項目反応理論によるパラメータの推定手続き。
Baker, F.B. & Kim, S-H. (2004) Item response theory: parameter estimation techniques. Marcel Dekker Inc. にMLE法によるBasic Program があります。使えるかもしれないと、Delphiに書き直してみました。取りあえずは同じ計算結果がでます。しかし、このままでは汎用に使えません。(タダだから当たり前ですね)。
私の理解力では歯が立たない本ですが、頭のリハビリでbasicのプログラムをdelphi(pascal)に書き換えてみました。書き換えてみると、入力データを作るルーチンがないと現実には使えないことがわかりました。それで間に合わせに作ってみました。
プログラムは2-parameter logistic model で、項目ごとのパラメータの推定をします。解説によると、「the examinees have been grouped into 10 intervals with known ability levels, ..」とあります。それで、全項目の合計点を各サンプルごとに算出し、適当に１０の得点範囲にして、計算ルーチンに渡します。もっと良い方法があるのでしょうが、わかりません。
豊田さんの「項目反応理論 入門編」の学力テスト1のデータから３０変量を取り出し、2パラメータモデルの結果P.52 表４．２と比べてみたのですが、識別力が0.1程度食い違い、困難度はもっとと言う有様。豊田さんのは周辺最尤推定値、このプログラムはMLE。違って当たり前ですが。
方法が違うためか。パグのためか。１０グループに分けたアルゴリズムがいい加減なためか、よくわかりません。もし、どなたか、MLE法のパラメータ推定プログラムをお持ちの方がいましたら、計算が合っているのか、教えてください。
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村上宣寛
（勤務先）
〒930-8555 富山市五福3190
富山大学教育学部学校心理学
TEL/FAX 076-445-6367
E-mail: murakami (at) edu.toyama-u.ac.jp
HomePage:http://psycho01.edu.toyama-u.ac.jp/
{ program to get maximum likelihood estimates of the
slope and intercept parameters for a single item
under a two parameter logistic icc model }
procedure TfrmIRT.btnOKClick( Sender: TObject );
var
data : array[ 1 .. 500, 1 ..30] of real;
sum : array[ 1.. 500 ] of real;
x,
rk,
fk : array[ 1 .. 10 ] of real;
sfw, sfwv, sfwv2, sfwx, sfwxv, sfwx2,
pai, dev, ph, w, v, dm,
p1, p2, p3, p4, p5, p6,
dcpt, da, cpt, a : real;
item,
nxl,
maxit : integer;
interval, min, max : real;
procedure Initialize;
begin
title := '[ 項目反応理論 by F.B.Baker and S.-H.Kim( IRTPET ) ]';
start_time := TimeToStr( Time );
start_date := DateToStr( Date );
filename := Edit1.text;
nxl := 10;
cpt := 0;
a :=1;
maxit := 100;
OpenPrinter;
WriteLn( f1 );
WriteLn( f1, title );
WriteLn( f1 );
WriteLn( f1,'ファイル名:', filename );
WriteLn( f1 );
end;
procedure InputData;
var
i : integer;
s : real;
dmy : array[ 1 .. 30 ] of real;
begin
AssignFile( f2, filename );
Reset( f2 );
ReadLn( f2, number_of_variables );
number_of_samples := 0;
while not eof( f2 ) do begin
for i := 1 to number_of_variables do begin
Read( f2, dmy[ i ] );
end;
ReadLn( f2 );
Inc( number_of_samples );
for i := 1 to number_of_variables do begin
data[ number_of_samples, i ] := dmy [ i ];
end;
// sum
s := 0;
for i := 1 to number_of_variables do begin
s := s + dmy[ i ];
end;
sum[ number_of_samples ] := s;
end;
CloseFile( f2 );
Write( f1,'サンプル数 =' );
WriteLn ( f1, number_of_samples : 8 );
end;
procedure FindMinMax;
var
i : integer;
begin
for i := 1 to number_of_samples do begin
if i = 1 then begin
max := sum[ i ];
min := sum[ i ];
end;
if min > sum[ i ] then begin
min := sum[ i ];
end;
if max < sum[ i ] then begin
max := sum[ i ];
end;
end;
interval := Round( ( max - min )/ 10 );
end;
// 合計得点の最小値と最大値を求め、適当に１０の得点範囲に区分し、項目の正当数、被験者数を算出した。もっと良い方法はないか。
procedure CalculateFrequency;
var
i : integer;
begin
// initial values
cpt := 0;
a :=1;
for i := 1 to 10 do begin
rk[ i ] := 0;
fk[ i ] := 0;
end;
for i := 1 to number_of_samples do begin
if ( sum[ i ] >= min) and ( sum[ i ] <= min + interval ) then begin
fk[ 1 ] := fk[ 1 ] + 1;
rk[ 1 ] :=rk[ 1 ] + data[ i , item ];
end;
end;
for i := 1 to number_of_samples do begin
if ( sum[ i ] > min + interval ) and ( sum[ i ] <= min + 2 * interval ) then begin
fk[ 2 ] := fk[ 2 ] + 1;
rk[ 2 ] :=rk[ 2 ] + data[ i , item ];
end;
end;
for i := 1 to number_of_samples do begin
if ( sum[ i ] > min + 2 *interval ) and ( sum[ i ] <= min + 3 * interval ) then begin
fk[ 3 ] := fk[ 3 ] + 1;
rk[ 3 ] :=rk[ 3 ] + data[ i , item ];
end;
end;
for i := 1 to number_of_samples do begin
if ( sum[ i ] > min + 3 *interval ) and ( sum[ i ] <= min + 4 * interval ) then begin
fk[ 4 ] := fk[ 4 ] + 1;
rk[ 4 ] :=rk[ 4 ] + data[ i , item ];
end;
end;
for i := 1 to number_of_samples do begin
if ( sum[ i ] > min + 4 *interval ) and ( sum[ i ] <= min + 5 * interval ) then begin
fk[ 5 ] := fk[ 5 ] + 1;
rk[ 5 ] :=rk[ 5 ] + data[ i , item ];
end;
end;
for i := 1 to number_of_samples do begin
