Grouped ternary diagrams
grouped_ternary_data.RdThe helper function for preparing the underlying data for creating grouped
ternary diagrams where the proportions of the compositional variables
are combined into groups and visualised on a ternary diagram.
These are very useful when we have multiple compositional variables that can
be grouped together by some hierarchical grouping structure. For example, grouping
species in a ecosystem based on the functions they perform, or grouping
political parties based on their national alliances. Grouping variables this
way allows us to reduce the dimensionality of the compositional data and
visualise it. This is akin to looking at a 2-d slice of the high
dimensional simplex. The relative proportions of each variable within a group
can be adjust to look at different slices of the simplex. Looking at multiple
such slices would enable us to create an approximation of how the response varies
across the original n-dimensional simplex. The output of this function can be passed to the
grouped_ternary_plot function to plot the results.
Usage
grouped_ternary_data(
prop,
FG,
values = NULL,
tern_vars = NULL,
conditional = NULL,
add_var = list(),
resolution = 3,
prediction = TRUE,
...
)Arguments
- prop
A character vector indicating the model coefficients corresponding to variable proportions. These variables should be compositional in nature (i.e., proportions should sum to 1).
- FG
A character vector specifying the groupings of the variables specified in `prop`.
- values
A numeric vector specifying the proportional split of the variables within a group. The default is to split the group proportion equally between each variable in the group.
- tern_vars
A character vector giving the names of the three variables to be shown in the ternary diagram.
- conditional
A data-frame describing the names of the compositional variables and their respective values at which to slice the simplex space. The format should be, for example, as follows:
data.frame("p1" = c(0, 0.5), "p2" = c(0.2, 0.1))
One figure would be created for each row in `conditional` with the respective values of all specified variables. Any compositional variables not specified in `conditional` will be assumed to be 0.- add_var
A list or data-frame specifying values for additional variables in the model other than the proportions (i.e. not part of the simplex design). This could be useful for comparing the predictions across different values for a non-compositional variable. If specified as a list, it will be expanded to show a plot for each unique combination of values specified, while if specified as a data-frame, one plot would be generated for each row in the data.
- resolution
A number between 1 and 10 describing the resolution of the resultant graph. A high value would result in a higher definition figure but at the cost of being computationally expensive.
- prediction
A logical value indicating whether to pass the final data to the `add_prediction` function and append the predictions to the data. Default value is
TRUE, but often it would be desirable to make additional changes to the data before making any predictions, so the user can set this toFALSEand manually call the `add_prediction` function.- ...
Arguments passed on to
add_predictionmodelA regression model object which will be used to make predictions for the observations in `data`. Will override `coefficients` if specified.
coefficientsIf a regression model is not available (or can't be fit in R), the regression coefficients from a model fit in some other language can be used to calculate predictions. However, the user would have to ensure there's an appropriate one-to-one positional mapping between the data columns and the coefficient values. Further, they would also have to provide a variance-covariance matrix of the coefficients in the `vcov` parameter if they want the associated CI for the prediction or it would not be possible to calculate confidence/prediction intervals using this method.
vcovIf regression coefficients are specified, then the variance-covariance matrix of the coefficients can be specified here to calculate the associated confidence interval around each prediction. Failure to do so would result in no confidence intervals being returned. Ensure `coefficients` and `vcov` have the same positional mapping with the data.
coeff_colsIf `coefficients` are specified and a one-to-one positional mapping between the data-columns and coefficient vector is not present. A character string or numeric index can be specified here to reorder the data columns and match the corresponding coefficient value to the respective data column. See the "Use model coefficients for prediction" section in examples.
conf.levelThe confidence level for calculating confidence/prediction intervals. Default is 0.95.
intervalType of interval to calculate:
- "none" (default)
No interval to be calculated.
- "confidence"
Calculate a confidence interval.
- "prediction"
Calculate a prediction interval.
Value
A data-frame containing compositional columns with names specified in `FG` and `prop` parameters along with any additional columns specified in `add_var` parameter and the following columns appended at the end.
- .x
The x-projection of the points within the ternary.
- .y
The y-projection of the points within the ternary.
