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<h1>Draw Plausible values</h1>
<small class="dont-index">Source: <a href='https://github.com/jansteinfeld/PP/blob/master/R/PV.R'><code>R/PV.R</code></a>, <a href='https://github.com/jansteinfeld/PP/blob/master/R/prints.R'><code>R/prints.R</code></a></small>
<div class="hidden name"><code>PV.Rd</code></div>
</div>
<div class="ref-description">
<p>This function draws <code>npv</code> plausible values for each person from their posterior density.</p>
</div>
<pre class="usage"><span class='fu'>PV</span><span class='op'>(</span><span class='va'>estobj</span>, <span class='va'>...</span><span class='op'>)</span>
<span class='co'># S3 method for fourpl</span>
<span class='fu'>PV</span><span class='op'>(</span><span class='va'>estobj</span>, npv <span class='op'>=</span> <span class='fl'>10</span>, approx <span class='op'>=</span> <span class='cn'>TRUE</span>, thinning <span class='op'>=</span> <span class='fl'>6</span>, burnin <span class='op'>=</span> <span class='fl'>10</span>, mult <span class='op'>=</span> <span class='fl'>2</span>, <span class='va'>...</span><span class='op'>)</span>
<span class='co'># S3 method for gpcm</span>
<span class='fu'>PV</span><span class='op'>(</span><span class='va'>estobj</span>, npv <span class='op'>=</span> <span class='fl'>10</span>, approx <span class='op'>=</span> <span class='cn'>TRUE</span>, thinning <span class='op'>=</span> <span class='fl'>6</span>, burnin <span class='op'>=</span> <span class='fl'>10</span>, mult <span class='op'>=</span> <span class='fl'>2</span>, <span class='va'>...</span><span class='op'>)</span>
<span class='co'># S3 method for gpcm4pl</span>
<span class='fu'>PV</span><span class='op'>(</span><span class='va'>estobj</span>, npv <span class='op'>=</span> <span class='fl'>10</span>, approx <span class='op'>=</span> <span class='cn'>TRUE</span>, thinning <span class='op'>=</span> <span class='fl'>6</span>, burnin <span class='op'>=</span> <span class='fl'>10</span>, mult <span class='op'>=</span> <span class='fl'>2</span>, <span class='va'>...</span><span class='op'>)</span>
<span class='co'># S3 method for pv</span>
<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='va'>x</span>, <span class='va'>...</span><span class='op'>)</span>
<span class='co'># S3 method for pv</span>
<span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span><span class='op'>(</span><span class='va'>object</span>, nrowmax <span class='op'>=</span> <span class='fl'>15</span>, <span class='va'>...</span><span class='op'>)</span></pre>
<h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
<table class="ref-arguments">
<colgroup><col class="name" /><col class="desc" /></colgroup>
<tr>
<th>estobj</th>
<td><p>An object which originates from using <code><a href='PP_4pl.html'>PP_4pl()</a></code>, <code><a href='PP_gpcm.html'>PP_gpcm()</a></code> or <code><a href='PPall.html'>PPall()</a></code>. EAP estimation is strongly recommended (<code>type = "eap"</code>), when plausible values are drawn afterwards, because the EAP estimate is used as starting point for the MH algorithm.</p></td>
</tr>
<tr>
<th>...</th>
<td><p>More arguments</p></td>
</tr>
<tr>
<th>npv</th>
<td><p>The number of (effectively returned) plausible values - default is 10.</p></td>
</tr>
<tr>
<th>approx</th>
<td><p>Whether a normal approximation <code>N(mu,sigma2)</code> is used to draw the plausible values. Default = TRUE. If FALSE a Metropolitan-Hastings-Algorithm will draw the values.</p></td>
</tr>
<tr>
<th>thinning</th>
<td><p>A numeric vector of length = 1. If approx = FALSE, a Metropolitan-Hastings-Algorithm draws the plausible values. To avoid autocorrelation, thinning takes every <b>kth</b> value as effective plausible value. The default is 6 (every 6th value is taken), which works appropriately in almost all cases here (with default settings).</p></td>
</tr>
<tr>
<th>burnin</th>
<td><p>How many draws should be discarded at the chains beginning? Default is 10 - and this seems reasonable high (probably 5 will be enough as well), because starting point is the EAP.</p></td>
</tr>
<tr>
<th>mult</th>
<td><p>Multiplication constant (default = 2). Use this parameter to vary the width of the proposal distribution - which is <code>N(theta_v,mult*SE_eap)</code> - when a MH-Algorithm is applied. So the constant quantifies the width in terms of multiples of the EAP standard error. 2 works fine with the default thinning. If the supplied value is large, thinning can take lower values without causing autocorrelation.</p></td>
</tr>
<tr>
<th>x</th>
