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Correcting measurement error in AMOS

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Salbod
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Correcting measurement error in AMOS

Salbod
Good afternoon,

Cole & Preacher (2014) mentioned

ColeAndPreacher.pdf

a correction for low reliabilities when analyzing manifest variables. I implemented their suggestion in Mplus. Can this be implemented in AMOS?

Title: Correction for Measurement Error Attenuation;
  Data:
      File is DataJune19.dat;
  Variable:
      NAMES ARE id, y1, x1, x2, m1, m2, age, sex;
      USEVARIABLES ARE y1-sex;
  ANALYSIS:
        TYPE = GENERAL;
 
  ! Reliability of y1 = .690, variance = 16.053;
  ! Reliability of x1 = .921, variance = 432.023;
  ! Reliability of x2 = .944, variance = 522.180;
  ! Reliability of m1 = .619, variance = 9.886;
  ! Reliability of m2 = .788, variance = 29.867;
  ! Sex and age is assumed to be perfectly reliabile;
 
  Model: y_1 by y1@1;
         x_1 by x1@1;
         x_2 by x2@1;
         m_1 by m1@1;
         m_2 by m2@1;
         m_1 ON x_1 x_2 age sex;
         m_2 ON x_1 x_2 age sex;
         y_1 ON x_1 x_2 m_1 m_2 age sex;

  ! Set measurement variance to (1-reliability)*(sample variance).
  !      y1 = (1-.690)*(16.053) = 4.9764;
  !      x1 = (1-.921)*(432.023) = 34.1298;
  !      x2 = (1-.944)*(522.180) = 29.2421;
  !      m1 = (1-.619)*(9.886) = 3.7666;
  !      m2 = (1-.788)*(29.867) = 6.3318;
 
         y1@4.9764;
         x1@34.1298;
        x2@29.2421;
         m1@3.7666;
         m2@6.3318;        
 
 
  Model indirect:
      y_1 IND x_1;
      y_1 IND x_2;

     
  Output: stdyx ;
*************************************************************

Any comments or suggestions will be greatly appreciated.
-Steve
Ryan
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Re: Correcting measurement error in AMOS

Ryan
Steve,

Using Object Properties, one can constrain the error variances by setting the value of the variance for the manifest variables to whatever value you want. Just work out what the estimated error variance would be using the formula you posted, and plug in that value as the error variance. It is really that simple. 

Just in case you are unaware of where that formula you posted comes from...

(1-reliability)*(sample variance)

According to Classical Test Theory, the formula above is the estimated standard error of measurement (SEM) squared. The reason it is squared is that the SEM is the standard deviation of the error scores, but you are interested in estimating the variance of the error scores.

HTH.

Ryan


On Mon, Jun 23, 2014 at 12:56 PM, Salbod <[hidden email]> wrote:
Good afternoon,

Cole & Preacher (2014) mentioned

ColeAndPreacher.pdf
<http://spssx-discussion.1045642.n5.nabble.com/file/n5726574/ColeAndPreacher.pdf>

a correction for low reliabilities when analyzing manifest variables. I
implemented their suggestion in Mplus. Can this be implemented in AMOS?

Title: Correction for Measurement Error Attenuation;
  Data:
      File is DataJune19.dat;
  Variable:
      NAMES ARE id, y1, x1, x2, m1, m2, age, sex;
      USEVARIABLES ARE y1-sex;
  ANALYSIS:
        TYPE = GENERAL;

  ! Reliability of y1 = .690, variance = 16.053;
  ! Reliability of x1 = .921, variance = 432.023;
  ! Reliability of x2 = .944, variance = 522.180;
  ! Reliability of m1 = .619, variance = 9.886;
  ! Reliability of m2 = .788, variance = 29.867;
  ! Sex and age is assumed to be perfectly reliabile;

  Model: y_1 by y1@1;
         x_1 by x1@1;
         x_2 by x2@1;
         m_1 by m1@1;
         m_2 by m2@1;
         m_1 ON x_1 x_2 age sex;
         m_2 ON x_1 x_2 age sex;
         y_1 ON x_1 x_2 m_1 m_2 age sex;

