/
Journal of Mathematical Psychology    Tutorial Tutorial on maximum likelihood estimation Journal of Mathematical Psychology    Tutorial Tutorial on maximum likelihood estimation

Journal of Mathematical Psychology Tutorial Tutorial on maximum likelihood estimation - PDF document

calandra-battersby
calandra-battersby . @calandra-battersby
Follow
680 views
Uploaded On 2014-12-17

Journal of Mathematical Psychology Tutorial Tutorial on maximum likelihood estimation - PPT Presentation

Theintendedaudienceofthistutorialare researchers who practice mathematical modeling of cognition but are unfamiliar with the estimation method 1nlike least2squares estimation which is primarily a descriptive tool M is a preferred method of parameter ID: 25325

Theintendedaudienceofthistutorialare researchers who practice mathematical

Share:

Link:

Embed:

Download Presentation from below link

Download Pdf The PPT/PDF document "Journal of Mathematical Psychology Tu..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.


Presentation Transcript

          !    " #DepartmentofPsychology,OhioStateUniversity,1885NeilAvenueMall,Columbus,OH43210-1222,USA$  % !&% ' ( % !)* ' " ++ ,"+%!    +      !     -./  ! !!      �#?B)22C)/ /D/ !/2)EEF2   . % 4  145/5   % !/�!/)E42)A2 "   ++ ," !     !     !    ! 2/ ++ 0    0  + %% ! +0 !+'  +   G //JournalofExperimentalPsychology' ! ! / ++  ! !  %  ++   !    % ' !   +  -4.    ! !  ,  ' +!   +         , + 2  ! / ++  ++  +%! ! + !  ! !0   + /?2! + ,         +,  ! !  !    //,@ :H  ,,= +/(= :@  ,,= +/(H 7 :4 % ,,= +/)(4+,,= +//   2.1.Probabilitydensityfunction?     !+ , ! %  !  +   0++ / !  !   ++        %    !  + /"   ,  ++ !  6 !' +!+'' ! ' /5 !0  +'' ! ' 3 %  ! I+ /5 +   % ,!   +'' ! '     !/?2 , ! ! 6 !  +'' ! ' !  !' ! I+ /!  probabilitydensityfunctionH?  + 6  +'' ' %! %  +    ++ 0 0 + %   //! 0 '+ %      /// + %  ! 6 !  2! + + /"!%!'2 % ,I,    ! + !    , !  +'' , H? ! %  + ' +  !  + H?!%!' % ,  ! H?,!   +   0  ' % ! + ,  ,4++  !  +     '    3  @   //   !  +''   , +   !' + // H?  % ' yyyAyyy ?//@ +'' ! '  + !+'' +  +!'  /I.J.Myung/JournalofMathematicalPsychology47(2003)90–100 0   0 ' ! ' 0 + &   ' !  !+ /  +  H? 0 ++ ?//" + %   !  0H?'  ! 0   +  0 '  + ?// 0    +  H? ' ! ' ' %  0   + 6  +'' ! % %     H?   !'% +     ! 6  ! /2.2.Likelihoodfunction7%  + % ,  +!H?0 0   !   +''  ! /" + %  + , H?0      C/%//)/"  , 0 % ,0 %  !' % ! ! /5!,0   !0 %  +' �7%  ' % !! ! !    ,6!  H?,  +'' !     ! + ' ,       % +! ! ! /% %  +' ,0 ! 6 likelihoodfunction' %    ! %  ! + %   +      ! + %  ' % !! !  ?  2+ '   + .3/,   ! !% '   +    !  0?/    +  !   ' 0  H?!   ! 5  !?/!, 0  ! 6 !!    ,!     !   +'    /4+ 6, H??/  ! % +  + % ,! 6 ! datascale/*   !,   !   + % +  ' % !! ,! 6 ! parameterscale/"  ,?/  +'' + ! % 6 !+ ,0  ?/    !JJ +''2 II+ + % 6 !!  /&    !  6 % ?//   ! % ' % !! ! +   2+  ! ! ' !  /I.J.Myung/JournalofMathematicalPsychology47(2003)90–100 '    + ' ! 0   ! ' 0/" !   0+ ,   ! 