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<h1>Estimation of Person Parameters and calculation of Person Fit for the 1,2,3,4-PL model and the GPCM.</h1>
<small class="dont-index">Source: <a href='https://github.com/jansteinfeld/PP/blob/master/R/PP.R'><code>R/PP.R</code></a></small>
<div class="hidden name"><code>PP.Rd</code></div>
</div>
<div class="ref-description">
<p>PP-package has been developed to easily compute ML, WL (Warm 1989), MAP, EAP and robust estimates of person parameters for a given response matrix and given item parameters of the 1,2,3,4-PL model (Birnbaum 1968, Barton & Lord 1981) and the GPCM (Muraki 1992). It provides c++ routines which makes estimation of parameters very fast. Additional some methods to calculate the person fit are provided like the infit-outfit-, lz- and lz*-idex. Read the vignettes for getting started with this package.</p>
</div>
<h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2>
<p>Barton, M. A., & Lord, F. M. (1981). An Upper Asymptote for the Three-Parameter Logistic Item-Response Model.</p>
<p>Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F.M. & Novick, M.R. (Eds.), Statistical theories of mental test scores. Reading, MA: Addison-Wesley.</p>
<p>Drasgow, F., Levine, M. V. & Williams, E. A. (1985) Appropriateness measurement with polychotomous item response models and standardized indices. <em>British Journal of Mathematical and Statistical Psychology</em>, <b>38(1)</b>, 67--86.</p>
<p>Muraki, Eiji (1992). A Generalized Partial Credit Model: Application of an EM Algorithm. Applied Psychological Measurement, 16, 159-176.</p>
<p>Samejima, Fumiko (1993). An approximation of the bias function of the maximum likelihood estimate of a latent variable for the general case where the item responses are discrete. Psychometrika, 58, 119-138.</p>
<p>Snijders, T. B. (2001) Asymptotic null distribution of person fit statistics with estimated person parameter. <em>Psychometrika</em>, <b>66(3)</b>, 331--342.</p>
<p>Warm, Thomas A. (1989). Weighted Likelihood Estimation Of Ability In Item Response Theory. Psychometrika, 54, 427-450.</p>
<p>Wright, B. D. & Masters, G. N. (1990). Computation of OUTFIT and INFIT Statistics. <em>Rasch Measurement Transactions</em>, 3:4, 84-85.</p>
<p>Yen, Y.-C., Ho, R.-G., Liao, W.-W., Chen, L.-J., & Kuo, C.-C. (2012). An empirical evaluation of the slip correction in the four parameter logistic models with computerized adaptive testing. Applied Psychological Measurement, 36, 75-87.</p>
<h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2>
<div class='dont-index'><p><a href='PPass.html'>PPass</a>, <a href='PP_gpcm.html'>PP_gpcm</a>, <a href='PP_4pl.html'>PP_4pl</a>, <a href='PPall.html'>PPall</a>, <a href='Pfit.html'>Pfit</a></p></div>
<h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
<p>Manuel Reif and Jan Steinfeld</p>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<pre class="examples"><div class='input'><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'># MLE estimation</span>
<span class='va'>res3plmle</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>,lowerA <span class='op'>=</span> <span class='va'>la</span>,type <span class='op'>=</span> <span class='st'>"mle"</span><span class='op'>)</span>
</div><div class='output co'>#> Estimating: 3pl model ...
#> type = mle
#> Estimation finished!</div><div class='input'><span class='co'># WLE estimation</span>
<span class='va'>res3plwle</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>,lowerA <span class='op'>=</span> <span class='va'>la</span>,type <span class='op'>=</span> <span class='st'>"wle"</span><span class='op'>)</span>
</div><div class='output co'>#> Estimating: 3pl model ...
#> type = wle
#> Estimation finished!</div><div class='input'><span class='co'># MAP estimation</span>
<span class='va'>res3plmap</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>,lowerA <span class='op'>=</span> <span class='va'>la</span>,type <span class='op'>=</span> <span class='st'>"map"</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: 3pl model ...
#> type = map
#> Estimation finished!</div><div class='input'>
<span class='co'># calculate person fit</span>
<span class='va'>res3plmlepfit</span> <span class='op'><-</span> <span class='fu'><a href='Pfit.html'>Pfit</a></span><span class='op'>(</span>respm<span class='op'>=</span><span class='va'>awm</span>,pp<span class='op'>=</span><span class='va'>res3plmle</span>,fitindices<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='st'>"infit"</span>,<span class='st'>"outfit"</span><span class='op'>)</span><span class='op'>)</span>
<span class='co'># or estimate person parameter and calculate person fit in one step </span>
<span class='va'>out</span> <span class='op'><-</span> <span class='fu'><a href='PPass.html'>PPass</a></span><span class='op'>(</span>respdf <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/data.frame.html'>data.frame</a></span><span class='op'>(</span><span class='va'>awm</span><span class='op'>)</span>,thres <span class='op'>=</span> <span class='va'>diffpar</span>, items<span class='op'>=</span><span class='st'>"all"</span>,
mod<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='st'>"1PL"</span><span class='op'>)</span>, fitindices<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='st'>"lz"</span>,<span class='st'>"lzstar"</span>,<span class='st'>"infit"</span>,<span class='st'>"outfit"</span><span class='op'>)</span><span class='op'>)</span>
</div><div class='output co'>#> Estimating: 1pl model ...
#> type = wle
#> Estimation finished!</div></pre>
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