Kalibrierung von Aufgaben für den Adaptiven Kurs (Jack2)
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Der Adaptiv Kurs ist ein geplantes Feature und ist aktuell nicht Nutzbar.
Im Folgenden wird ein Verfahren beschrieben, um einen Adaptiven Kurs manuell (nach dem Rasch-Model?)zu Kalibrieren.
Um die Aufgaben für den Adaptiven Kurs zu Kalibrieren muss vorher das Folgende beachtet werden:
a) Aktuell ist in Jack ein dichotomisches Modell (4pl <math> p_i({\theta})=c_i + \frac{d_i-c_i}{1+e^{-a_i({\theta}-b_i)}} </math> wobei <math>a_i</math> ist die maximale Steigung von <math>p_i</math>; <math>b_i</math> die Schwierigkeit der Aufgabe; <math>c_i</math> die untere Asymtote; <math>d_i</math> die obere Asymtote) implementiert. Das bedeutet im Modell wird angenommen, das es nur Richtig oder Falsch als Antwort genommen wird.
b) Es werden Daten wie die Teilnehmer die Aufgaben abgeschlossen haben benötigt.
c) Es wird angenommen, das jeder Teilnehmer jede Aufgabe genau einmal (egal, ob korrekt oder falsch) Absolviert hat.
d) Es wird angenommen, das die Aufgaben voneinander unabhängig sind.
e) Es wird das R-Paket eRm benötigt.
Schritt 1.
Die Daten werden in eine Matrix eingetragen. Als Zeilen werden die Studenten genommen, als Spalten die Aufgaben. Die jeweiligen Einträge der Matrix entsprechen dem Ergebnis (1 für Korrekt, 0 für Falsch) des einzelnen Teilnehmer zur Aufgabe. Die Einträge der Matrix (a_ij)i€I,j€J ergeben sich also durch : a_ij= Ergebnis von Teilnehmer i in Aufgabe j.
Bsp. (aus dem R-Paket "eRm"; P** sind die einzelnen Studenten; I** die Fragen) :
I1 I2 I3 I4 I5 I6 I7 I8 I9 I10 I11 I12 I13 I14 I15 I16 I17 I18 I19 I20 I21 I22 I23 I24 I25 I26 I27 I28 I29 I30 P1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 P2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 P3 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 P4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 P5 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 P6 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 P7 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 P8 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 P9 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 P10 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 0 P11 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 P12 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 P13 1 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 P14 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 P15 1 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 P16 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 P17 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 P18 1 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 P19 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 P20 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 P21 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 P22 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 1 0 1 P23 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 0 P24 0 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 P25 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 P26 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 P27 0 1 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 P28 1 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 0 0 P29 1 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 P30 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 P31 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 1 0 1 P32 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 P33 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 P34 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 0 P35 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 P36 1 0 1 0 0 1 0 1 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 1 P37 1 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 P38 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 0 1 P39 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 1 0 0 0 1 P40 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 0 1 P41 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 P42 1 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 P43 1 1 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 P44 1 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 P45 1 1 1 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 P46 1 1 1 1 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 P47 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 P48 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 P49 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 1 1 1 1 0 P50 1 1 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 1 P51 1 0 1 0 0 1 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 0 1 P52 1 0 1 0 0 0 1 0 1 0 1 1 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 1 P53 0 1 0 0 1 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 1 0 1 0 1 1 P54 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 1 P55 1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 0 0 1 P56 1 1 1 1 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 P57 0 0 1 1 0 0 1 1 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 0 0 1 P58 1 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 P59 0 1 1 0 1 1 1 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 1 0 0 0 P60 1 0 1 0 0 1 0 0 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 1 1 1 0 0 0 1 P61 1 1 1 1 0 1 1 1 1 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 P62 1 1 1 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 P63 1 0 1 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 0 1 0 1 P64 1 1 0 0 0 1 1 1 0 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 1 0 0 0 1 P65 1 0 0 0 0 1 1 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 1 0 1 1 1 0 1 P66 1 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 P67 1 0 1 1 0 0 1 1 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 1 1 0 1 P68 1 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 0 1 1 1 1 0 0 1 1 1 0 1 P69 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 1 1 P70 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 P71 1 0 1 0 0 1 0 1 1 1 1 1 0 0 0 1 0 0 0 1 0 0 1 1 1 1 1 0 1 1 P72 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 1 P73 0 0 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 P74 1 1 1 0 1 1 1 1 0 0 0 0 1 0 1 1 1 1 0 1 1 0 0 1 0 1 0 1 0 1 P75 1 1 1 0 0 1 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 1 1 1 1 P76 1 1 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 0 0 0 1 1 1 0 1 P77 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 1 P78 0 0 1 1 0 1 1 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 P79 1 1 1 0 0 1 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 1 0 1 0 1 0 1 P80 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 P81 1 0 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 0 1 0 1 1 1 P82 1 0 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 P83 1 1 1 1 0 1 1 1 1 0 1 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 1 1 P84 1 1 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 P85 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 P86 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 P87 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 1 1 P88 1 0 1 1 1 1 1 1 1 0 0 1 0 0 1 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 P89 1 0 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 0 P90 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 0 0 P91 1 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 P92 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 0 1 0 1 1 P93 1 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 P94 1 1 1 1 0 1 1 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 P95 1 1 1 1 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 P96 1 1 0 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 P97 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 P98 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 P99 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 P100 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Schritt 2.