if ( sum[ i ] > min + 5 *interval ) and ( sum[ i ] <= min + 6 * interval ) then begin
fk[ 6 ] := fk[ 6 ] + 1;
rk[ 6 ] := rk[ 6 ] + data[ i , item ];
end;
end;
for i := 1 to number_of_samples do begin
if ( sum[ i ] > min + 6 *interval ) and ( sum[ i ] <= min + 7 * interval ) then begin
fk[ 7 ] := fk[ 7 ] + 1;
rk[ 7 ] := rk[ 7 ] + data[ i , item ];
end;
end;
for i := 1 to number_of_samples do begin
if ( sum[ i ] > min + 7 *interval ) and ( sum[ i ] <= min + 8 * interval ) then begin
fk[ 8 ] := fk[ 8 ] + 1;
rk[ 8 ] := rk[ 8 ] + data[ i , item ];
end;
end;
for i := 1 to number_of_samples do begin
if ( sum[ i ] > min + 8 *interval ) and ( sum[ i ] <= min + 9 * interval ) then begin
fk[ 9 ] := fk[ 9 ] + 1;
rk[ 9 ] := rk[ 9 ] + data[ i , item ];
end;
end;
for i := 1 to number_of_samples do begin
if ( sum[ i ] > min + 9 *interval ) then begin
fk[ 10 ] := fk[ 10 ] + 1;
rk[ 10 ] := rk[ 10 ] + data[ i , item ];
end;
end;
// for k=1 to nxl:read x(k):next k:rem read ability levels
x[ 1 ] := -4.0000;
x[ 2 ] := -3.1111;
x[ 3 ] := -2.2222;
x[ 4 ] := -1.3333;
x[ 5 ] := -0.4444;
x[ 6 ] := 0.4444;
x[ 7 ] := 1.3333;
x[ 8 ] := 2.2222;
x[ 9 ] := 3.1111;
x[ 10 ] := 4.0000;
end;
{
//本に載っていたデータ。コメントアウトしてある
procedure CalculateFrequency;
begin
cpt := 0;
a :=1;
// for k=1 to nxl:read x(k):next k:rem read ability levels
x[ 1 ] := -4.0000;
x[ 2 ] := -3.1111;
x[ 3 ] := -2.2222;
x[ 4 ] := -1.3333;
x[ 5 ] := -0.4444;
x[ 6 ] := 0.4444;
x[ 7 ] := 1.3333;
x[ 8 ] := 2.2222;
x[ 9 ] := 3.1111;
x[ 10 ] := 4.0000;
// for k=1 to nxl:read rk(k):next k:rem read number correct responses
rk[ 1 ] := 6;
rk[ 2 ] := 17;
rk[ 3 ] := 20;
rk[ 4 ] := 34;
rk[ 5 ] := 51;
rk[ 6 ] := 68;
rk[ 7 ] := 81;
rk[ 8 ] := 90;
rk[ 9 ] := 95;
rk[ 10 ] :=97;
// for k=1 to nxl:read fk(k):next k:rem read number at ability level
fk[ 1 ] := 100;
fk[ 2 ] := 100;
fk[ 3 ] := 100;
fk[ 4 ] := 100;
fk[ 5 ] := 100;
fk[ 6 ] := 100;
fk[ 7 ] := 100;
fk[ 8 ] := 100;
fk[ 9 ] := 100;
fk[ 10 ] :=100;
end;
}
// パラメータ推定手続き
procedure itembio;
var
nit, k :integer;
begin
for nit :=1 to maxit do begin
sfw := 0; sfwv := 0; sfwv2 := 0; sfwx := 0; sfwxv := 0; sfwv2 := 0; sfwx2 :=0;
for k := 1 to nxl do begin // theta loop
if fk[ k ] <> 0 then begin
pai := rk[ k ] / fk[ k ];
dev:= cpt + a * x[ k ];
ph := 1 / ( 1 + exp(-dev));
w := ph * ( 1 - ph );
if w >= 0.0000009 then begin
v := ( pai - ph ) / w;
p1 := fk[ k ] * w;
p2 := p1 * v;
p3 := p2 * v;
p4 := p1 * x[ k ];
p5 := p4 * x[ k ];
p6 := p4 * v;
sfw := sfw + p1;
sfwv := sfwv + p2;
sfwx := sfwx + p4;
sfwxv:= sfwxv+ p6;
sfwx2:= sfwx2 + p5;
sfwv2:= sfwv2 + p3;
end;
end;
end;
if sfw > 0 then begin
dm := sfw * sfwx2 - sfwx * sfwx;
if dm >0.000099 then begin
dcpt := ( sfwv * sfwx2 - sfwxv * sfwx ) / dm;
da := ( sfw * sfwxv - sfwx * sfwv ) / dm;
cpt := cpt + dcpt;
a := a + da;
if (abs(cpt) > 30 ) or (abs(a) > 20) then begin
WriteLn( f1, 'out of bounds error ' );
exit;
end;
if (abs(dcpt)<=0.05) and (abs(da)<=0.05) then exit;
end;
// WriteLn( f1, 'reached maximum number of iterations' );
end;
if sfw<=0 then WriteLn( f1, 'out of bounds error ' );
end;
end;
procedure OutputParameters;
var
df : integer;
diff : real;
begin
WriteLn( f1 );
WriteLn( f1 );
diff := -cpt / a;
df := nxl - 2;
WriteLn( f1, 'item No.' , item :3 );
WriteLn( f1, 'intercept= ', cpt : 8: 4 );
WriteLn( f1, 'slope= ', a : 8 : 4 );
WriteLn( f1, 'a (discrimination) = ', a : 8 : 4 );
WriteLn( f1, 'b (difficulty) = ', diff : 8 : 4 );
WriteLn( f1, 'chi-square= ', sfwv2 : 8 : 4 );
WriteLn( f1, 'd.f.= ', df : 4 );
end;
{
{ main }
begin
Initialize;
InputData;
FindMinMax;
// 面倒だから全項目のパラメータを自動的に算出
for item := 1 to number_of_variables do begin
CalculateFrequency;
itembio;
OutputParameters;
end;
JobInformation;
WinExec( 'PrintOut', SW_SHOW );
Close;
end;
豊田さんの学力１データ
30
1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1
0 1 1 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1
0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 1
1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 0
1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 0 0 1
