PersonParameters.jl

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Getting started ​

After successful installation you are ready to estimate person parameters. In this simple example we will estimate person parameters for a simulated data set assuming a Rasch model.

Simulating data ​

First, we need to aquire item parameters. In a Rasch model there is only a single item parameter, the item difficulty (b). Assuming a test with 10 items we therefore need 10 item difficulty parameters. For this example we draw these from a standard normal distribution.

julia
difficulties = randn(10)
10-element Vector{Float64}:
 -1.0404288511750712
  0.2146514070141379
 -0.3562695662666039
 -1.4314998994618426
 -0.499040165316529
 -0.07974473485930385
  0.40123961808781694
  0.793190395589391
  1.1926174603489277
  1.0964576513238238

Next, responses need to be simulated. Assuming 20 test-takers we simply randomly generate a response matrix where each test-taker responds to each item.

julia
responses = rand(20, 10) .> 0.5
20×10 BitMatrix:
 1  0  0  0  1  1  1  1  0  0
 1  0  1  0  0  0  0  0  1  1
 1  0  0  0  1  0  0  1  0  0
 0  1  0  0  0  1  0  1  1  0
 1  0  0  1  1  1  0  0  0  1
 1  0  1  0  1  0  0  0  1  1
 0  0  0  0  1  1  1  1  1  0
 1  0  1  0  0  1  1  1  1  0
 1  1  0  1  0  0  0  1  0  1
 1  1  0  1  0  1  1  1  1  0
 1  0  1  0  1  1  0  0  1  0
 1  0  0  1  0  1  0  1  1  0
 0  1  0  0  1  1  1  1  0  0
 0  1  1  1  0  0  1  1  0  0
 1  0  0  1  0  1  1  0  1  1
 1  0  0  1  1  0  0  0  0  1
 1  1  1  1  1  0  1  0  1  0
 1  1  1  0  0  0  0  1  0  0
 1  1  1  0  1  0  0  0  1  1
 1  0  1  0  0  0  1  1  1  0

Estimation of person parameters ​

Given the item parameters difficulties and response matrix responses, we are ready to estimate person parameters. To do this only a single call to person_parameters is required. person_parameters accepts 4 arguments: the model type M, some responses, item parameters betas and an estimation algorithm alg. For this example we chose simple maximum likelihood estimation using the MLE algorithm[1].

julia
using PersonParameters

pp = person_parameters(OnePL, responses, difficulties, MLE())
20-element PersonParameterResult{OneParameterLogisticModel, PersonParameter{Float64}, MLE{Roots.Secant}}:
 PersonParameter{Float64}(0.037961098910380374, 0.6828137955581843)
 PersonParameter{Float64}(-0.4347765337022231, 0.6964062194255234)
 PersonParameter{Float64}(-0.9459744421932545, 0.7393266417630334)
 PersonParameter{Float64}(-0.43477653370222313, 0.6964062194255234)
 PersonParameter{Float64}(0.037961098910380436, 0.6828137955581843)
 PersonParameter{Float64}(0.0379610989103803, 0.6828137955581843)
 PersonParameter{Float64}(0.037961098910380256, 0.6828137955581843)
 PersonParameter{Float64}(0.5086219559336693, 0.6934083716370472)
 PersonParameter{Float64}(0.03796109891038032, 0.6828137955581843)
 PersonParameter{Float64}(1.0135193279697836, 0.7335819408873576)
 PersonParameter{Float64}(0.037961098910380305, 0.6828137955581843)
 PersonParameter{Float64}(0.03796109891038044, 0.6828137955581843)
 PersonParameter{Float64}(0.037961098910380464, 0.6828137955581843)
 PersonParameter{Float64}(0.03796109891038037, 0.6828137955581843)
 PersonParameter{Float64}(0.5086219559336694, 0.6934083716370472)
 PersonParameter{Float64}(-0.43477653370222324, 0.6964062194255234)
 PersonParameter{Float64}(1.0135193279697836, 0.7335819408873576)
 PersonParameter{Float64}(-0.43477653370222313, 0.6964062194255234)
 PersonParameter{Float64}(0.5086219559336693, 0.6934083716370472)
 PersonParameter{Float64}(0.03796109891038041, 0.6828137955581843)

The resulting PersonParameterResult object contains the estimated person parameters for all 20 test-takers. The estimate of a single person can be obtained by indexing the pp object.

julia
pp17 = pp[17]
PersonParameter{Float64}(1.0135193279697836, 0.7335819408873576)

The PersonParameter object consists of the estimate and standard error of estimation for a single test-taker. To access the values you can use value and se respectivelty.

julia
value(pp17)
1.0135193279697836
julia
se(pp17)
0.7335819408873576

How to continue from here? ​

For specific use cases see one of our guides:

Or you can dive straight into the API Reference.

  1. For a full list of implemented algorithms see the API Reference. ↩︎