Exploratory ANOVA Decomposition

Performs an exploratory decomposition of a numeric response variable into additive components (global mean, main effects, interaction effects, and residuals) using a sequential mean sweeping algorithm. It supports both balanced and unbalanced designs, and can account for nested factor structures.

Usage

eda_mean_sweep(
  data,
  ...,
  max_order = 1,
  nesting = NULL,
  p = 1,
  tukey = FALSE,
  base = exp(1)
)

Arguments

data

A data frame containing the response and factor variables.

...

Unquoted variable names: The first variable must be the numeric response, followed by one or more factor variables.

max_order

An integer specifying the maximum order of interaction effects to include. Main effects are always computed if factors are provided.

max_order = 1: (default) Only main effects are calculated and included in the decomposition.
max_order = 2: Main effects and all two-way interactions among the specified factors are included.
max_order = k: Main effects and all interaction terms up to order k are included.

nesting

A list of character vectors specifying nested relationships. Each element should be a pair like c("Parent", "Child") indicating that Child is nested within Parent. If provided, the function will automatically reorder the sweeping sequence to ensure that parent factors are swept before their nested children.

p

Numeric. A power transformation to apply to the response variable before decomposition.

tukey

Logical. If TRUE, Tukey's transformation is applied. If FALSE, a Box-Cox style transformation is used.

base

Numeric. The base for the logarithm if a logarithmic transformation (p=0) is applied. Defaults to exp(1) (natural logarithm).

Value

A list of class "eda_mean_sweep" with the following components:

global: The common or global mean
response: The name of the response variable used in the analysis.
effects: A named list of main and interaction effects. Each element is a named vector of centered effects, representing the deviations from the adjusted mean attributable to that factor or interaction.
residuals: A numeric vector of residuals after the global mean and all specified effects have been "swept out" (subtracted) from the response variable.
long: The original data frame with an added residuals column, which can be useful for further exploratory plotting.

Details

This function implements the value-splitting and sweeping procedure central to Exploratory Data Analysis (EDA) of Analysis of Variance (ANOVA). It systematically decomposes the response variable into additive overlays, which when recombined, recover the original data.

The decomposition process is sequential: the global mean is first removed, then main effects are calculated and subtracted, followed by interaction effects up to max_order. Each effect is calculated as the mean deviation from the previously swept y for its respective levels, and then subtracted, leaving the remaining y for subsequent effects or as residuals.

Nested factors are specifically handled by computing their effects within each level of their parent factor ensuring appropriate variance attribution.

Unbalanced designs are supported by calculating group wise means allowing for a robust decomposition even when cell counts are unequal.

Important consideration for factor order: The order in which factors are specified can significantly affect the decomposition, particularly when factors are correlated or nested. Factors listed earlier in the arguments are "swept" first and may absorb variation that might otherwise be attributed to factors listed later in the arguments. To manage this, the nesting argument provides a structured way to enforce a logical sweeping sequence, ensuring parent factors are accounted for before their nested children.

References

Hoaglin, D. C., Mosteller, F., & Tukey, J. W. (1991). Fundamentals of Exploratory Analysis of Variance. Wiley.

Examples

# A one-way analysis of chickwts. "weight" is the response and "feed" is
# the factor. First column passed to the function must be the response variable
# ("weight" in this example)
M0 <- eda_mean_sweep(chickwts, weight, feed)

# Global (overall) mean weight
M0$global
#> [1] 261.3099

# Effect level values
M0$effects
#> $feed
#>     casein  horsebean    linseed   meatmeal    soybean  sunflower 
#>   62.27347 -101.10986  -42.55986   15.59923  -14.88129   67.60681 
#> 

# Compare residuals' spread to those of the effects
plot(M0, label = TRUE)


# A two-way analysis without replicates (i.e. one value per cell)
M0 <- eda_mean_sweep(inf_mort, perc, region, edu)
plot(M0, label = TRUE)


# A two -way analysis with replicates (i.e. multiple values per cell)
# Include 2-way interaction effects
M0 <- eda_mean_sweep(feav5_12, Weight, Level, Type, max_order = 2)
plot(M0, label = TRUE)


# A three-way analysis with nested factors. There are two embedded nests:
# Sample embedded under Run and Run embedded under Lot.
# Response variable is decomposed across ALL factors leaving 0 residuals
M0 <- eda_mean_sweep(feav5_14, Absorption, Lot, Run, Sample,
                     nesting = list(c("Lot", "Run"), c("Run","Sample")))
plot(M0, rotate = TRUE)


# A traditional ANOVA table can be generated from the eda_mean_sweep object
eda_anova_table(M0)
#>                    Effect           SS df           MS            F  p
#> 1                  Common 8.176608e+01  1 8.176608e+01           NA NA
#> 2                     Lot 4.234740e-01  4 1.058685e-01 6.760589e+31  0
#> 3        Run (within Lot) 1.134349e+00 24 4.726456e-02 3.018237e+31  0
#> 4 Sample (within Lot:Run) 7.819953e-01  1 7.819953e-01 4.993694e+32  0
#> 5                Residual 7.046845e-32 45 1.565966e-33           NA NA

# A three-way analysis with one nested factor (State within Grouping)
# If there is just one nesting object, the nesting argument can be passed
# a c() object without the need of embedding it in a list() object
M0 <- eda_mean_sweep(feav1_5, votes, State, Year, Grouping,
                     nesting = c("Grouping", "State"))
plot(M0, rotate = TRUE)


# A three-way analysis with 2-way interactions
M0 <- eda_mean_sweep(feav6_8, Hard, Dentist, Method, Alloy, Temp, max_order = 2)
plot(M0, rotate = TRUE, order = FALSE) # Preserve factor order as entered in arguments

plot(M0, rotate = TRUE) # By default, factors are ordered by range


# A three-way analysis with 3-way interactions
M0 <- eda_mean_sweep(feav6_8, Hard, Dentist, Method, Alloy, Temp, max_order = 3)
plot(M0, rotate = TRUE)