<td><p>An object of class <code>pv</code> which is the result of using the <code>PV()</code> function</p></td>
</tr>
<tr>
<th>object</th>
<td><p>An object of class <code>pv</code> which is the result of using the <code>PV()</code> function</p></td>
</tr>
<tr>
<th>nrowmax</th>
<td><p>When printing the matrix of estimates - how many rows should be shown? Default = 15.</p></td>
</tr>
</table>
<h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
<p>The function returns a list which main element is <code>pvdraws</code>. This is a matrix of size number_of_persons x npv - so if 10 plausible values are requested for 100 persons, a 100x10 matrix is returned.</p>
<h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2>
<p>Mislevy, R. J. (1991). Randomization-based inference about latent variables from complex samples. Psychometrika, 56(2), 177-196.</p>
<p>Von Davier, M., Gonzalez, E., & Mislevy, R. (2009). What are plausible values and why are they useful. IERI monograph series, 2, 9-36.</p>
<p>Kruschke, J. (2010). Doing Bayesian data analysis: A tutorial introduction with R. Academic Press.</p>
<h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2>
<div class='dont-index'><p><a href='PP_gpcm.html'>PP_gpcm</a>, <a href='PP_4pl.html'>PP_4pl</a>, <a href='JKpp.html'>JKpp</a></p></div>
<h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
<p>Manuel Reif</p>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<pre class="examples"><div class='input'><span class='co'>################# Plausible values #############################################################</span>
<span class='co'>### 4 PL model ######</span>
<span class='co'>### data creation ##########</span>
<span class='fu'><a href='https://rdrr.io/r/base/Random.html'>set.seed</a></span><span class='op'>(</span><span class='fl'>1522</span><span class='op'>)</span>
<span class='co'># intercepts</span>
<span class='va'>diffpar</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span><span class='op'>(</span><span class='op'>-</span><span class='fl'>3</span>,<span class='fl'>3</span>,length<span class='op'>=</span><span class='fl'>12</span><span class='op'>)</span>
<span class='co'># slope parameters</span>
<span class='va'>sl</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/Round.html'>round</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/stats/Uniform.html'>runif</a></span><span class='op'>(</span><span class='fl'>12</span>,<span class='fl'>0.5</span>,<span class='fl'>1.5</span><span class='op'>)</span>,<span class='fl'>2</span><span class='op'>)</span>
<span class='va'>la</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/Round.html'>round</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/stats/Uniform.html'>runif</a></span><span class='op'>(</span><span class='fl'>12</span>,<span class='fl'>0</span>,<span class='fl'>0.25</span><span class='op'>)</span>,<span class='fl'>2</span><span class='op'>)</span>
<span class='va'>ua</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/Round.html'>round</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/stats/Uniform.html'>runif</a></span><span class='op'>(</span><span class='fl'>12</span>,<span class='fl'>0.8</span>,<span class='fl'>1</span><span class='op'>)</span>,<span class='fl'>2</span><span class='op'>)</span>
<span class='co'># response matrix</span>
<span class='va'>awm</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/matrix.html'>matrix</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/sample.html'>sample</a></span><span class='op'>(</span><span class='fl'>0</span><span class='op'>:</span><span class='fl'>1</span>,<span class='fl'>10</span><span class='op'>*</span><span class='fl'>12</span>,replace<span class='op'>=</span><span class='cn'>TRUE</span><span class='op'>)</span>,ncol<span class='op'>=</span><span class='fl'>12</span><span class='op'>)</span>
<span class='co'># EAP estimation - 2pl model</span>
<span class='va'>res2pleap</span> <span class='op'><-</span> <span class='fu'><a href='PP_4pl.html'>PP_4pl</a></span><span class='op'>(</span>respm <span class='op'>=</span> <span class='va'>awm</span>,thres <span class='op'>=</span> <span class='va'>diffpar</span>, slopes <span class='op'>=</span> <span class='va'>sl</span>,type <span class='op'>=</span> <span class='st'>"eap"</span><span class='op'>)</span>
</div><div class='output co'>#> <span class='warning'>Warning: all mu's are set to 0! </span></div><div class='output co'>#> <span class='warning'>Warning: all sigma2's are set to 1! </span></div><div class='output co'>#> Estimating: 2pl model ...
