<div dir="ltr">

<p class="MsoNormal"><span lang="EN-US">Dear all,</span></p>

<p class="MsoNormal"><span lang="EN-US">I would appreciate your thoughts on output from Winsteps showing person dimensionality for a simulated
data. My apologies for the lengthy post; I highlighted my questions so that
they are easy to see.</span></p>

<p class="MsoNormal"><span lang="EN-US"> </span></p>

<p class="MsoNormal"><span lang="EN-US">For the
simulation, I created a normally distributed sample of 1,000 persons and
distributed 140 multiple-choice items equally across a range of difficulties. Five hundred persons never
guessed on unknown test items (instead, they responded with an “I don’t know”
option), and the other 500 persons always guessed. For the latter, unknown items
had a 25% chance of being answered correctly. The resulting dataset was Rasch analyzed, with persons labeled as either “IDK” or “guesser”.</span></p>

<p class="MsoNormal"><span lang="EN-US"> </span></p>

<p class="MsoNormal"><span lang="EN-US">My thoughts/questions on the output below:</span></p>

<p class="MsoNormal"><span lang="EN-US">By conventional criteria, the unexplained variance
in the first contrast is too small to be considered a secondary dimension. This
seems to be supported by the low values for residual loadings. However, there
is an obvious and extreme pattern of person loadings according to whether they
were guessers or not (this pattern continues with remarkable consistency
throughout).</span></p>

<p class="MsoNormal"><span lang="EN-US"> </span></p>

<p class="MsoNormal"><b style><span lang="EN-US">In
your opinions, would it be appropriate to refer to this as a dimension? If not,
how might it be referred to?  </span></b><span lang="EN-US">I am considering describing this as
something like “The pattern of residual loadings in the data suggests [quite
clearly?] that test scores reflect not only the primary latent construct but
also willingness to skip unknown test items. <b style>Would you agree with that interpretation of the data?</b></span></p>

<p class="MsoNormal"><span lang="EN-US"> </span></p>

<p class="MsoNormal"><span lang="EN-US">It should also be noted that person numbers
are ordered according to ability; 1 = lowest ability, 1000 = highest ability.
>From this it also seems evident to me that the persons most affected by this
are those of lowest ability (the guessers in the right hand column are ordered
more or less from low to high throughout). This makes sense to me as low-ability guessers
would have to most to gain. <b style>Does this interpretation
make sense to you?</b></span></p><p class="MsoNormal"><br><span lang="EN-US"></span></p><p class="MsoNormal"><span lang="EN-US"><span style>Best,</span></span></p><p class="MsoNormal"><br><span lang="EN-US"></span></p><p class="MsoNormal"><span lang="EN-US"><span style>Tim Stoeckel</span><b style><br></b></span></p>