0 0 1 0 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0
1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1
1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1
1 1 1 1 0 1 0 0 1 0 0 0 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 0
1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 1
1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 1 0 0 1 0 0 1 1 1
0 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1
1 0 1 1 1 1 0 0 0 1 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 1 0 0 0
1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 0 1 0
1 0 0 1 1 1 0 0 1 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 1 0 1 0 1 1 0 1
1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 1
1 1 0 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 0 1
1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 1
1 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1
0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0
1 0 1 1 1 1 1 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0
1 1 1 1 1 0 1 0 1 0 1 1 1 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 1 1
1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1
0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 0 1 1 0
1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0
1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 1 1 0 1 1 1 1
1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 0 0 1 1 0 0 0 0 1 0 0 1 0 1
1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 0 0 0 0 1
0 1 1 1 0 1 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0
1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1
1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 0 0 1
0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 1 1 0 0 1 1
1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 0 1
0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1
1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1
0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1
1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0
1 0 1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0 1 0 1 1
0 0 1 1 1 1 1 0 1 0 1 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 0 0 1 0
0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1
0 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0
1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1
1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0
0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0
1 1 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0
1 0 0 1 0 1 1 0 1 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 0 0 0 1 1
1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1
0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 1
0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 0 1 0 1
1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 1 0 1 0 0 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 1 0 1 1 1
0 1 1 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0
1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1
1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 0 1 0 1
1 1 1 1 0 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 1
1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 0 0 0 0 1
0 1 0 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1
1 1 1 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0
1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1
0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 0
0 1 1 0 1 1 1 0 1 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 1
1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 0 0 1 0 0
1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 1
1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1
1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1
1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1
1 0 1 0 0 1 1 0 1 1 0 0 0 1 1 1 0 1 1 1 0 0 0 1 1 0 0 1 0 1
1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1
1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 0 0 1 0 0 0 1 1