#> type = eap
#> Estimation finished!</div><div class='input'>
<span class='co'># draw 10 plausible values</span>
<span class='va'>res_pv</span> <span class='op'><-</span> <span class='fu'>PV</span><span class='op'>(</span><span class='va'>res2pleap</span><span class='op'>)</span>
<span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span><span class='op'>(</span><span class='va'>res_pv</span><span class='op'>)</span>
</div><div class='output co'>#> PP Version: 0.6.3.11
#>
#> Call: PV.fourpl(estobj = res2pleap)
#> - job started @ Mon May 24 13:27:58 2021
#>
#> Estimation type: Plausible values
#>
#> -------------------------------------
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
#> [1,] 0.6953 -0.4238 0.5376 0.1220 1.1666 -0.4869 0.3956 -0.1345 0.4868
#> [2,] 1.8993 1.3331 1.9698 2.6371 2.9233 1.6535 1.2706 2.0875 3.1040
#> [3,] -0.1233 0.3234 0.2542 1.1840 0.8564 1.2455 0.2902 2.0925 0.9092
#> [4,] -0.0955 0.4056 -0.0211 1.1267 -0.3397 1.2787 0.3276 0.0335 0.7451
#> [5,] -0.3687 0.4171 0.0624 0.9619 0.6330 1.1589 -0.1714 1.2052 1.0300
#> [6,] -0.1402 -0.8282 -0.0552 -0.6590 -0.2023 0.3184 -0.2779 -0.7942 -0.4154
#> [7,] 0.4481 -0.6536 1.5925 0.1980 0.4367 -0.5248 -0.5444 0.8554 -0.1203
#> [8,] -1.0657 -0.1015 -0.5556 -0.5727 -0.8175 0.2507 0.2714 -0.5924 -0.4320
#> [9,] -0.1300 0.8070 0.9653 1.0756 0.0884 -0.4184 0.7620 -0.3311 0.7093
#> [10,] 0.0168 -0.0284 -1.0015 -1.0178 -0.5916 -1.1864 -2.0544 -0.0423 0.1119
#> [,10]
#> [1,] 1.4409
#> [2,] 2.9403
#> [3,] 0.5839
#> [4,] -0.1149
#> [5,] 0.0241
#> [6,] 0.2265
#> [7,] 0.9147
#> [8,] -1.3009
#> [9,] -0.2065
#> [10,] -0.2729</div><div class='input'>
<span class='co'># draw 10 plausible values - use a metropolitan hastings algorithm</span>
<span class='va'>res_pv2</span> <span class='op'><-</span> <span class='fu'>PV</span><span class='op'>(</span><span class='va'>res2pleap</span>,approx <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span>
<span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span><span class='op'>(</span><span class='va'>res_pv2</span><span class='op'>)</span>
</div><div class='output co'>#> PP Version: 0.6.3.11
#>
#> Call: PV.fourpl(estobj = res2pleap, approx = FALSE)
#> - job started @ Mon May 24 13:27:58 2021
#>
#> Estimation type: Plausible values
#>
#> -------------------------------------
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
#> [1,] 0.5176 0.6702 0.8384 0.1567 0.3942 0.3183 1.1856 0.4123 1.3934
#> [2,] 2.6354 1.7938 2.2411 0.9559 1.5905 1.8675 1.9793 2.1926 2.4647
#> [3,] 1.1811 0.9038 0.2391 0.3320 0.5533 0.0269 0.3355 0.7387 2.3213
#> [4,] 0.6674 1.2358 -0.1539 0.4765 -0.9007 0.0618 -0.0947 0.1080 0.3025
#> [5,] 1.2287 0.7294 1.1350 0.1083 0.2721 0.2760 0.1822 0.9192 -0.1466
#> [6,] -0.3054 0.4222 0.1953 -0.1967 -1.2530 -0.9176 0.8579 -1.0329 -0.1456
#> [7,] -0.3392 1.3096 0.8709 0.1195 1.0242 0.6261 1.1982 0.1842 0.1152
#> [8,] -1.2496 -1.1042 0.2793 0.6694 -1.1338 -0.2512 -0.3135 -0.2266 -0.8891
#> [9,] 0.9876 1.1833 -0.3425 0.2033 -0.2409 1.1824 -0.5005 0.4128 1.8582
#> [10,] 0.1786 -0.3631 -0.1823 -0.8970 0.0599 -1.4422 -0.2283 -1.0609 0.3647
#> [,10]
#> [1,] 0.9946
#> [2,] 2.4778
#> [3,] 0.8432
#> [4,] -0.5142
#> [5,] 1.0123
#> [6,] 0.7441
#> [7,] 0.7339
#> [8,] -0.7373
#> [9,] 0.4449
#> [10,] -1.4295</div><div class='input'>
<span class='co'># ------ check the PVs</span>
<span class='co'># -- autocorrelation?</span>
