Example L1 Continuous response model

 

Bland and Altman (1986) report on a study to compare the standard Wright peak flow meter with the (then) new Mini Wright peak flow meter. The data that accompany this study (pefr.dat) contain the repeated measurements of peak expiratory flow rate (PEFR) obtained from a sample of 17 individuals. These subjects had their PFER measured twice using the new Mini Wright peak flow meter and twice using the Standard Wright peak flow meter. To avoid instrument effects being confounded with prior experience effects, the instruments were used in random order.

 

Reference

 

Bland, J. M., and Altman, D., G., (1986), Statistical methods for assessing agreement between two methods of clinical measurement, Lancet, 1, 307-310.

 

 

Data description

 

Number of observations (rows): 34

Number of variables (columns): 4

 

Variable description:

 

id= person identifier

occasion=occasion {1,2}

wp=Standard Wright meter PEFR

wm=Mini Wright meter PEFR

 

 

The first few lines of pefr.dat look like

 

 

 

Sabre commands

 

out pefr.log

trace pefr.trace

data id occasion wp wm

read pefr.dat

case id

yvar wm

family g

constant cons

lfit cons

dis m

dis e

mass 64

scale 110

fit cons

dis m

dis e

stop

 

 

 

Sabre log file

 

<S> trace pefr.trace

<S> data id occasion wp wm

<S> read pefr.dat

 

         34 observations in dataset

 

<S> case id

<S> yvar wm

<S> family g

<S> constant cons

<S> lfit cons

 

    Iteration       Log. lik.       Difference

    __________________________________________

        1          -207.71303

 

<S> dis m

 

    X-vars            Y-var

    ______________________________

    cons              wm

 

    Univariate model

    Standard linear

 

    Number of observations             =      34

 

    X-var df           =     1

 

    Log likelihood =     -207.71303     on      33 residual degrees of freedom

 

<S> dis e

 

    Parameter              Estimate         Std. Err.

    ___________________________________________________

    cons                    453.91           18.954

    sigma                   110.52

 

<S> mass 64

<S> scale 110

<S> fit cons

 

    Initial Homogeneous Fit:

 

    Iteration       Log. lik.       Difference

    __________________________________________

        1          -207.71303

 

 

    Iteration       Log. lik.         Step      End-points     Orthogonality

                                     length    0          1      criterion

    ________________________________________________________________________

        1          -206.22336        1.0000    fixed  fixed      orthogonal

        2          -205.97710        1.0000    fixed  fixed      orthogonal

        3          -205.73103        1.0000    fixed  fixed      orthogonal

        4          -205.48502        1.0000    fixed  fixed      orthogonal

        5          -205.23897        1.0000    fixed  fixed      orthogonal

        6          -204.99279        1.0000    fixed  fixed      orthogonal

        7          -204.74639        1.0000    fixed  fixed      orthogonal

        8          -204.49970        1.0000    fixed  fixed      orthogonal

        9          -204.25266        1.0000    fixed  fixed      orthogonal

       10          -204.00524        1.0000    fixed  fixed      orthogonal

       11          -203.75742        1.0000    fixed  fixed      orthogonal

       12          -203.50919        1.0000    fixed  fixed      orthogonal

       13          -203.26056        1.0000    fixed  fixed      orthogonal

       14          -203.01158        1.0000    fixed  fixed      orthogonal

       15          -202.76232        1.0000    fixed  fixed      orthogonal

       16          -202.51287        1.0000    fixed  fixed      orthogonal

       17          -202.26335        1.0000    fixed  fixed      orthogonal

       18          -202.01391        1.0000    fixed  fixed      orthogonal

       19          -201.76474        1.0000    fixed  fixed      orthogonal

       20          -197.43520        1.0000    fixed  fixed      orthogonal

       21          -194.32273        1.0000    fixed  fixed      orthogonal

       22          -192.79269        1.0000    fixed  fixed      orthogonal

       23          -184.54051        1.0000    fixed  fixed      0.10893E-01

       24          -184.40094        1.0000    fixed  fixed      orthogonal

       25          -183.89355        1.0000    fixed  fixed      0.37130E-01

       26          -183.40135        0.5000    fixed  fixed      0.45536E-01

       27          -183.39902        1.0000    fixed  fixed      0.43827E-01

       28          -183.39902        1.0000    fixed  fixed

 

<S> dis m

 

    X-vars            Y-var             Case-var

    ________________________________________________

    cons              wm                id

 

    Univariate model

    Standard linear

    Gaussian random effects

 

    Number of observations             =      34

    Number of cases                    =      17

 

    X-var df           =     1

    Sigma df           =     1

    Scale df           =     1

 

    Log likelihood =     -183.39902     on      31 residual degrees of freedom

 

<S> dis e

 

    Parameter              Estimate         Std. Err.

    ___________________________________________________

    cons                    453.24           5.8776

    sigma                   18.558           2.6582

    scale                   112.23           4.4993

 

<S> stop