1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 1
0 1 1 0 0 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0
1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 0 1 0 1
1 0 1 1 0 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 0 0 0 0
0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1
1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 0 0 0 1 1
0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 0 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1
1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0
1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1
0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1
1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 1 0 0 0
1 1 1 1 1 0 1 0 1 0 1 1 1 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1
0 0 1 1 1 0 1 0 1 1 1 1 1 0 1 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0
1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1
1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1
1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1
1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 1 0 1 0 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 0 1 1 0 1 1 1 1 1 1 0 1 0 0 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1
1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0
0 1 0 0 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 0 0 1 0
1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 1
0 1 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1
0 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1
0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1 0 0 0 0 1
0 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 1 0 1
1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0 1
1 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0
0 1 0 0 0 1 1 0 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 0 0 0 1 0 0 0
1 1 1 1 1 0 1 0 1 0 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 0 1 0 1 1
1 0 0 1 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1
1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 0 1
1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 1 1 1 1 0 1
1 1 1 1 1 1 0 0 1 0 1 1 1 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0
1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 0 0 0 1 1
0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1
0 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 1
1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1
0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 0 0 0 0 0 1
1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 0 1 1 1
0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 1 0 0 1
1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 0 1 0 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1
1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 1 0 0
1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1
1 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 1 0
0 1 1 1 1 0 1 0 1 0 1 1 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 0 0 1
1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 1 0 0 1 0 0 1 0 1 1 0 0
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0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 0 1 1 0 0 1 0 0 1 0 0 1 0 1
0 0 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0
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1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0
1 1 1 1 0 1 1 0 0 1 0 1 1 0 1 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1
1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 1 0 0 0 0 1
0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 1 1 0 1 0 0 1 1 1
0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0
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1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1
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1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0
1 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 0 1
1 0 0 1 0 0 1 0 1 1 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0