<span class='va'>autocor</span> <span class='op'><-</span> <span class='kw'>function</span><span class='op'>(</span><span class='va'>acv</span><span class='op'>)</span>
<span class='op'>{</span>
<span class='fu'><a href='https://rdrr.io/r/stats/cor.html'>cor</a></span><span class='op'>(</span><span class='va'>acv</span><span class='op'>[</span><span class='op'>-</span><span class='fl'>1</span><span class='op'>]</span>,<span class='va'>acv</span><span class='op'>[</span><span class='op'>-</span><span class='fu'><a href='https://rdrr.io/r/base/length.html'>length</a></span><span class='op'>(</span><span class='va'>acv</span><span class='op'>)</span><span class='op'>]</span><span class='op'>)</span>
<span class='op'>}</span>
<span class='va'>res_pvac</span> <span class='op'><-</span> <span class='fu'>PV</span><span class='op'>(</span><span class='va'>res2pleap</span>,approx <span class='op'>=</span> <span class='cn'>FALSE</span>,npv <span class='op'>=</span> <span class='fl'>200</span><span class='op'>)</span>
<span class='co'># independent draws - so there cannot be any systematic autocorrelation when</span>
<span class='co'># approx = TRUE. So this acts as a kind of benchmark for the MH-Alg.</span>
<span class='va'>res_pvac2</span> <span class='op'><-</span> <span class='fu'>PV</span><span class='op'>(</span><span class='va'>res2pleap</span>,approx <span class='op'>=</span> <span class='cn'>TRUE</span>,npv <span class='op'>=</span> <span class='fl'>200</span><span class='op'>)</span>
<span class='fu'><a href='https://rdrr.io/r/base/apply.html'>apply</a></span><span class='op'>(</span><span class='va'>res_pvac</span><span class='op'>$</span><span class='va'>pvdraws</span>,<span class='fl'>1</span>,<span class='va'>autocor</span><span class='op'>)</span>
</div><div class='output co'>#> [1] -0.09218511 -0.09269937 -0.02118295 -0.10091570 -0.04938669 -0.04611125
#> [7] -0.04625685 -0.02323778 -0.10955832 -0.08582139</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/apply.html'>apply</a></span><span class='op'>(</span><span class='va'>res_pvac2</span><span class='op'>$</span><span class='va'>pvdraws</span>,<span class='fl'>1</span>,<span class='va'>autocor</span><span class='op'>)</span>
</div><div class='output co'>#> [1] 0.0334621629 -0.1829705082 0.0348347988 -0.1514444247 -0.0932831102
#> [6] -0.0421735214 -0.1183732851 0.0202321291 -0.0008060551 -0.0892993107</div><div class='input'>
<span class='co'># -- autocorrelation distr?</span>
<span class='fu'><a href='https://rdrr.io/r/base/apply.html'>apply</a></span><span class='op'>(</span><span class='va'>res_pvac</span><span class='op'>$</span><span class='va'>pvdraws</span>,<span class='fl'>1</span>,<span class='va'>quantile</span><span class='op'>)</span>
</div><div class='output co'>#> [,1] [,2] [,3] [,4] [,5] [,6]
#> 0% -1.1189126 0.6482584 -0.8599093 -1.17206073 -1.06657367 -1.9113879
#> 25% 0.1243905 1.6327885 0.2907127 -0.05658439 -0.03965872 -0.5590972
#> 50% 0.5966065 2.1110250 0.7791557 0.37603789 0.54105135 -0.1806396
#> 75% 1.1131146 2.6571856 1.1399531 0.73833154 1.01487874 0.1831070
#> 100% 2.7299487 3.7852102 2.1300067 2.24528325 1.92887105 1.7386137
#> [,7] [,8] [,9] [,10]
#> 0% -1.39552654 -2.9369528 -0.89186083 -2.5718982
#> 25% -0.03756925 -1.1410654 0.04793972 -1.2907359
#> 50% 0.44731563 -0.5981778 0.46023882 -0.9884915
#> 75% 0.93801834 -0.1137122 0.89671504 -0.4047435
