MixedModelsSim

This package provides some utility functions for generating experimental designs, especially those with crossed factors.

Installation

MixedModelsSim is registered in the Julia package registry and can be installed via the pkg REPL:

(@v1.5) pkg> add MixedModelsSim

Purpose

This package provides functions to facilitate generating experimental designs, especially designs with crossed grouping factors such as "Subject" and "Item" in addition to experimental factors. The experimental factors can be within-subject or within-item or between-subject and between-item.

This package uses structures from the Tables package. In particular, a data table can be viewed as a rowtable, which is a vector of NamedTuples, or a columntable which is a NamedTuple of vectors (or something similar).

For those with experience in R just think of a NamedTuple as being like R's list type. It's an ordered, named collection.

Changes in v0.2

Version 0.2 brings extensive changes to the API, both to take better advantage of new features in MixedModels.jl 3.0 and to eliminate the direct dependency on DataFrames.jl.

• There is now extensive use of row tables instead of DataFrames.
• simulate_waldtests has been removed. This functionality is now provided by the coefpvalues property provided of MixedModelBootstrap.
• Similarly, sim_to_df has been removed because DataFrame(bootstrapsim.coefpvalues) provides the same content.

Examples

To create a design with each of five subjects, three old and two young, tested on each of three items, first create the subject table

julia> using MixedModelsSim, DataFrames, Tables
julia> subject = (subj = ["S1","S2","S3","S4","S5"], age=["O","O","O","Y","Y"]);
julia> typeof(subject)
NamedTuple{(:subj, :age),Tuple{Array{String,1},Array{String,1}}}

julia> rowtable(subject)
5-element Array{NamedTuple{(:subj, :age),Tuple{String,String}},1}:
 (subj = "S1", age = "O")
 (subj = "S2", age = "O")
 (subj = "S3", age = "O")
 (subj = "S4", age = "Y")
 (subj = "S5", age = "Y")

then create the design as the product of an item table (defined inline here) and the subject table

julia> design = factorproduct((item = ["I1","I2","I3"],), subject)
15-element Array{NamedTuple{(:item, :subj, :age),Tuple{String,String,String}},1}:
(item = "I1", subj = "S1", age = "O")
(item = "I2", subj = "S1", age = "O")
(item = "I3", subj = "S1", age = "O")
(item = "I1", subj = "S2", age = "O")
(item = "I2", subj = "S2", age = "O")
(item = "I3", subj = "S2", age = "O")
(item = "I1", subj = "S3", age = "O")
(item = "I2", subj = "S3", age = "O")
(item = "I3", subj = "S3", age = "O")
(item = "I1", subj = "S4", age = "Y")
(item = "I2", subj = "S4", age = "Y")
(item = "I3", subj = "S4", age = "Y")
(item = "I1", subj = "S5", age = "Y")
(item = "I2", subj = "S5", age = "Y")
(item = "I3", subj = "S5", age = "Y")

The design can be converted to a DataFrame and the strings pooled to save storage.

julia> design |> DataFrame |> pooled!
15×3 DataFrame
│ Row │ item   │ subj   │ age    │
│     │ String │ String │ String │
├─────┼────────┼────────┼────────┤
│ 1   │ I1     │ S1     │ O      │
│ 2   │ I2     │ S1     │ O      │
│ 3   │ I3     │ S1     │ O      │
│ 4   │ I1     │ S2     │ O      │
│ 5   │ I2     │ S2     │ O      │
│ 6   │ I3     │ S2     │ O      │
│ 7   │ I1     │ S3     │ O      │
│ 8   │ I2     │ S3     │ O      │
│ 9   │ I3     │ S3     │ O      │
│ 10  │ I1     │ S4     │ Y      │
│ 11  │ I2     │ S4     │ Y      │
│ 12  │ I3     │ S4     │ Y      │
│ 13  │ I1     │ S5     │ Y      │
│ 14  │ I2     │ S5     │ Y      │
│ 15  │ I3     │ S5     │ Y      │

julia> describe(ans)
3×8 DataFrame
│ Row │ variable │ mean    │ min    │ median  │ max    │ nunique │ nmissing │ eltype   │
│     │ Symbol   │ Nothing │ String │ Nothing │ String │ Int64   │ Nothing  │ DataType │
├─────┼──────────┼─────────┼────────┼─────────┼────────┼─────────┼──────────┼──────────┤
│ 1   │ item     │         │ I1     │         │ I3     │ 3       │          │ String   │
│ 2   │ subj     │         │ S1     │         │ S5     │ 5       │          │ String   │
│ 3   │ age      │         │ O      │         │ Y      │ 2       │          │ String   │

Background on tables and tuples

In Julia tuples are created by listing the contents, surrounded by parentheses and separated by commas.

julia> Tables.istable(subject)
true

julia> Tables.schema(subject)
Tables.Schema:
 :subj  String
 :age   String

 julia> DataFrame(subject)
 5×2 DataFrame
 │ Row │ subj   │ age    │
 │     │ String │ String │
 ├─────┼────────┼────────┤
 │ 1   │ S1     │ Y      │
 │ 2   │ S2     │ Y      │
 │ 3   │ S3     │ Y      │
 │ 4   │ S4     │ O      │
 │ 5   │ S5     │ O      │

The curiously trailing comma

To distinguish creating a named tuple of length 1 from an assignment with parentheses around it a comma is required after the first named element. To create an item table with only three item identifiers, the expression must be written

julia> items = (item = ["I1", "I2", "I3"],)
(item = ["I1", "I2", "I3"],)

with that curiously trailing comma. In general, trailing commas are allowed in the creation of tuples or in argument lists but in this case the trailing comma is mandatory.

Generating factors with n levels

The nlevels utility function can be used to generate a vector of length n with a given tag. For example, the vector of subject levels can be generated as

julia> show(nlevels(5, 'S'))
["S1", "S2", "S3", "S4", "S5"]

The default tag is S so this sequence could be generated more simply as

julia> show(nlevels(5))
["S1", "S2", "S3", "S4", "S5"]

Acknowledgements

The development of this package was supported by the Center for Interdisciplinary Research, Bielefeld (ZiF) Cooperation Group "Statistical models for psychological and linguistic data".