Java tutorial
/* * Copyright 2012 J. Patrick Meyer * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ package com.itemanalysis.psychometrics.irt.equating; import com.itemanalysis.psychometrics.irt.model.*; import org.apache.commons.math3.stat.descriptive.moment.Mean; import org.apache.commons.math3.stat.descriptive.moment.StandardDeviation; import org.apache.commons.math3.util.Precision; import org.junit.Test; import java.util.LinkedHashMap; import static junit.framework.Assert.assertEquals; public class MeanSigmaMethodTest { @Test public void meanSigmaTest3PL() { System.out.println("Mean Sigma Test 3PL"); double[] aX = { 0.455118, 0.583871, 0.754398, 0.663274, 1.068977, 0.967194, 0.347868, 1.457918, 0.701952, 1.407967, 1.299285 }; double[] bX = { -0.710086, -0.856669, 0.021221, 0.050618, 0.961047, 0.194976, 2.276794, 1.024128, 2.240131, 1.555634, 2.158933 }; double[] cX = { 0.208748, 0.203834, 0.159961, 0.123961, 0.298628, 0.053538, 0.148927, 0.24527, 0.08529, 0.078897, 0.10753 }; double[] aY = { 0.441595, 0.572995, 0.598719, 0.604125, 0.990164, 0.808079, 0.413973, 1.355437, 0.633562, 1.134661, 0.925521 }; double[] bY = { -1.334933, -1.321004, -0.709831, -0.353942, 0.531956, -0.115649, 2.553812, 0.581109, 1.896027, 1.079013, 2.133706 }; double[] cY = { 0.155883, 0.191298, 0.117663, 0.081759, 0.302443, 0.064791, 0.240967, 0.224322, 0.079396, 0.063009, 0.125873 }; int n = aX.length; LinkedHashMap<String, ItemResponseModel> irmX = new LinkedHashMap<String, ItemResponseModel>(); LinkedHashMap<String, ItemResponseModel> irmY = new LinkedHashMap<String, ItemResponseModel>(); ItemResponseModel irm; for (int i = 0; i < n; i++) { String name = "V" + i; irm = new Irm3PL(aX[i], bX[i], cX[i], 1.0); irmX.put(name, irm); irm = new Irm3PL(aY[i], bY[i], cY[i], 1.0); irmY.put(name, irm); } MeanSigmaMethod ms = new MeanSigmaMethod(irmX, irmY, true); ms.setPrecision(4); assertEquals(" Intercept test", -0.5042, ms.getIntercept(), 1e-4); assertEquals(" Scale test", 1.1761, ms.getScale(), 1e-4); } /** * Tests the calculations needed for mean/mean and mean/sigma scale linking. * Item parameters and true values obtained from example 2 from the STUIRT * program by Michael Kolen and colleagues. Note that the original example * used teh PARSCALE version of item parameters. These were converted to * ICL type parameters by subtracting a step from the item difficulty. * */ @Test public void mixedFormatDescriptiveStatisticsTestFormX() { System.out.println("Mixed format descriptive statistics test Form X"); ItemResponseModel[] irm = new ItemResponseModel[17]; irm[0] = new Irm3PL(0.751335, -0.897391, 0.244001, 1.7); irm[1] = new Irm3PL(0.955947, -0.811477, 0.242883, 1.7); irm[2] = new Irm3PL(0.497206, -0.858681, 0.260893, 1.7); irm[3] = new Irm3PL(0.724000, -0.123911, 0.243497, 1.7); irm[4] = new Irm3PL(0.865200, 0.205889, 0.319135, 1.7); irm[5] = new Irm3PL(0.658129, 0.555228, 0.277826, 1.7); irm[6] = new Irm3PL(1.082118, 0.950549, 0.157979, 1.7); irm[7] = new Irm3PL(0.988294, 1.377501, 0.084828, 1.7); irm[8] = new