  ! Set measurement variance to (1-reliability)*(sample variance).
  !      y1 = (1-.690)*(16.053) = 4.9764;
  !      x1 = (1-.921)*(432.023) = 34.1298;
  !      x2 = (1-.944)*(522.180) = 29.2421;
  !      m1 = (1-.619)*(9.886) = 3.7666;
  !      m2 = (1-.788)*(29.867) = 6.3318;

         y1@4.9764;
         x1@34.1298;
        x2@29.2421;
         m1@3.7666;
         m2@6.3318;


  Model indirect:
      y_1 IND x_1;
      y_1 IND x_2;


  Output: stdyx ;
*************************************************************

Any comments or suggestions will be greatly appreciated.
-Steve




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Ryan
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Re: Correcting measurement error in AMOS

Ryan
It's getting late...I misstated how to constrain the error variances in my initial paragraph. I provide corrections in my original response below in CAPS:

On Mon, Jun 23, 2014 at 11:55 PM, Ryan Black <[hidden email]> wrote:
Steve,

Using Object Properties, one can constrain the error variances by setting the value of the variance for ERROR TERM OF EACH manifest variable to whatever value you want. Just work out what the estimated error variance would be using the formula you posted, and plug in that value as the VARIANCE FOR THE ERROR TERMS. It is really that simple. 

Just in case you are unaware of where that formula you posted comes from...

(1-reliability)*(sample variance)

According to Classical Test Theory, the formula above is the estimated standard error of measurement (SEM) squared. The reason it is squared is that the SEM is the standard deviation of the error scores, but you are interested in estimating the variance of the error scores.

HTH.

Ryan


On Mon, Jun 23, 2014 at 12:56 PM, Salbod <[hidden email]> wrote:
Good afternoon,

Cole & Preacher (2014) mentioned

ColeAndPreacher.pdf
<http://spssx-discussion.1045642.n5.nabble.com/file/n5726574/ColeAndPreacher.pdf>

a correction for low reliabilities when analyzing manifest variables. I
implemented their suggestion in Mplus. Can this be implemented in AMOS?

Title: Correction for Measurement Error Attenuation;
  Data:
      File is DataJune19.dat;
  Variable:
      NAMES ARE id, y1, x1, x2, m1, m2, age, sex;
      USEVARIABLES ARE y1-sex;
  ANALYSIS:
        TYPE = GENERAL;

  ! Reliability of y1 = .690, variance = 16.053;
  ! Reliability of x1 = .921, variance = 432.023;
  ! Reliability of x2 = .944, variance = 522.180;
  ! Reliability of m1 = .619, variance = 9.886;
  ! Reliability of m2 = .788, variance = 29.867;
  ! Sex and age is assumed to be perfectly reliabile;

  Model: y_1 by y1@1;
         x_1 by x1@1;
         x_2 by x2@1;
         m_1 by m1@1;
         m_2 by m2@1;
         m_1 ON x_1 x_2 age sex;
         m_2 ON x_1 x_2 age sex;
         y_1 ON x_1 x_2 m_1 m_2 age sex;

  ! Set measurement variance to (1-reliability)*(sample variance).
  !      y1 = (1-.690)*(16.053) = 4.9764;
  !      x1 = (1-.921)*(432.023) = 34.1298;
  !      x2 = (1-.944)*(522.180) = 29.2421;
  !      m1 = (1-.619)*(9.886) = 3.7666;
  !      m2 = (1-.788)*(29.867) = 6.3318;

         y1@4.9764;
         x1@34.1298;
        x2@29.2421;
         m1@3.7666;
         m2@6.3318;


  Model indirect:
      y_1 IND x_1;
      y_1 IND x_2;


  Output: stdyx ;
*************************************************************

Any comments or suggestions will be greatly appreciated.
-Steve




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View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Correcting-measurement-error-in-AMOS-tp5726574.html
Sent from the SPSSX Discussion mailing list archive at Nabble.com.

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD


===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
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