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Mixed-Model fit - DF mismatch v. SAS/JMP

To: s-news@lists.biostat.wustl.edu
Subject: Mixed-Model fit - DF mismatch v. SAS/JMP
From: KINLEY_ROBERT@LILLY.COM
Date: Mon, 01 Sep 2003 09:28:37 +0100

Can someone help ?

I am getting a disagreement between lme() in Splus and what [ I hope ! ] is the equivalent fit using JMP.

Everything agrees except the degrees of freedom assigned to the standard error to be used in the t-test (and confidence interval) for the slope term.

JMP says 3 df and lme() says 1 df.

( Differences in parameterisation lead to numerically different fixed-factor effects,  but the fitted values are identical).

Full details follow ... if anyone can point me in the right direction I'd be very grateful.

I have the dataset called 'TF' :-

  Strength     type AnalDay    Assay StorageDays AssayOcc
1        4 FinalSol       0  40.4355           0        1
2        4 FinalSol       4  41.0857           4        2
3        4 FinalSol       7  40.8318           7        3
4       10 FinalSol       0 103.6812           0        1
5       10 FinalSol       4 104.5013           4        2
6       10 FinalSol       7 104.1406           7        3
7       20 FinalSol       0 195.6095           0        1
8       20 FinalSol       4 196.6439           4        2
9       20 FinalSol       7 196.1706           7        3

and I'm trying to fit the model   Assay = Strength + AssayOcc + StorageDays

where
Strength is a fixed effect factor,
StorageDays is a fixed slope effect per day , assumed common to all 3 strengths
AssayOcc is random effect for variability between assay occasions

SPLUS :-

> lme(fixed = Assay ~ Strength + StorageDays, data = "" random =  ~ 1 | AssayOcc)

Linear mixed-effects model fit by REML
 Data: TF
       AIC      BIC    logLik
  18.22203 15.87866 -3.111015

Random effects:
 Formula:  ~ 1 | AssayOcc
        (Intercept)   Residual
StdDev:   0.4563897 0.09662428

Fixed effects: Assay ~ Strength + StorageDays
               Value Std.Error DF  t-value p-value
(Intercept) 113.4024 0.4309204  4  263.163  <.0001
  Strength1  31.6617 0.0394467  4  802.645  <.0001
  Strength2  41.2318 0.0227746  4 1810.431  <.0001
StorageDays   0.0751 0.0925766  1    0.811  0.5661

Standardized Within-Group Residuals:
       Min        Q1           Med         Q3      Max
 -1.019119 -0.107893 -0.0007243514 0.08046544 1.127012

Number of Observations: 9
Number of Groups: 3

 > intervals.lme(TF.lme)

Approximate 95% confidence intervals

 Fixed effects:
                  lower         est.      upper
(Intercept)  112.205987 113.40241396 114.598841
  Strength1   31.552162  31.66168333  31.771205
  Strength2   41.168540  41.23177222  41.295005
StorageDays   -1.101194   0.07510225   1.251399

 Random Effects:
  Level: AssayOcc
                    lower      est.    upper
sd((Intercept)) 0.1115825 0.4563897 1.866705

 Within-group standard error:
      lower       est.    upper
 0.04832077 0.09662428 0.193214


JMP (also REML) :-



Note the 3 df in the Denominator for 'StorageDays' in the  Effects Tests table, and the consequently narrower confidence interval in the Parameter Estimates table.

                                thanks                Bob


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