Irm3PL(1.248923, 1.614355, 0.181874, 1.7); irm[9] = new Irm3PL(1.116682, 2.353932, 0.246856, 1.7); irm[10] = new Irm3PL(0.438171, 3.217965, 0.309243, 1.7); irm[11] = new Irm3PL(1.082206, 4.441864, 0.192339, 1.7); double[] step1 = { 0, -1.09327, 1.101266 }; irm[12] = new IrmGPCM(0.269994, step1, 1.7); double[] step2 = { 0, 1.526148, 1.739176 }; irm[13] = new IrmGPCM(0.972506, step2, 1.7); double[] step3 = { 0, 1.362356, 5.566958 }; irm[14] = new IrmGPCM(0.378812, step3, 1.7); double[] step4 = { 0, 1.486566, -0.071229, 1.614823 }; irm[15] = new IrmGPCM(0.537706, step4, 1.7); double[] step5 = { 0, 1.425413, 2.630705, 3.242696 }; irm[16] = new IrmGPCM(0.554506, step5, 1.7); Mean discriminationX = new Mean(); Mean difficultyX = new Mean(); Mean difficultyMeanX = new Mean(); StandardDeviation difficultySdX = new StandardDeviation(false);//Do not correct for bias. Use N in the denominator, not N-1. for (int j = 0; j < 17; j++) { irm[j].incrementMeanMean(discriminationX, difficultyX); irm[j].incrementMeanSigma(difficultyMeanX, difficultySdX); } // System.out.println("Mean/mean descriptive statistics for Form X"); // System.out.println("a-mean: " + discriminationX.getResult()); // System.out.println("b-mean: " + difficultyX.getResult()); assertEquals("Mean/mean check: discrimination mean", 0.7719, Precision.round(discriminationX.getResult(), 4), 1e-5); assertEquals("Mean/mean check: difficulty mean", 1.3566, Precision.round(difficultyX.getResult(), 4), 1e-5); assertEquals("Mean/mean check: Number of difficulties (including steps) ", 24, difficultyX.getN(), 1e-3); // System.out.println(); // System.out.println("Mean/sigma descriptive statistics for Form X"); // System.out.println("b-mean: " + difficultyMeanX.getResult()); // System.out.println("b-sd: " + difficultySdX.getResult()); // System.out.println("b-N: " + difficultyMeanX.getN() + ", " + difficultySdX.getN()); assertEquals("Mean/sigma check: difficulty mean", 1.3566, Precision.round(difficultyMeanX.getResult(), 4), 1e-5); assertEquals("Mean/sigma check: difficulty sd", 1.6372, Precision.round(difficultySdX.getResult(), 4), 1e-5); assertEquals("Mean/sigma check: Number of difficulties (including steps) ", 24, difficultyMeanX.getN(), 1e-3); assertEquals("Mean/sigma check: Number of difficulties (including steps) ", 24, difficultySdX.getN(), 1e-3); } /** * Tests the calculations needed for mean/mean and mean/sigma scale linking. * Item parameters and true values obtained from example 2 from the STUIRT * program by Michael Kolen and colleagues. Note that the original example * used teh PARSCALE version of item parameters. These were converted to * ICL type parameters by subtracting a step from the item difficulty. * */ @Test public void mixedFormatDescriptiveStatisticsTestFormY() { System.out.println("Mixed format descriptive statistics test Form Y"); ItemResponseModel[] irm = new ItemResponseModel[17]; irm[0] = new Irm3PL(0.887276, -1.334798, 0.134406, 1.7); irm[1] = new Irm3PL(1.184412, -1.129004, 0.237765, 1.7); irm[2] = new Irm3PL(0.609412, -1.464546, 