0'   '% + + /"  , ! 0 + ,   !     + 2!   JJ II '% 2! + + + !' + %     * !  % '   !!   !  ! %  ! !   !, +          ' ++ ,  , +'' ! '   !   ! /7%   !   + % ! !   +'' ! ' ?/,0     !6! + %   2+!  !  !+'' ! ' / ++ maximumlikelihoodestimation -.,! % + !'$/5/?  ,    !  !+'' ! '      ' % !! JJ   ,II0       %  + %        !    + %  ,0   '    2! + + , ! MLEestimate,!!  !'?  + ,?/, -.    0    2 !%  +'' ! '  +!   -.     0 '  + ?/5!  -.++ ,  ++        %    ! ' % !!  ,     !   2  !  +'' ! '     ' % !!    /3.1.Likelihoodequation -.     !  ' 3 /"   ,0  0 0  + -.    0    ! 3 /? +  % 2  , -.    '  !'   2  ! , '  0 ,    !      -.    '  !'     /5   2  ! ,!   ' ,  ,    0+ !    3  0 likelihoodequation  '  ! 6        !   '   +    6 ! % % %   + /   ! 3  +     2!     -.    /5!! !   '  6 !       !    , 6 ! % %   %  /'    ,  +  2  !  !' %    +   +  , %    ' ! '   !'   !! % %  2  !! 00     %    -.+ ! , !  + % 2+ '   + % 6 !% ? ,'       ! .3/),0 '  2  ! &  , 6 ! % %  2  ! ! dLwnydw w w @ 3  3  ' !  ! -.    '  !      +      ,    ,  !! % %  2  ! !! % ! dLwnydw w 0    % ,!  !/"+  , 0 % ,  +' '     -.    , + 0  ! %%  + ! H?  2 /"   , -.     '   2 +    / '! 2 +    3 6!+  +     2  !/ ! ' =!  9   ! 6 !       %  !  3   !   negativedenite  , 2 '  !%  !   + I.J.Myung/JournalofMathematicalPsychology47(2003)90–100       '2   2! 2+ +      %   2 0  + + ,0  '    '   ' +   / JJ   II  + !' ! %       %  +/4+ 6,    ,'       + %  , 0 + % '  !'!!     + %+  0   0+     !  +% !+   /H   +    !  0 +!   ! !/   % + , 0'  0?/,    +  G! !  % %  !/ /,+ @?/ +   + +++ + ! 6 ! /. +   ++ !    '   0 !       + % ' 0  0 %   /3.2.Localmaxima" 0    +    !       + %   3    2  !0' !/?!+   +      + 0  +       +% +  +   ++ !'  /" + %       ! ' /H + !+     + % ,  !+    +! '2+   + % /  ! localmaxima+' /5  + ,?/      + %  + 0 !  +  + @ ! globalmaximum,   + %  + 0 ! + 5,0  '2+   /4 ,   + %  0 !  '2+    + =/1  ,           +' /" !,%   23  % ' ! % + ! + %! +' ,        %  /?  + ,   !     % %   +    + ! !        0    '  ! +  !/;   ++ , ! 0  6!   '   ' !/ ?//5  +  2  ! 6   2+  ! / @ '   0  + 5!= 0  /   0! +   % +   + / 5   +    0  ! K +  ,7  ,:L  ,A%    +' ,    ,    '  ' + +         6! I.J.Myung/JournalofMathematicalPsychology47(2003)90–100 3.3.Relationtoleast-squaresestimation$    -.0  + %   mostlikely  % +! ! ! /"-4.,   !,0  + %   +%! mostaccurate! +  ! ,  !   0  ! 6  ! !  3 2 /? ,-4.,sumofsquareserror44.' 0 ' % !+ !  &#x !00; !   ! I+ !  ' % /&    + %  5 -.,6! + %     44.   3  2 +    /   -4.'G     +' , + 0  ! 2 0  +   + /   ' 0  0 !     % 2 % 3  /"  ,-4.     ! !  -.    , + !      ! ' ! ++   ! +  /5 +     +'%  !   '  !  ! + !+0  !     + ! ! /;  , -. !' +   ! -4.,  +'' !    0!6 '   + '  ,  , ! !    $ ,A    , 0 % ,0  0 !   / 0 ' %  ! + !    !  ! ' !0   % /"  ,    2  ! 3%     44.,!   ,  + %  '  !!    -.-4./ "   ,"+   ++   +      !    /  !,"   ! %           + //$':;  ,); ,A; !:.''  ,5  2!     % ' ++ !!  ! + ,"+%!   +  -. 0 ,+0 ! +  /- ' + %  ,  ,! ! I+ !  +'2'       0 !  ! 6 !+0  ! &#x -5;7.2; +   ! &#x -5;7.2;4++  !  ' % 0   +   '2 % !++      ;     !   %'   ! /; ! '6   ' % !! !   ! 6 /5++  -. 3 + 6  H? ! undereachmodel/! ,6 0    ' % !++ '  !'!%!  '    + '   ' ! + !  ;    ' ! ' !0 +''   H? +0  ! ! +   !  '  !+0 &#x -5;7.2; +  � 0     0+  ' !  ! H? '% 3 /? , +'' + ' +'' ! ' / /.3/'  !  !/   , H?  ! .3/'  !' + + +'' + .3/0 !  3 ,.3//4 !,    ! '6 !  ,5 ,    !++' !     +     /"+ , H?'  !' + +&0,   I    ! + !    , !  !2  !  +0  ! % ' ?  ! , H? +  !6    !   /I.J.Myung/JournalofMathematicalPsychology47(2003)90–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yung/JournalofMathematicalPsychology47(2003)90–100  ++ !  ' ! ' !,  ! ' !/? ,   %  +2  3 ! 3%  ' 0  -.!-4.!  !' ! 0  % ,! + !+++   4.1.MLEinterpretation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yung/JournalofMathematicalPsychology47(2003)90–100     6      #        # 9     "   # 6*:   *: " #   "*:      "*.   6,!;' (!;! �    � �?=     "        #    6  - 6    "    - "       $     $  - 76*6- -8@$      - 7*-"*"-8@$              �=  #    6     "$ 6        .   #             #       )=  #   "       "$"        .   #             #    ! "$#     /                  !          9    $      %&  '(% (%&  (% (% )(*#+% , (*#+%&  #(% (% "! (-..% / (% ($                   *1+2*-*3         I.J.Myung/JournalofMathematicalPsychology47(2003)90–100 %! 5  ,9//"   !       !++ /�" ,@/&/,:= ,Secondinternationalsymposiumoninformationtheory++/)A/�@!+  5 ! K!/@  ! ,;/9/,:=0 ,=/4//   +   !    /JournalofMathematical,CCC/@ ,//,:H  ,K/5//Mathematicalstatistics* !,&#x12.; =59! 2!,"/= ,7/,:@  ,$/-//Statisticalinference! !//67% ,&#x12.; =5H' /H 7 , /9/,:4 % , ///Probabilityandstatistics! !//@ ,&#x12.;  55!!2;  /K +  ,4/,7  ,=/H/,:L  , //A/*+   '  ! /,))A/- '  ,K//"  2   + ! !  /PsychologicalReview,)/-  ,9/,:N ,;/A)/Modelselection/& 0O ,&#x12.; &O ! /,@/@/)/   !%! /JournalofExperimentalPsychology,)A)C/ ,"//,? , /,:@0 , /;//4+   !    /JournalofMathematicalPsychology , /5/, ,"//,:N ,4//0! !     +   !  /Psychological,/$ ,$/A/5    %/Psychological,CA/$',H/=/,9 ,4/,:; 5// +      /JournalofExperimentalPsychology:Learning,Memory,andCognition,))/                     6       "*9  % 6   6 6 6     6  6*:/ *: //   *:         "*:      "*.   6"-9    6 6 6     "    - 6  - "       $  - 76*6- -8@$       - 7*-"*"-8@$              �= /  6       6    $ 6      6      9  6     )= /  6      "      $"        6      9  6  I.J.Myung/JournalofMathematicalPsychology47(2003)90–100 $',H/=/,:; 5/./)/* ! !  &#x ,-;ٕ.; 53   % ! +   /Psychological,)/4 07/A/.    !  ! /Annalsof,))/4+,5//Probabilitytheoryandstatisticalinference/= 2'! ,&#x,-37;䀀1K= '! 1%   /1 , /,: = !,/-//   +  +   (   , +    ! /Psychological,CCC/LN! ,//90 6  +  ! ' /PsychonomicBulletin&Review,)C/; ,/H/A/*     &#x,-37;䀀 =  $'!; &#x -2;p.8;)53   % ! +   /PsychologicalReview,A)/; !,//,:.''  ,./@//*   /PsychologicalScience,C/I.J.Myung/JournalofMathematicalPsychology47(2003)90–100