Lasse die Werte durch res <- RM(raschdat1, sum0 = TRUE) berechnen.
Resultat:
> summary(res)
Results of RM estimation:
Call: RM(X = raschdat1, sum0 = TRUE)
Conditional log-likelihood: -1434.482
Number of iterations: 28
Number of parameters: 29
Item (Category) Difficulty Parameters (eta): with 0.95 CI:
Estimate Std. Error lower CI upper CI
I2 -0.051 0.216 -0.475 0.373
I3 -0.782 0.222 -1.217 -0.347
I4 0.650 0.228 0.204 1.096
I5 1.301 0.254 0.802 1.799
I6 -0.099 0.216 -0.523 0.324
I7 -0.682 0.220 -1.113 -0.250
I8 -0.732 0.221 -1.165 -0.299
I9 -0.534 0.218 -0.961 -0.106
I10 1.108 0.245 0.628 1.587
I11 0.650 0.228 0.204 1.096
I12 -0.388 0.217 -0.813 0.037
I13 1.511 0.267 0.988 2.034
I14 2.116 0.316 1.497 2.735
I15 -0.340 0.216 -0.764 0.085
I16 0.597 0.226 0.154 1.041
I17 -0.340 0.216 -0.764 0.085
I18 0.094 0.217 -0.332 0.520
I19 0.759 0.231 0.306 1.211
I20 -0.682 0.220 -1.113 -0.250
I21 -0.937 0.226 -1.379 -0.495
I22 -0.989 0.227 -1.434 -0.544
I23 -0.682 0.220 -1.113 -0.250
I24 -0.003 0.217 -0.427 0.422
I25 0.814 0.233 0.358 1.271
I26 -1.207 0.234 -1.665 -0.749
I27 0.094 0.217 -0.332 0.520
I28 0.290 0.220 -0.140 0.721
I29 0.759 0.231 0.306 1.211
I30 -0.732 0.221 -1.165 -0.299
Item Easiness Parameters (beta) with 0.95 CI:
Estimate Std. Error lower CI upper CI
beta I1 1.565 0.249 1.077 2.053
beta I2 0.051 0.216 -0.373 0.475
beta I3 0.782 0.222 0.347 1.217
beta I4 -0.650 0.228 -1.096 -0.204
beta I5 -1.301 0.254 -1.799 -0.802
beta I6 0.099 0.216 -0.324 0.523
beta I7 0.682 0.220 0.250 1.113
beta I8 0.732 0.221 0.299 1.165
beta I9 0.534 0.218 0.106 0.961
beta I10 -1.108 0.245 -1.587 -0.628
beta I11 -0.650 0.228 -1.096 -0.204
beta I12 0.388 0.217 -0.037 0.813
beta I13 -1.511 0.267 -2.034 -0.988
beta I14 -2.116 0.316 -2.735 -1.497
beta I15 0.340 0.216 -0.085 0.764
beta I16 -0.597 0.226 -1.041 -0.154
beta I17 0.340 0.216 -0.085 0.764
beta I18 -0.094 0.217 -0.520 0.332
beta I19 -0.759 0.231 -1.211 -0.306
beta I20 0.682 0.220 0.250 1.113
beta I21 0.937 0.226 0.495 1.379
beta I22 0.989 0.227 0.544 1.434
beta I23 0.682 0.220 0.250 1.113
beta I24 0.003 0.217 -0.422 0.427
beta I25 -0.814 0.233 -1.271 -0.358
beta I26 1.207 0.234 0.749 1.665
beta I27 -0.094 0.217 -0.520 0.332
beta I28 -0.290 0.220 -0.721 0.140
beta I29 -0.759 0.231 -1.211 -0.306
beta I30 0.732 0.221 0.299 1.165
Estimate ist die "Schwierigkeit".