0.15139, 1.7); irm[3] = new Irm3PL(0.923812, -0.576435, 0.240097, 1.7); irm[4] = new Irm3PL(0.822776, -0.476357, 0.192369, 1.7); irm[5] = new Irm3PL(0.707818, -0.235189, 0.189557, 1.7); irm[6] = new Irm3PL(1.306976, 0.242986, 0.165553, 1.7); irm[7] = new Irm3PL(1.295471, 0.598029, 0.090557, 1.7); irm[8] = new Irm3PL(1.366841, 0.923206, 0.172993, 1.7); irm[9] = new Irm3PL(1.389624, 1.380666, 0.238008, 1.7); irm[10] = new Irm3PL(0.293806, 2.02807, 0.203448, 1.7); irm[11] = new Irm3PL(0.885347, 3.152928, 0.195473, 1.7); double[] step1 = { 0, -1.387347, 0.399117 }; irm[12] = new IrmGPCM(0.346324, step1, 1.7); double[] step2 = { 0, 0.756514, 0.956014 }; irm[13] = new IrmGPCM(1.252012, step2, 1.7); double[] step3 = { 0, 0.975303, 4.676299 }; irm[14] = new IrmGPCM(0.392282, step3, 1.7); double[] step4 = { 0, 0.643405, -0.418869, 0.804394 }; irm[15] = new IrmGPCM(0.660841, step4, 1.7); double[] step5 = { 0, 0.641293, 1.750488, 2.53802 }; irm[16] = new IrmGPCM(0.669612, step5, 1.7); Mean discriminationX = new Mean(); Mean difficultyX = new Mean(); Mean difficultyMeanX = new Mean(); StandardDeviation difficultySdX = new StandardDeviation(false);//Do not correct for bias. Use N in the denominator, not N-1. for (int j = 0; j < 17; j++) { irm[j].incrementMeanMean(discriminationX, difficultyX); irm[j].incrementMeanSigma(difficultyMeanX, difficultySdX); } // System.out.println("Mean/mean descriptive statistics for Form X"); // System.out.println("a-mean: " + discriminationX.getResult()); // System.out.println("b-mean: " + difficultyX.getResult()); assertEquals("Mean/mean check: discrimination mean", 0.8820, Precision.round(discriminationX.getResult(), 4), 1e-5); assertEquals("Mean/mean check: difficulty mean", 0.6435, Precision.round(difficultyX.getResult(), 4), 1e-5); assertEquals("Mean/mean check: Number of difficulties (including steps) ", 24, difficultyX.getN(), 1e-3); // System.out.println(); // System.out.println("Mean/sigma descriptive statistics for Form X"); // System.out.println("b-mean: " + difficultyMeanX.getResult()); // System.out.println("b-sd: " + difficultySdX.getResult()); // System.out.println("b-N: " + difficultyMeanX.getN() + ", " + difficultySdX.getN()); assertEquals("Mean/sigma check: difficulty mean", 0.6435, Precision.round(difficultyMeanX.getResult(), 4), 1e-5); assertEquals("Mean/sigma check: difficulty sd", 1.4527, Precision.round(difficultySdX.getResult(), 4), 1e-5); assertEquals("Mean/sigma check: Number of difficulties (including steps) ", 24, difficultyMeanX.getN(), 1e-3); assertEquals("Mean/sigma check: Number of difficulties (including steps) ", 24, difficultySdX.getN(), 1e-3); } /** * Tests the calculations needed for mean/mean and mean/sigma scale linking. * Item parameters and true values obtained from example 2 from the STUIRT * program by Michael Kolen and colleagues. Note that the original example * used teh PARSCALE version of item parameters. These were converted to * ICL type parameters by subtracting a step from the item difficulty. * */ @Test public