#> 100% 2.07215601 0.9584107 2.37528014 0.9008073</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/apply.html'>apply</a></span><span class='op'>(</span><span class='va'>res_pvac2</span><span class='op'>$</span><span class='va'>pvdraws</span>,<span class='fl'>1</span>, <span class='va'>quantile</span><span class='op'>)</span>
</div><div class='output co'>#> [,1] [,2] [,3] [,4] [,5] [,6]
#> 0% -1.91636101 0.01988437 -1.2642093 -1.29134152 -1.441746554 -1.8945768
#> 25% 0.06152027 1.66679080 0.2228406 -0.04999196 0.009426829 -0.5331227
#> 50% 0.65586226 2.08172297 0.6867953 0.36135697 0.552124816 -0.1308765
#> 75% 0.96952681 2.57572512 1.1293040 0.68278043 0.973946245 0.2960726
#> 100% 2.39979403 3.93395552 2.3552885 1.69208634 1.878495326 1.9703464
#> [,7] [,8] [,9] [,10]
#> 0% -1.40250925 -2.4268740 -1.38035907 -2.3991210
#> 25% 0.04597495 -0.9474394 0.02987099 -1.1518491
#> 50% 0.46163170 -0.5717532 0.46486795 -0.7977427
#> 75% 0.93354670 -0.1431859 0.88224389 -0.4279617
#> 100% 2.03832546 1.2638010 1.99662599 0.6953115</div><div class='input'>
<span class='co'>### GPCM model ######</span>
<span class='co'># some threshold parameters</span>
<span class='va'>THRES</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/matrix.html'>matrix</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='op'>-</span><span class='fl'>2</span>,<span class='op'>-</span><span class='fl'>1.23</span>,<span class='fl'>1.11</span>,<span class='fl'>3.48</span>,<span class='fl'>1</span>
,<span class='fl'>2</span>,<span class='op'>-</span><span class='fl'>1</span>,<span class='op'>-</span><span class='fl'>0.2</span>,<span class='fl'>0.5</span>,<span class='fl'>1.3</span>,<span class='op'>-</span><span class='fl'>0.8</span>,<span class='fl'>1.5</span><span class='op'>)</span>,nrow<span class='op'>=</span><span class='fl'>2</span><span class='op'>)</span>
<span class='co'># slopes</span>
<span class='va'>sl</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0.5</span>,<span class='fl'>1</span>,<span class='fl'>1.5</span>,<span class='fl'>1.1</span>,<span class='fl'>1</span>,<span class='fl'>0.98</span><span class='op'>)</span>
<span class='va'>awmatrix</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/matrix.html'>matrix</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>1</span>,<span class='fl'>0</span>,<span class='fl'>2</span>,<span class='fl'>0</span>,<span class='fl'>1</span>,<span class='fl'>1</span>,<span class='fl'>1</span>,<span class='fl'>0</span>,<span class='fl'>0</span>,<span class='fl'>1</span>
,<span class='fl'>2</span>,<span class='fl'>0</span>,<span class='fl'>0</span>,<span class='fl'>0</span>,<span class='fl'>0</span>,<span class='fl'>0</span>,<span class='fl'>0</span>,<span class='fl'>0</span>,<span class='fl'>0</span>,<span class='fl'>1</span>,<span class='fl'>1</span>,<span class='fl'>2</span>,<span class='fl'>2</span>,<span class='fl'>1</span>,<span class='fl'>1</span>,<span class='fl'>1</span>,<span class='fl'>1</span>,<span class='fl'>0</span>,<span class='fl'>0</span>,<span class='fl'>1</span><span class='op'>)</span>,byrow<span class='op'>=</span><span class='cn'>TRUE</span>,nrow<span class='op'>=</span><span class='fl'>5</span><span class='op'>)</span>
<span class='co'># EAP estimation</span>