<p class="MsoNormal"><span lang="EN-US"> </span></p>

<p class="MsoNormal" style="text-align:left" align="left"><b style><span lang="EN-US">Output from Table 24 of Winsteps:</span></b></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-family:&quot;Courier New&quot;" lang="EN-US">Table of STANDARDIZED RESIDUAL variance (in
Eigenvalue units)</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-family:&quot;Courier New&quot;" lang="EN-US"><span style>                                                
</span>-- Empirical --<span style>    </span>Modeled</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-family:&quot;Courier New&quot;" lang="EN-US">Total raw variance in observations<span style>     </span>=<span style>      
</span>1629.2 100.0%<span style>         </span>100.0%</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-family:&quot;Courier New&quot;" lang="EN-US"><span style>  </span>Raw
variance explained by measures<span style>   </span>=<span style>        </span>629.2<span style> 
</span>38.6%<span style>          </span>38.7%</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-family:&quot;Courier New&quot;" lang="EN-US"><span style>    </span>Raw
variance explained by persons<span style>  </span>=<span style>        </span>184.7<span style> 
</span>11.3%<span style>          </span>11.4%</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-family:&quot;Courier New&quot;" lang="EN-US"><span style>    </span>Raw
Variance explained by items<span style>    </span>=<span style>        </span>444.6<span style> 
</span>27.3%<span style>          </span>27.3%</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-family:&quot;Courier New&quot;" lang="EN-US"><span style>  </span>Raw
unexplained variance (total)<span style>     </span>=<span style>       </span>1000.0<span style> 
</span>61.4% 100.0%<span style>   </span>61.3%</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-family:&quot;Courier New&quot;" lang="EN-US"><span style>   
</span>Unexplned variance in 1st contrast =<span style>         </span>23.2<span style>  
</span>1.4%<span style>   </span>2.3%</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-family:&quot;Courier New&quot;" lang="EN-US"><span style>   
</span>Unexplned variance in 2nd contrast =<span style>         </span>13.1<span style>   
</span>.8%<span style>   </span>1.3%</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-family:&quot;Courier New&quot;" lang="EN-US"><span style>   
</span>Unexplned variance in 3rd contrast =<span style>         </span>12.6<span style>   
</span>.8%<span style>   </span>1.3%</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-family:&quot;Courier New&quot;" lang="EN-US"><span style>    </span>Unexplned
variance in 4th contrast =<span style>        
</span>12.4<span style>    </span>.8%<span style>   </span>1.2%</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-family:&quot;Courier New&quot;" lang="EN-US"> </span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">STANDARDIZED RESIDUAL
LOADINGS FOR PERSON (SORTED BY LOADING)</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US"><span style> </span></span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">---------------------------------------------------------
--------------------------------------------------</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|CON-<span style>  </span>|<span style>      
</span>|<span style>   </span><span style>    </span>INFIT OUTFIT| ENTRY<span style>              </span>| |<span style>       </span>|<span style>      
</span>INFIT OUTFIT| ENTRY<span style>              </span>|</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">| TRAST|LOADING|MEASURE<span style>  </span>MNSQ MNSQ |NUMBER PERSON<span style>       </span>| |LOADING|MEASURE<span style>  </span>MNSQ MNSQ |NUMBER PERSON<span style>       </span>|</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|------+-------+-------------------+--------------------|
|-------+-------------------+--------------------|</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.47 |<span style>    </span>1.11<span style> 
</span>.63<span style>  </span>.47 |A<span style>  </span>901 IDK<span style>     
</span>901 | |<span style>  </span>-.43 |<span style>     </span>.07 1.51 1.61 |a<span style>   </span>98 guesser<span style>  
</span>98 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.42 |<span style>    </span>1.30<span style> 
</span>.67<span style>  </span>.47 |B<span style>  </span>911 IDK<span style>     
</span>911 | |<span style>  </span>-.42 |<span style>     </span>.29 1.53 1.74 |b<span style>  </span>108 guesser<span style> 
</span>108 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.42 |<span style>    </span>1.54<span style> 
</span>.72<span style>  </span>.47 |C<span style>  </span>959 IDK<span style>     
</span>959 | |<span style>  </span>-.41 |<span style>    </span>-.16 1.67 1.90 |c<span style>    </span>4 guesser<span style>   
</span>4 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.39 |<span style>     </span>.34<span style> 
</span>.68<span style>  </span>.55 |D<span style>  </span>755 IDK<span style>     
</span>755 | |<span style>  </span>-.41 |<span style>    </span>-.16 1.57 1.79 |d<span style>   </span>78 guesser<span style>  
</span>78 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.38 |<span style>    </span>1.02<span style> 
</span>.69<span style>  </span>.51 |E<span style>  </span>929 IDK<span style>     
</span>929 | |<span style>  </span>-.36 |<span style>    </span>-.07 1.54 1.84 |e<span style>   </span>36 guesser<span style>  
</span>36 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.36 |<span style>    </span>1.11<span style> 
</span>.70<span style>  </span>.55 |F<span style>  </span>823 IDK<span style>     
</span>823 | |<span style>  </span>-.36 |<span style>    </span>-.07 1.54 1.74 |f<span style>   </span>90 guesser<span style>  
</span>90 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.36 |<span style>     </span>.70<span style> 
</span>.71<span style>  </span>.55 |G<span style>  </span>837 IDK<span style>     
</span>837 | |<span style>  </span>-.35 |<span style>    </span>-.35 1.60 1.98 |g<span style>    </span>8 guesser<span style>   