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1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0
実行結果
かなり食い違う。しかし、もっともらしい印象もある。
[ 項目反応理論 by F.B.Baker and S.-H.Kim( IRTPET ) ]
ファイル名:C:\My_Programs\Toolbox\項目反応理論入門データ\gaku1-30.dat
サンプル数 = 226
item 1
intercept= 1.0693
slope= 0.5245
a (discrimination) = 0.5245
b (difficulty) = -2.0387
chi-square= 6.3265
d.f.= 8
item 2
intercept= 0.8953
slope= 0.4362
a (discrimination) = 0.4362
b (difficulty) = -2.0523
chi-square= 8.5326
d.f.= 8
item 3
intercept= 2.0995
slope= 0.6808
a (discrimination) = 0.6808
b (difficulty) = -3.0840
chi-square= 2.3783
d.f.= 8
item 4
intercept= 1.7417
slope= 0.6660
a (discrimination) = 0.6660
b (difficulty) = -2.6151
chi-square= 4.1265
d.f.= 8
item 5
intercept= 0.3764
slope= 0.4797
a (discrimination) = 0.4797
b (difficulty) = -0.7845
chi-square= 6.7664
d.f.= 8
item 6
intercept= 1.4696
slope= 0.7027
a (discrimination) = 0.7027
b (difficulty) = -2.0914
chi-square= 9.8749
d.f.= 8
item 7
intercept= 2.0262
slope= 0.8669
a (discrimination) = 0.8669
b (difficulty) = -2.3373
chi-square= 4.3151
d.f.= 8
item 8
intercept= -0.7171
slope= 0.6843
a (discrimination) = 0.6843
b (difficulty) = 1.0479
chi-square= 5.5541
d.f.= 8
item 9
intercept= 2.1126
slope= 0.8707
a (discrimination) = 0.8707
b (difficulty) = -2.4263
chi-square= 4.3667
d.f.= 8
item 10
intercept= 1.1868
slope= 0.5550
a (discrimination) = 0.5550
b (difficulty) = -2.1382
chi-square= 19.1833
d.f.= 8
item 11
intercept= 1.2262
slope= 0.5218
a (discrimination) = 0.5218
b (difficulty) = -2.3500
chi-square= 5.8651
d.f.= 8
item 12
intercept= 2.8287
slope= 1.0596
a (discrimination) = 1.0596
b (difficulty) = -2.6697
chi-square= 8.1197
d.f.= 8
item 13
intercept= 2.5498
slope= 0.8848
a (discrimination) = 0.8848
b (difficulty) = -2.8819
chi-square= 10.7184
d.f.= 8
item 14
intercept= 0.8531
slope= 0.7043
a (discrimination) = 0.7043
b (difficulty) = -1.2114
chi-square= 7.8854
d.f.= 8
item 15
intercept= 0.9080
slope= 0.7137
a (discrimination) = 0.7137
b (difficulty) = -1.2722
chi-square= 12.0859
d.f.= 8
item 16
intercept= 0.1354
slope= 0.7543
a (discrimination) = 0.7543
b (difficulty) = -0.1795
chi-square= 5.8722
d.f.= 8
item 17
intercept= -0.5197
slope= 0.6504
a (discrimination) = 0.6504
b (difficulty) = 0.7990
chi-square= 9.9868
d.f.= 8
item 18
intercept= -0.9822
slope= 0.6896
a (discrimination) = 0.6896
b (difficulty) = 1.4243
chi-square= 7.3454
d.f.= 8
item 19
intercept= 1.0764
slope= 0.6718
a (discrimination) = 0.6718
b (difficulty) = -1.6023
chi-square= 9.4465
d.f.= 8
item 20
intercept= -0.2286
slope= 0.5476
a (discrimination) = 0.5476
b (difficulty) = 0.4175
chi-square= 6.2059
d.f.= 8
item 21
intercept= 0.5205
slope= 0.7810
a (discrimination) = 0.7810
b (difficulty) = -0.6664
chi-square= 8.4482
d.f.= 8
item 22
intercept= 0.8702
slope= 0.7548
a (discrimination) = 0.7548
b (difficulty) = -1.1528
chi-square= 11.6412
d.f.= 8
item 23
intercept= -0.0445
slope= 0.8769
a (discrimination) = 0.8769
b (difficulty) = 0.0507
chi-square= 6.5764
d.f.= 8
item 24
intercept= 0.0417
slope= 0.5467
a (discrimination) = 0.5467
b (difficulty) = -0.0763
chi-square= 24.8556
d.f.= 8
item 25
intercept= 2.0656
slope= 0.6895
a (discrimination) = 0.6895
b (difficulty) = -2.9958
chi-square= 3.3952
d.f.= 8
item 26
intercept= -1.4381
slope= 0.5352
a (discrimination) = 0.5352
b (difficulty) = 2.6870
chi-square= 4.7227
d.f.= 8
item 27
intercept= -0.6702
slope= 0.6832
a (discrimination) = 0.6832
b (difficulty) = 0.9809
chi-square= 19.2514
d.f.= 8
item 28
intercept= -0.3919
slope= 0.4705
a (discrimination) = 0.4705
b (difficulty) = 0.8330
chi-square= 0.5933
d.f.= 8
item 29
intercept= -0.9487
slope= 0.6749
a (discrimination) = 0.6749
b (difficulty) = 1.4058
chi-square= 10.4817
d.f.= 8
item 30
intercept= 0.8416
slope= 0.6685
a (discrimination) = 0.6685
b (difficulty) = -1.2589
chi-square= 4.5815
d.f.= 8
[ Job Information ]
Date =2005/04/13 --- 2005/04/13
Time =13:58:29 --- 13:58:29
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