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equate.jl's Introduction

Equate

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Equate test scores under the equivalent or non-equivalent group with anchor test design.

Supported methods

  • SG (Single Group design)

    • Linear
    • Mean
    • Equipercentile

  • NEAT (Non-Equivalent group design with Anchor Test design)

    • Tucker (Linear equating under some assumptions)
    • Braun & Holland (Linear equating using synthetic population)
    • Chained Linear (also Mean)
    • Chained Equipercentile
    • Frequency Estimation (Equipercentile equating using synthetic population)

  • Presmoothing

    • Log linear smoothing with an arbitrary degree.

  • Kernel smoothong

    • Gaussian kernel is only supported now.
    • The optimal bandwidth can be estimated.

Example1: SG design.

  1. Prepare data set. Integer or Float vector.
using Distributions, Random
Random.seed!(1234)
X = rand(BetaBinomial(100, 4, 10), 500);
Y = rand(BetaBinomial(100, 6, 10), 500);
  1. Convert the data vector to FreqTab
# `data` must be Real vector
julia> ftX = freqtab(X; scale = 0:1:100)
Frequency table stats.
         N :      500 
   Missing :        0 
       min :        1 
      maxs :       71 
         μ : 28.39000 
         σ : 12.68921 
  kurtosis : 0.00127 
  skewness : 0.52615 


julia> ftY = freqtab(Y; scale = 0:1:100)
Frequency table stats.
         N :      500 
   Missing :        0 
       min :        6 
      maxs :       77 
         μ : 37.04000 
         σ : 13.11115 
  kurtosis : -0.44152 
  skewness : 0.22442
  1. Presmoothing by using presmoothing
  2. (Optional) Continuization by using KernelSmoothing
  3. Equate score X to scale Y by the arbitrary method.
# Linear Equating
julia> eq_lin = Linear(ftX, ftY)
Equating design: EG
Equated method: Linear.
To show the table, extract `table` element.

# Equipercentile equating
julia> eq_eqp = Equipercentile(ftX, ftY)
Equating design: EG
Equated method: Equipercentile(lower).
To show the table, extract `table` element.
  1. Evaluate SEE (Standard Error of Equating). Now, Only BasicSampling(n) is supported.
julia> using Bootstrap, Random
julia> Random.seed!(1234)

julia> @time bootse_lin = bootstrap(x -> coef(Linear(x...)), eq_lin.data, BasicSampling(1000))
  1.727280 seconds (10.12 M allocations: 458.347 MiB, 5.56% gc time, 63.60% compilation time)
Bootstrap Sampling
  Estimates:
     Var │ Estimate  Bias         StdError
         │ Float64   Float64      Float64
    ─────┼─────────────────────────────────
       1 │  1.03325  0.000560431  0.043795
       2 │  7.70597  0.00756638   1.2771
  Sampling: BasicSampling
  Samples:  1000
  Data:     NamedTuple{(:X, :Y), Tuple{Equate.FreqTab, Equate.FreqTab}}: { X 500 × Y 500 }

equate.jl's People

Contributors

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Stargazers

Diego Javier Zea avatar

Watchers

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equate.jl's Issues

[Feature request] Return coefficient in the linear equating.

For now, the functions to linear equating (e.g. Linear() ) don't return equating coefficient and return only a concordance table.

So I propose to enhance these functions and related structs to be able to return coefficients too.

struct ResultLinear <: SGEquateMethod
    table::DataFrame
    coefficients::Tuples # (A = 1.0, K = 0.0)
end

Thanks.

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Handling missing values

For now, freqtab function cannot treat the vector which contains any missing value.

In general, the missing values in the data frame could be omitted before analyzing. However, for example, in single group design, assuming that one subject does not response to Test A but response Test B and we want to take the equivalent score A on scale B, we should choose methods to handle this missing as below.

  1. Remove records contains any missing from both tests and calculate moments or percentile.
  2. Preserve records on the test in which the subject responds at least. In other words, this method is removing missing values separately.

freqtab should be designed to be able to choose which method the user wants to use.

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