- .add_str_ID
An identifier column for grouping the cartesian product of all additional columns specified in `add_var` parameter (if `add_var` is specified).
- .Sp
An identifier column specifying the functional group along which the high dimensional simplex is sliced (if there are more than 3 groups).
- .Value
The value (between 0 and 1) along the direction of functional group in `.Sp` at which the high dimensional simplex is sliced.
- .Facet
An identifier column formed by combining `.Sp` and `.value` to group observations within a specific slice of the high dimensional simplex.
- .Pred
The predicted response for each observation. (if `prediction` is
TRUE)- .Lower
The lower limit of the prediction/confidence interval for each observation.
- .Upper
The upper limit of the prediction/confidence interval for each observation.
Examples
library(DImodels)
## Load data
data(sim3)
## Fit model
mod <- glm(response ~ 0 + (p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9)^2,
data = sim3)
## Create data
## We have nine (p1 to p9) variables here and using \code{\link{conditional_ternary}}
## to visualise the simplex space won't be very helpful as there are too
## variables to condition on
## Instead we group the nine-variables into three groups called "G", "L" and "H"
head(grouped_ternary_data(model = mod,
prop = paste0("p", 1:9),
FG = c("G","G","G","G","G","L","L","H","H"),
resolution = 1))
#> Warning: The proportional split of species in the groups was not specified in `values`,
#> assuming an equal split for species in each group.
#> ✔ Finished data preparation.
#> G L H .x .y p1 p2 p3 p4 p5 p6 p7
#> 1 0 1.0000000 0.000000000 0.000000000 0 0 0 0 0 0 0.5000000 0.5000000
#> 2 0 0.9949749 0.005025126 0.005025126 0 0 0 0 0 0 0.4974874 0.4974874
#> 3 0 0.9899497 0.010050251 0.010050251 0 0 0 0 0 0 0.4949749 0.4949749
#> 4 0 0.9849246 0.015075377 0.015075377 0 0 0 0 0 0 0.4924623 0.4924623
#> 5 0 0.9798995 0.020100503 0.020100503 0 0 0 0 0 0 0.4899497 0.4899497
#> 6 0 0.9748744 0.025125628 0.025125628 0 0 0 0 0 0 0.4874372 0.4874372
#> p8 p9 .Pred
#> 1 0.000000000 0.000000000 7.493868
#> 2 0.002512563 0.002512563 7.517016
#> 3 0.005025126 0.005025126 7.540053
#> 4 0.007537688 0.007537688 7.562977
#> 5 0.010050251 0.010050251 7.585788
#> 6 0.012562814 0.012562814 7.608488
## By default the variables within a group take up an equal share of the
## group proportion. So for example, each point along the above ternary
## would have a 50:50 split of the variables in the group "L" or "H", thus
## the vertex where "L" is 1, would mean that p6 and p7 are 0.5 each,
## similarly, the vertex "H" is made up of 0.5 of p8 and p9 while the "G"
## vertex is comprised of 0.2 of each of p1, p2, p3, p4, and p5. The concepts
## also extend to points along the edges and interior of the ternary.
## Change the proportional split of species within an FG by using `values`
## `values` takes a numeric vector where the position of each element
## describes the proportion of the corresponding species within the
## corresponding FG
## For examples this vector describes, 2-% each of p1, p2, p3, p4 and p5,
## in G, 0% and 100% of p6 and p7, respectively in G2 and 30% and 70% of
## p8 and p9, respectively in G3.
vals <- c(0.2, 0.2, 0.2, 0.2, 0.2,
0, 1,
0.3, 0.7)
head(grouped_ternary_data(prop = paste0("p", 1:9),
FG = c("G","G","G","G","G","L","L","H","H"),
values = vals,
resolution = 1,
model = mod))
#> ✔ Finished data preparation.