void mixedFormatMeanSigmaTest() { System.out.println("Mixed format mean/sigma test"); LinkedHashMap<String, ItemResponseModel> itemFormX = new LinkedHashMap<String, ItemResponseModel>(); LinkedHashMap<String, ItemResponseModel> itemFormY = new LinkedHashMap<String, ItemResponseModel>(); itemFormX.put("Item1", new Irm3PL(0.751335, -0.897391, 0.244001, 1.7)); itemFormX.put("Item2", new Irm3PL(0.955947, -0.811477, 0.242883, 1.7)); itemFormX.put("Item3", new Irm3PL(0.497206, -0.858681, 0.260893, 1.7)); itemFormX.put("Item4", new Irm3PL(0.724000, -0.123911, 0.243497, 1.7)); itemFormX.put("Item5", new Irm3PL(0.865200, 0.205889, 0.319135, 1.7)); itemFormX.put("Item6", new Irm3PL(0.658129, 0.555228, 0.277826, 1.7)); itemFormX.put("Item7", new Irm3PL(1.082118, 0.950549, 0.157979, 1.7)); itemFormX.put("Item8", new Irm3PL(0.988294, 1.377501, 0.084828, 1.7)); itemFormX.put("Item9", new Irm3PL(1.248923, 1.614355, 0.181874, 1.7)); itemFormX.put("Item10", new Irm3PL(1.116682, 2.353932, 0.246856, 1.7)); itemFormX.put("Item11", new Irm3PL(0.438171, 3.217965, 0.309243, 1.7)); itemFormX.put("Item12", new Irm3PL(1.082206, 4.441864, 0.192339, 1.7)); double[] step1 = { 0, -1.09327, 1.101266 }; itemFormX.put("Item13", new IrmGPCM(0.269994, step1, 1.7)); double[] step2 = { 0, 1.526148, 1.739176 }; itemFormX.put("Item14", new IrmGPCM(0.972506, step2, 1.7)); double[] step3 = { 0, 1.362356, 5.566958 }; itemFormX.put("Item15", new IrmGPCM(0.378812, step3, 1.7)); double[] step4 = { 0, 1.486566, -0.071229, 1.614823 }; itemFormX.put("Item16", new IrmGPCM(0.537706, step4, 1.7)); double[] step5 = { 0, 1.425413, 2.630705, 3.242696 }; itemFormX.put("Item17", new IrmGPCM(0.554506, step5, 1.7)); itemFormY.put("Item1", new Irm3PL(0.887276, -1.334798, 0.134406, 1.7)); itemFormY.put("Item2", new Irm3PL(1.184412, -1.129004, 0.237765, 1.7)); itemFormY.put("Item3", new Irm3PL(0.609412, -1.464546, 0.15139, 1.7)); itemFormY.put("Item4", new Irm3PL(0.923812, -0.576435, 0.240097, 1.7)); itemFormY.put("Item5", new Irm3PL(0.822776, -0.476357, 0.192369, 1.7)); itemFormY.put("Item6", new Irm3PL(0.707818, -0.235189, 0.189557, 1.7)); itemFormY.put("Item7", new Irm3PL(1.306976, 0.242986, 0.165553, 1.7)); itemFormY.put("Item8", new Irm3PL(1.295471, 0.598029, 0.090557, 1.7)); itemFormY.put("Item9", new Irm3PL(1.366841, 0.923206, 0.172993, 1.7)); itemFormY.put("Item10", new Irm3PL(1.389624, 1.380666, 0.238008, 1.7)); itemFormY.put("Item11", new Irm3PL(0.293806, 2.02807, 0.203448, 1.7)); itemFormY.put("Item12", new Irm3PL(0.885347, 3.152928, 0.195473, 1.7)); double[] step1y = { 0, -1.387347, 0.399117 }; itemFormY.put("Item13", new IrmGPCM(0.346324, step1y, 1.7)); double[] step2y = { 0, 0.756514, 0.956014 }; itemFormY.put("Item14", new IrmGPCM(1.252012, step2y, 1.7)); double[] step3y = { 0, 0.975303, 4.676299 }; itemFormY.put("Item15", new IrmGPCM(0.392282, step3y, 1.7)); double[] step4y = { 0, 0.643405, -0.418869, 0.804394 }; itemFormY.put("Item16", new IrmGPCM(0.660841, step4y, 1.7)); double[] step5y = { 0, 0.641293, 1.750488, 2.53802 }; itemFormY.put("Item17", new IrmGPCM(0.669612, step5y, 1.7)); MeanSigmaMethod meanSigmaMethod = new MeanSigmaMethod(itemFormX, itemFormY, true); meanSigmaMethod.setPrecision(6); double B = meanSigmaMethod.getIntercept(); double A = meanSigmaMethod.getScale(); // System.out.println("Slope: " + A); // System.out.println("Intercept: " + B); assertEquals("Mean/sigma slope test", 0.887294, A, 1e-6); assertEquals("Mean/sigma intercept test", -0.560159, B, 1e-6); } @Test public void mixedFormatMeanSigmaTestPARSCALE() { System.out.println("Mixed format mean/sigma test: Parscale parameters"); LinkedHashMap<String, ItemResponseModel> itemFormX = new LinkedHashMap<String, ItemResponseModel>(); LinkedHashMap<String, ItemResponseModel> itemFormY = new LinkedHashMap<String, ItemResponseModel>(); itemFormX.put("Item1", new Irm3PL(0.751335, -0.897391, 0.244001, 1.7)); itemFormX.put("Item2", new Irm3PL(0.955947, -0.811477, 0.242883, 1.7)); itemFormX.put("Item3", new Irm3PL(0.497206, -0.858681, 0.260893, 1.7)); itemFormX.put("Item4", new Irm3PL(0.724000, -0.123911, 0.243497, 1.7)); itemFormX.put("Item5", new Irm3PL(0.865200, 0.205889, 0.319135, 1.7)); itemFormX.put("Item6", new Irm3PL(0.658129, 0.555228, 0.277826, 1.7)); itemFormX.put("Item7", new Irm3PL(1.082118, 0.950549, 0.157979, 1.7)); itemFormX.put("Item8", new Irm3PL(0.988294, 1.377501, 0.084828, 1.7)); itemFormX.put("Item9", new Irm3PL(1.248923, 1.614355, 0.181874, 1.7)); itemFormX.put("Item10", new Irm3PL(1.116682, 2.353932, 0.246856, 1.7)); itemFormX.put("Item11", new Irm3PL(0.438171, 3.217965, 0.309243, 1.7)); itemFormX.put("Item12", new Irm3PL(1.082206, 4.441864, 0.192339, 1.7)); double[] step1 = { 1.097268, -1.097268 }; itemFormX.put("Item13", new IrmGPCM2(0.269994, 0.003998, step1, 1.7)); double[] step2 = { 0.106514, -0.106514 }; itemFormX.put("Item14", new IrmGPCM2(0.972506, 1.632662, step2, 1.7)); double[] step3 = { 2.102301, -2.102301 }; itemFormX.put("Item15", new IrmGPCM2(0.378812, 3.464657, step3, 1.7)); double[] step4 = { -0.476513, 1.081282, -0.604770 }; itemFormX.put("Item16", new IrmGPCM2(0.537706, 1.010053, step4, 1.7)); double[] step5 = { 1.00752, -0.197767, -0.809758 }; itemFormX.put("Item17", new IrmGPCM2(0.554506, 2.432938, step5, 1.7)); itemFormY.put("Item1", new Irm3PL(0.887276, -1.334798, 0.134406, 1.7)); itemFormY.put("Item2", new Irm3PL(1.184412, -1.129004, 0.237765, 1.7)); itemFormY.put("Item3", new Irm3PL(0.609412, -1.464546, 0.15139, 1.7)); itemFormY.put("Item4", new Irm3PL(0.923812, -0.576435, 0.240097, 1.7)); itemFormY.put("Item5", new Irm3PL(0.822776, -0.476357, 0.192369, 1.7)); itemFormY.put("Item6", new Irm3PL(0.707818, -0.235189, 0.189557, 1.7)); itemFormY.put("Item7", new Irm3PL(1.306976, 0.242986, 0.165553, 1.7)); itemFormY.put("Item8", new Irm3PL(1.295471, 0.598029, 0.090557, 1.7)); itemFormY.put("Item9", new Irm3PL(1.366841, 0.923206, 0.172993, 1.7)); itemFormY.put("Item10", new Irm3PL(1.389624, 1.380666, 0.238008, 1.7)); itemFormY.put("Item11", new Irm3PL(0.293806, 2.02807, 0.203448, 1.7)); itemFormY.put("Item12", new