</span>8 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.35 |<span style>    </span>1.07<span style> 
</span>.68<span style>  </span>.49 |H<span style>  </span>831 IDK<span style>     
</span>831 | |<span style>  </span>-.34 |<span style>    </span>-.68 1.60 2.16 |h<span style>    </span>2 guesser<span style>   
</span>2 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.35 |<span style>     </span>.88<span style> 
</span>.70<span style>  </span>.52 |I<span style>  </span>919 IDK<span style>     
</span>919 | |<span style>  </span>-.34 |<span style>    </span>-.07 1.65 2.00 |i<span style>   </span>50 guesser<span style>  
</span>50 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.34 |<span style>    </span>1.16<span style> 
</span>.73<span style>  </span>.52 |J<span style>  </span>909 IDK<span style>     
</span>909 | |<span style>  </span>-.34 |<span style>    </span>-.07 1.48 1.78 |j<span style>   </span>38 guesser<span style>  
</span>38 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.33 |<span style>     </span>.57<span style> 
</span>.71<span style>  </span>.64 |K<span style>  </span>735 IDK<span style>     
</span>735 | |<span style>  </span>-.34 |<span style>     </span>.48 1.41 1.49 |k<span style>  </span>182 guesser<span style> 
</span>182 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.32 |<span style>     </span>.34<span style> 
</span>.70<span style>  </span>.60 |L<span style>  </span>613 IDK<span style>     
</span>613 | |<span style>  </span>-.33 |<span style>     </span>.07 1.39 1.51 |l<span style>  </span>140 guesser<span style> 
</span>140 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.31 |<span style>     </span>.52<span style> 
</span>.67<span style>  </span>.73 |M<span style>  </span>825 IDK<span style>     
</span>825 | |<span style>  </span>-.33 |<span style>     </span>.52 1.34 1.29 |m<span style>  </span>474 guesser<span style> 
</span>474 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.31 |<span style>    </span>1.45<span style> 
</span>.76<span style>  </span>.52 |N<span style>  </span>953 IDK<span style>     
</span>953 | |<span style>  </span>-.33 |<span style>    </span>-.49 1.37 1.75 |n<span style>   </span>40 guesser<span style>  
</span>40 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.31 |<span style>    </span>-.25<span style> 
</span>.68<span style>  </span>.62 |O<span style>  </span>347 IDK<span style>     
</span>347 | |<span style>  </span>-.32 |<span style>     </span>.61 1.39 1.48 |o<span style>  </span>240 guesser<span style> 
</span>240 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.30 |<span style>     </span>.79<span style> 
</span>.72<span style>  </span>.57 |P<span style>  </span>791 IDK<span style>     
</span>791 | |<span style>  </span>-.31 |<span style>    </span>-.30 1.72 2.12 |p<span style>   </span>22 guesser<span style>  
</span>22 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.30 |<span style>     </span>.39<span style> 
</span>.66<span style>  </span>.57 |Q<span style>  </span>641 IDK<span style>     
</span>641 | |<span style>  </span>-.30 |<span style>     </span>.16 1.29 1.39 |q<span style>  </span>104 guesser<span style> 
</span>104 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.30 |<span style>    </span>1.49<span style> 
</span>.77<span style>  </span>.53 |R <span style> </span>906 guesser<span style> 
</span>906 | |<span style>  </span>-.29 |<span style>     </span>.16 1.33 1.50 |r<span style>   </span>94 guesser<span style>  
</span>94 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.29 |<span style>     </span>.48<span style> 
</span>.71<span style>  </span>.57 |S<span style>  </span>617 IDK<span style>     
</span>617 | |<span style>  </span>-.29 |<span style>    </span>-.11 1.49 1.66 |s<span style>   </span>46 guesser<span style>  
</span>46 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.29 |<span style>    </span>1.64<span style> 
</span>.80<span style>  </span>.56 |T<span style>  </span>969 IDK<span style>     
</span>969 | |<span style>  </span>-.29 |<span style>     </span>.25 1.42 1.69 |t<span style>  </span>106 guesser<span style> 
</span>106 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.29 |<span style>    </span>1.69<span style> 
</span>.79<span style>  </span>.52 |U<span style>  </span>983 IDK<span style>     
</span>983 | |<span style>  </span>-.28 |<span style>     </span>.57 1.47 1.63 |u<span style>  </span>184 guesser<span style> 
</span>184 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.29 |<span style>     </span>.34<span style> 
</span>.72<span style>  </span>.59 |V<span style>  </span>701 IDK<span style>     
</span>701 | |<span style>  </span>-.28 |<span style>     </span>.02 1.49 1.63 |v<span style>   </span>34 guesser<span style>  
</span>34 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1 <span style>  </span>|<span style>   </span>.29
|<span style>     </span>.25<span style> 
</span>.74<span style>  </span>.63 |W<span style>  </span>569 IDK<span style>     
</span>569 | |<span style>  </span>-.28 |<span style>     </span>.70 1.30 1.16 |w<span style>  </span>368 guesser<span style> 
</span>368 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.29 |<span style>     </span>.02<span style> 
</span>.75<span style>  </span>.60 |X<span style>  </span>413 IDK<span style>     
</span>413 | |<span style>  </span>-.28 |<span style>    </span>-.68 1.41 1.83 |x<span style>   </span>12 guesser<span style>  
</span>12 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.28 |<span style>    </span>-.30<span style> 
</span>.73<span style>  </span>.62 |Y<span style>  </span>195 IDK<span style>     
</span>195 | |<span style>  </span>-.27 |<span style>     </span>.34 1.49 1.63 |y<span style>  </span>128 guesser<span style> 
</span>128 |</span></p>

<p class="MsoNormal" style="text-align:left" align="left"><span style="font-size:8pt;font-family:&quot;Courier New&quot;" lang="EN-US">|<span style>  </span>1<span style>  
</span>|<span style>   </span>.28 |<span style>     </span>.11<span style> 
</span>.69<span style>  </span>.57 |Z<span style>  </span>497 IDK<span style>     
</span>497 | |<span style>  </span>-.27 |<span style>    </span>-.63 1.53 2.09 |z<span style>   </span>32 guesser<span style>  
</span>32 |</span></p>

</div>