#> G L H .x .y p1 p2 p3 p4 p5 p6 p7
#> 1 0 1.0000000 0.000000000 0.000000000 0 0 0 0 0 0 0 1.0000000
#> 2 0 0.9949749 0.005025126 0.005025126 0 0 0 0 0 0 0 0.9949749
#> 3 0 0.9899497 0.010050251 0.010050251 0 0 0 0 0 0 0 0.9899497
#> 4 0 0.9849246 0.015075377 0.015075377 0 0 0 0 0 0 0 0.9849246
#> 5 0 0.9798995 0.020100503 0.020100503 0 0 0 0 0 0 0 0.9798995
#> 6 0 0.9748744 0.025125628 0.025125628 0 0 0 0 0 0 0 0.9748744
#> p8 p9 .Pred
#> 1 0.000000000 0.000000000 7.110611
#> 2 0.001507538 0.003517588 7.135017
#> 3 0.003015075 0.007035176 7.159316
#> 4 0.004522613 0.010552764 7.183509
#> 5 0.006030151 0.014070352 7.207595
#> 6 0.007537688 0.017587940 7.231576
## Can also add any additional experimental structures
## Notice .add_str_ID in the data
head(grouped_ternary_data(prop = paste0("p", 1:9),
FG = c("G","G","G","G","G","L","L","H","H"),
add_var = list("treatment" = c("50", "150")),
values = vals,
model = mod,
resolution = 1))
#> ✔ Finished data preparation.
#> G L H .x .y p1 p2 p3 p4 p5 p6 p7
#> 1 0 1.0000000 0.000000000 0.000000000 0 0 0 0 0 0 0 1.0000000
#> 2 0 0.9949749 0.005025126 0.005025126 0 0 0 0 0 0 0 0.9949749
#> 3 0 0.9899497 0.010050251 0.010050251 0 0 0 0 0 0 0 0.9899497
#> 4 0 0.9849246 0.015075377 0.015075377 0 0 0 0 0 0 0 0.9849246
#> 5 0 0.9798995 0.020100503 0.020100503 0 0 0 0 0 0 0 0.9798995
#> 6 0 0.9748744 0.025125628 0.025125628 0 0 0 0 0 0 0 0.9748744
#> p8 p9 treatment .add_str_ID .Pred
#> 1 0.000000000 0.000000000 50 treatment: 50 7.110611
#> 2 0.001507538 0.003517588 50 treatment: 50 7.135017
#> 3 0.003015075 0.007035176 50 treatment: 50 7.159316
#> 4 0.004522613 0.010552764 50 treatment: 50 7.183509
#> 5 0.006030151 0.014070352 50 treatment: 50 7.207595
#> 6 0.007537688 0.017587940 50 treatment: 50 7.231576
## It could be desirable to take the output of this function and add
## additional variables to the data before making predictions
## Use `prediction = FALSE` to get data without any predictions
grouped_data <- grouped_ternary_data(prop = paste0("p", 1:9),
FG = c("G","G","G","G","G","L","L","H","H"),
values = vals,
resolution = 1,
prediction = FALSE)
#> ✔ Finished data preparation.
grouped_data$treatment <- 250
# Add predictions
head(add_prediction(data = grouped_data, model = mod))
#> G L H .x .y p1 p2 p3 p4 p5 p6 p7
#> 1 0 1.0000000 0.000000000 0.000000000 0 0 0 0 0 0 0 1.0000000
#> 2 0 0.9949749 0.005025126 0.005025126 0 0 0 0 0 0 0 0.9949749
#> 3 0 0.9899497 0.010050251 0.010050251 0 0 0 0 0 0 0 0.9899497
#> 4 0 0.9849246 0.015075377 0.015075377 0 0 0 0 0 0 0 0.9849246
#> 5 0 0.9798995 0.020100503 0.020100503 0 0 0 0 0 0 0 0.9798995
#> 6 0 0.9748744 0.025125628 0.025125628 0 0 0 0 0 0 0 0.9748744
#> p8 p9 treatment .Pred
#> 1 0.000000000 0.000000000 250 7.110611
#> 2 0.001507538 0.003517588 250 7.135017
#> 3 0.003015075 0.007035176 250 7.159316
#> 4 0.004522613 0.010552764 250 7.183509
#> 5 0.006030151 0.014070352 250 7.207595
#> 6 0.007537688 0.017587940 250 7.231576