<span class='va'>resgpcmeap</span> <span class='op'><-</span> <span class='fu'><a href='PP_gpcm.html'>PP_gpcm</a></span><span class='op'>(</span>respm <span class='op'>=</span> <span class='va'>awmatrix</span>,thres <span class='op'>=</span> <span class='va'>THRES</span>, slopes <span class='op'>=</span> <span class='va'>sl</span>,type <span class='op'>=</span> <span class='st'>"eap"</span><span class='op'>)</span>
</div><div class='output co'>#> <span class='warning'>Warning: all mu's are set to 0! </span></div><div class='output co'>#> <span class='warning'>Warning: all sigma2's are set to 1! </span></div><div class='output co'>#> Estimating: GPCM ...
#> type = eap
#> Estimation finished!</div><div class='input'>
<span class='va'>res_gpcmpv</span> <span class='op'><-</span> <span class='fu'>PV</span><span class='op'>(</span><span class='va'>resgpcmeap</span>,approx <span class='op'>=</span> <span class='cn'>FALSE</span>,npv <span class='op'>=</span> <span class='fl'>20</span><span class='op'>)</span>
<span class='co'>### GPCM and 4PL model ######</span>
<span class='co'># some threshold parameters</span>
<span class='va'>THRES</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/matrix.html'>matrix</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='op'>-</span><span class='fl'>2</span>,<span class='op'>-</span><span class='fl'>1.23</span>,<span class='fl'>1.11</span>,<span class='fl'>3.48</span>,<span class='fl'>1</span>
,<span class='fl'>2</span>,<span class='op'>-</span><span class='fl'>1</span>,<span class='op'>-</span><span class='fl'>0.2</span>,<span class='fl'>0.5</span>,<span class='fl'>1.3</span>,<span class='op'>-</span><span class='fl'>0.8</span>,<span class='fl'>1.5</span><span class='op'>)</span>,nrow<span class='op'>=</span><span class='fl'>2</span><span class='op'>)</span>
<span class='co'># slopes</span>
<span class='va'>sl</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0.5</span>,<span class='fl'>1</span>,<span class='fl'>1.5</span>,<span class='fl'>1.1</span>,<span class='fl'>1</span>,<span class='fl'>0.98</span><span class='op'>)</span>
<span class='va'>THRESx</span> <span class='op'><-</span> <span class='va'>THRES</span>
<span class='va'>THRESx</span><span class='op'>[</span><span class='fl'>2</span>,<span class='fl'>1</span><span class='op'>:</span><span class='fl'>3</span><span class='op'>]</span> <span class='op'><-</span> <span class='cn'>NA</span>
<span class='co'># for the 4PL item the estimated parameters are submitted, </span>
<span class='co'># for the GPCM items the lower asymptote = 0 </span>
<span class='co'># and the upper asymptote = 1.</span>
<span class='va'>la</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0.02</span>,<span class='fl'>0.1</span>,<span class='fl'>0</span>,<span class='fl'>0</span>,<span class='fl'>0</span>,<span class='fl'>0</span><span class='op'>)</span>
<span class='va'>ua</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0.97</span>,<span class='fl'>0.91</span>,<span class='fl'>1</span>,<span class='fl'>1</span>,<span class='fl'>1</span>,<span class='fl'>1</span><span class='op'>)</span>
<span class='va'>awmatrix</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/matrix.html'>matrix</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>1</span>,<span class='fl'>0</span>,<span class='fl'>1</span>,<span class='fl'>0</span>,<span class='fl'>1</span>,<span class='fl'>1</span>,<span class='fl'>1</span>,<span class='fl'>0</span>,<span class='fl'>0</span>,<span class='fl'>1</span>
