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</o:shapelayout></xml><![endif]--></head><body lang=EN-AU link=blue vlink=purple><div class=WordSection1><p class=MsoNormal>Can anyone help me write the equation for a multidimensional multifaceted partial credit DIF model? <o:p></o:p></p><p class=MsoNormal>I have 2 dimensions, Scenario complexity (-D), Time condition(-T), Group membership(+G), Group membership by Time condition interaction (+G*T) and a Step structure(+S)<o:p></o:p></p><p class=MsoNormal><o:p>&nbsp;</o:p></p><p class=MsoNormal>I have written a few other equations for unidimensional models using the format &nbsp;below and would like to build the next equation using the same format.<o:p></o:p></p><p class=MsoNormal><o:p>&nbsp;</o:p></p><p class=MsoNormal>Thanks<o:p></o:p></p><p class=MsoNormal>Peter<o:p></o:p></p><p class=MsoNormal><o:p>&nbsp;</o:p></p><p class=MsoNormal><o:p>&nbsp;</o:p></p><p class=MsoBodyText style='margin-bottom:3.0pt;text-align:justify;line-height:200%'><span style='font-size:12.0pt;line-height:200%;font-family:"Times New Roman","serif"'>&nbsp;&nbsp;&nbsp;&nbsp; <span style='position:relative;top:17.0pt;mso-text-raise:-17.0pt'><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
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</xml><![endif]--></span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (1)<o:p></o:p></span></p><p class=MsoBodyText style='margin-bottom:3.0pt;text-align:justify;line-height:200%'><span style='font-size:12.0pt;line-height:200%;font-family:"Times New Roman","serif"'>&nbsp;&nbsp;&nbsp;&nbsp; where:<br>&nbsp;&nbsp;&nbsp;&nbsp; <span style='position:relative;top:7.0pt;mso-text-raise:-7.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1026" type="#_x0000_t75" style='width:21pt;height:18.6pt' o:ole="" fillcolor="window">
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</xml><![endif]--></span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = Probability of person <u>n</u> scoring <u>j</u> on scenario <u>i</u> under conditions of time <u>k</u><o:p></o:p></span></p><p class=MsoBodyText style='margin-bottom:3.0pt;text-align:justify;line-height:200%'><span style='font-size:12.0pt;line-height:200%;font-family:"Times New Roman","serif"'>&nbsp;&nbsp;&nbsp;&nbsp; <span style='position:relative;top:7.0pt;mso-text-raise:-7.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1027" type="#_x0000_t75" style='width:28.2pt;height:18.6pt' o:ole="" fillcolor="window">
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</xml><![endif]--></span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = Difficulty of scoring step <u>j</u> relative to step <u>j</u>-1. <o:p></o:p></span></p><p class=MsoNormal><o:p>&nbsp;</o:p></p><p class=MsoNormal><o:p>&nbsp;</o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:9.0pt;font-family:"Arial","sans-serif";color:#003300'>_______________________________________________<o:p></o:p></span></p><p class=MsoNormal><span style='color:#003300'><img width=99 height=38 id="Picture_x0020_1" src="cid:image001.jpg@01CD1EE8.7096CF30" alt="cid:image003.jpg@01CAC6B6.113EDB40"></span><span style='color:#003300'> </span><span lang=EN-US style='color:#7F7F7F'>Measurement, Analysis &amp; Reporting</span><span lang=EN-US style='font-size:12.0pt;font-family:"Times New Roman","serif";color:#003300'><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:9.0pt;font-family:"Arial","sans-serif";color:#003300'><o:p>&nbsp;</o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:9.0pt;font-family:"Arial","sans-serif";color:#003300'><o:p>&nbsp;</o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-family:"Elephant","serif";color:#1F497D'>Peter Congdon<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:9.0pt;font-family:"Arial","sans-serif";color:#7F7F7F'>Principal Consultant<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:9.0pt;font-family:"Arial","sans-serif";color:#7F7F7F'>Mobile: 0434 000 561<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:9.0pt;font-family:"Arial","sans-serif";color:#003300'>email: </span><span lang=EN-US style='color:#1F497D'><a href="mailto:peter@kmetrics.com.au"><span style='font-size:9.0pt;color:#1F497D'>peter@kmetrics.com.au</span></a></span><span lang=EN-US style='font-size:9.0pt;font-family:"Arial","sans-serif";color:#003300'><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:9.0pt;font-family:"Arial","sans-serif";color:#003300'>web: </span><span lang=EN-US style='color:navy'><a href="http://www.kmetrics.com.au/"><span style='font-size:9.0pt;color:#003300'>www.kmetrics.com.au</span></a></span><span lang=EN-US style='font-size:9.0pt;font-family:"Arial","sans-serif";color:#003300'><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:9.0pt;font-family:"Arial","sans-serif";color:#003300'>_______________________________________________<o:p></o:p></span></p><p class=MsoNormal><o:p>&nbsp;</o:p></p></div></body></html>