferObject
  Casuarina_rls[Casuarina_rand_objects, 2] <- c("Mean", "Countries",
                                                "InocTime", "Provences",
                                                "Reps", "Countries^InocTime",
                                                "Inoc^Provences",
                                                "{Row x Col}[Rep]")  
  hasserls(object = Casuarina_objects,
           randomisation.objects = Casuarina_rls,
           random.arrows = Casuarina_rand_arrows,
           check.confound.df = "N", showpartialRLS = "N",
           arrow.pos = 10,
           smaller.fontlabelmultiplier = 1.5,
           hasse.font = "sans")
} else {
  message("Install package 'dae' to run the final examples.")
}

A block design for an experiment in human-computer interaction

Description

This is a block design to compare two methods (mouse and stylus) of drawing a map in a computer file. The design involved 12 subjects randomised in 6 days and 2 tests (morning/afternoon) within each day, across 2 rooms. The design is based on 2x2 Latin squares; see Example 7 Brien and Bailey (2006) for more details.

Usage

data(human)

Format

A data frame of 24 observations on 7 variables. The 7 variables/factors included in the design are:

Subject

Categoric factor with levels 1-12.

Day

Categoric factor with levels 1-6.

Room

Categoric factor with levels A and B.

Period

Categoric factor with levels Morning and Afternoon.

Method

Categoric factor with levels Mouse and Stylus.

Sequence

Categoric factor with levels 1 and 2.

Test

Categoric factor with levels 1-24.

Source

Brien, C.J. and Bailey, R.A. (2006). "Multiple randomizations (with discussion)". *Journal of the Royal Statistical Society B*, 68, pp. 571-609.

Examples

data("human")
human

Objects to be used for restricted layout structure Hasse diagram

Description

Returns an object of class "rls" that contains the structural objects of the layout structure. The output can be used in a consecutive function to generate the Hasse diagram of the restricted layout structure of the experimental design.

Usage

itemlist(datadesign, randomfacsid = NULL)

Arguments

Details

The function requires a dataframe containing the variables corresponding to the experimental factors only (i.e., no response variables). Using the randomfacsid argument, the factors and generalised factors that correspond to random effects can be identified.

Value

The function returns an object of class "rls" which is a list with the following components:

design - The design dataframe containing all of the factors present in the layout structure. This is identical to the input argument datadesign.

finaleffectsnames - A character vector consisting of all structural objects (factors and generalised factors) in the layout structure.

finalstructure - A table that shows the relationships between the structural objects in the layout structure.

finaleffects - A vector containing the final factor orders.

finalrandomeffects - A vector containing 0 or 1 entries for factors or generalised factors corresponding to fixed (entry = 0) or random (entry = 1) effects.

confoundings - Defines the equivalent factors and generalised factors.

nfactors - The number of factors/variables of the design dataframe.

outputlistip1 - A list of items required to generate the restricted layout structure.

nestednames - List of matrices containing the nested version of the factor and generalised factor names.

TransferObject - A Nx2 matrix where N equals the total number of structural objects. The first column contains the structural objects in the layout structure, and the second column has "Mean" for the first entry and "NULL" for the remaining entries.

Author(s)

Damianos Michaelides, Simon Bate, and Marion Chatfield

References

Bate, S.T. and Chatfield, M.J. (2016a), Identifying the structure of the experimental design. Journal of Quality Technology, 48, 343-364.

Bate, S.T. and Chatfield, M.J. (2016b), Using the structure of the experimental design and the randomization to construct a mixed model. Journal of Quality Technology, 48, 365-387.

Box, G.E.P., Hunter, J.S., and Hunter, W.G., (1978), Statistics for Experimenters. Wiley.

Joshi, D.D. (1987), Linear Estimation and Design of Experiments. Wiley Eastern, New Delhi.

Williams, E.R., Matheson, A.C. and Harwood, C.E. (2002), Experimental design and analysis for tree improvement. 2nd edition. CSIRO, Melbourne, Australia.

Examples

# Examples using built-in data: concrete, dental, human, analytical

# Fractional factorial design for asphalt concrete production
concrete_objects <- itemlist(datadesign=concrete)
print(concrete_objects)

# Crossover design for a dental study
dental_objects <- itemlist(datadesign=dental, randomfacsid=c(0,1,0,0,0))
summary(dental_objects)

# Block design for an experiment assessing human-computer interaction
human_objects <- itemlist(datadesign=human, randomfacsid=c(1,1,0,0,0,0,1))
print(human_objects)

# Cross-nested design for an analytical method investigation
analytical_objects <- itemlist(datadesign=analytical, 
                               randomfacsid=c(0,0,1,1,1,0,0,0))
summary(analytical_objects)

# Examples using data from the dae package (conditionally loaded)
if (requireNamespace("dae", quietly = TRUE)) {
  data(BIBDWheat.dat, package = "dae")
  BIBDWheat <- BIBDWheat.dat[, -4]
  BIBDWheat$Plots <- c(1:30)
  BIBDWheat_objects <- itemlist(datadesign=BIBDWheat)
  print(BIBDWheat_objects)
}

Print and Summary of rls objects

Description

Print and Summary of objects of class "rls".

Usage

## S3 method for class 'rls'
print(x, ...)

## S3 method for class 'rls'
summary(object, ...)

Arguments

Value

The functions return the structural objects of the Layout Structure and a matrix that the users need to edit with the randomisation objects to pass in the hasserls function.

Note

For examples see itemlist and hasserls.

Author(s)

Damianos Michaelides, Simon Bate, and Marion Chatfield