,<span class='fl'>2</span>,<span class='fl'>0</span>,<span class='fl'>0</span>,<span class='fl'>0</span>,<span class='fl'>0</span>,<span class='fl'>0</span>,<span class='fl'>0</span>,<span class='fl'>0</span>,<span class='fl'>0</span>,<span class='fl'>1</span>
,<span class='fl'>1</span>,<span class='fl'>2</span>,<span class='fl'>2</span>,<span class='fl'>1</span>,<span class='fl'>1</span>,<span class='fl'>1</span>,<span class='fl'>1</span>,<span class='fl'>0</span>,<span class='fl'>0</span>,<span class='fl'>1</span><span class='op'>)</span>,byrow<span class='op'>=</span><span class='cn'>TRUE</span>,nrow<span class='op'>=</span><span class='fl'>5</span><span class='op'>)</span>
<span class='va'>model2est</span> <span class='op'><-</span> <span class='fu'><a href='findmodel.html'>findmodel</a></span><span class='op'>(</span><span class='va'>THRESx</span><span class='op'>)</span>
<span class='co'># EAP estimation</span>
<span class='va'>respcmeap1</span> <span class='op'><-</span> <span class='fu'><a href='PPall.html'>PPall</a></span><span class='op'>(</span>respm <span class='op'>=</span> <span class='va'>awmatrix</span>,thres <span class='op'>=</span> <span class='va'>THRESx</span>,
slopes <span class='op'>=</span> <span class='va'>sl</span>,lowerA <span class='op'>=</span> <span class='va'>la</span>, upperA<span class='op'>=</span><span class='va'>ua</span>, type <span class='op'>=</span> <span class='st'>"eap"</span>,
model2est<span class='op'>=</span><span class='va'>model2est</span><span class='op'>)</span>
</div><div class='output co'>#> Estimating: mixed 4PL, GPCM ...
#> type = eap
#> Estimation finished!</div><div class='input'>
<span class='va'>res_mixedpv_1</span> <span class='op'><-</span> <span class='fu'>PV</span><span class='op'>(</span><span class='va'>respcmeap1</span>,approx <span class='op'>=</span> <span class='cn'>FALSE</span>,npv <span class='op'>=</span> <span class='fl'>200</span><span class='op'>)</span>
<span class='co'># rowMeans of plausible values should approximate the EAPs</span>
<span class='fu'><a href='https://rdrr.io/r/base/colSums.html'>rowMeans</a></span><span class='op'>(</span><span class='va'>res_mixedpv_1</span><span class='op'>$</span><span class='va'>pvdraws</span><span class='op'>)</span>
</div><div class='output co'>#> [1] 0.093466412 -0.083368876 -1.607109734 1.298907846 0.004484088</div><div class='input'><span class='co'># EAPs</span>
<span class='va'>respcmeap1</span>
</div><div class='output co'>#> estimate SE
#> [1,] 0.0682 0.5905
#> [2,] -0.0653 0.5950
#> [3,] -1.5237 0.7046
#> [4,] 1.3112 0.6142
#> [5,] -0.0417 0.6119</div><div class='input'>
<span class='co'># show the quantiles of the empirical distribution</span>
<span class='fu'><a href='https://rdrr.io/r/base/apply.html'>apply</a></span><span class='op'>(</span><span class='va'>res_mixedpv_1</span><span class='op'>$</span><span class='va'>pvdraws</span>,<span class='fl'>1</span>,<span class='va'>quantile</span><span class='op'>)</span>
</div><div class='output co'>#> [,1] [,2] [,3] [,4] [,5]
#> 0% -1.3485464 -1.57470138 -3.8011143 -0.01345653 -1.45492521
#> 25% -0.3082155 -0.54806041 -2.0808571 0.82804669 -0.50233232
#> 50% 0.1284492 -0.01708521 -1.5534572 1.27125852 0.00656254
#> 75% 0.4943450 0.33145978 -1.0425829 1.72900086 0.49265666
#> 100% 1.6374132 1.49828104 0.2286223 2.90438148 1.62675981</div><div class='input'>
</div></pre>
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