Irm3PL(0.885347, 3.152928, 0.195473, 1.7)); double[] step1y = { 0.893232, -0.893232 }; itemFormY.put("Item13", new IrmGPCM2(0.346324, -0.494115, step1y, 1.7)); double[] step2y = { 0.099750, -0.099750 }; itemFormY.put("Item14", new IrmGPCM2(1.252012, 0.856264, step2y, 1.7)); double[] step3y = { 1.850498, -1.850498 }; itemFormY.put("Item15", new IrmGPCM2(0.392282, 2.825801, step3y, 1.7)); double[] step4y = { -0.300428, 0.761846, -0.461417 }; itemFormY.put("Item16", new IrmGPCM2(0.660841, 0.342977, step4y, 1.7)); double[] step5y = { 1.001974, -0.107221, -0.894753 }; itemFormY.put("Item17", new IrmGPCM2(0.669612, 1.643267, step5y, 1.7)); MeanSigmaMethod meanSigmaMethod = new MeanSigmaMethod(itemFormX, itemFormY, true); meanSigmaMethod.setPrecision(6); double B = meanSigmaMethod.getIntercept(); double A = meanSigmaMethod.getScale(); // System.out.println("Slope: " + A); // System.out.println("Intercept: " + B); assertEquals("Mean/sigma slope test", 0.887294, A, 1e-6); assertEquals("Mean/sigma intercept test", -0.560159, B, 1e-6); } @Test public void mixedFormtRaschPCMTest() { System.out.println("Mixed format mean/sigma test: Rasch and PCM"); LinkedHashMap<String, ItemResponseModel> itemFormX = new LinkedHashMap<String, ItemResponseModel>(); LinkedHashMap<String, ItemResponseModel> itemFormY = new LinkedHashMap<String, ItemResponseModel>(); itemFormX.put("Item1", new Irm3PL(1.0, -3.188047976, 0.0, 1.7)); itemFormX.put("Item2", new Irm3PL(1.0, 1.031760328, 0.0, 1.7)); itemFormX.put("Item3", new Irm3PL(1.0, 0.819040914, 0.0, 1.7)); itemFormX.put("Item4", new Irm3PL(1.0, -2.706947360, 0.0, 1.7)); itemFormX.put("Item5", new Irm3PL(1.0, -0.094527077, 0.0, 1.7)); itemFormX.put("Item6", new Irm3PL(1.0, 0.689697135, 0.0, 1.7)); itemFormX.put("Item7", new Irm3PL(1.0, -0.551837153, 0.0, 1.7)); itemFormX.put("Item8", new Irm3PL(1.0, -0.359559276, 0.0, 1.7)); double[] step1x = { -0.146619694, -0.636399040, 0.783018734 }; itemFormX.put("Item9", new IrmPCM(-1.451470831, step1x, 1.0)); itemFormY.put("Item1", new Irm3PL(1.0, -3.074599226, 0.0, 1.7)); itemFormY.put("Item2", new Irm3PL(1.0, 1.012824350, 0.0, 1.7)); itemFormY.put("Item3", new Irm3PL(1.0, 0.868538408, 0.0, 1.7)); itemFormY.put("Item4", new Irm3PL(1.0, -2.404483603, 0.0, 1.7)); itemFormY.put("Item5", new Irm3PL(1.0, 0.037402866, 0.0, 1.7)); itemFormY.put("Item6", new Irm3PL(1.0, 0.700747420, 0.0, 1.7)); itemFormY.put("Item7", new Irm3PL(1.0, -0.602555046, 0.0, 1.7)); itemFormY.put("Item8", new Irm3PL(1.0, -0.350426446, 0.0, 1.7)); double[] step1y = { -0.185885988, -0.61535623, 0.801242218 }; itemFormY.put("Item9", new IrmPCM(-1.267744832, step1y, 1.0)); MeanSigmaMethod meanSigmaMethod = new MeanSigmaMethod(itemFormX, itemFormY, true); meanSigmaMethod.setPrecision(6); double B = meanSigmaMethod.getIntercept(); double A = meanSigmaMethod.getScale(); // System.out.println("Slope: " + A); // System.out.println("Intercept: " + B); assertEquals("Mean/sigma slope test", 0.950133, A, 1e-6); assertEquals("Mean/sigma intercept test", 0.060406, B, 1e-6); } }