[R-sig-ME] Mixed Model for Travel Distance

[Chuck Cleland]

Hello:
  I am attempting to model the distance that clients travel to a
treatment program.  There are 14385 clients nested in 83 treatment
programs (the grouping factor).  The raw data are in miles driven from
the client's residence to the treatment program.  A natural logarithm
transformation of miles driven works well to reduce the positive skew in
miles driven.  I fit a model with lme() that looks like this:

Linear mixed-effects model fit by REML
 Data: dist.df
       AIC      BIC    logLik
  38145.37 38319.54 -19049.68

Random effects:
 Formula: ~1 | PROGRAM
        (Intercept)  Residual
StdDev:   0.4268969 0.8988483

Fixed effects: log(DIST5DZ + 1) ~ QUAD + BEAL_TRI + log(RZIPAREA + 1) +
log(PZIPAREA + 1) + AGE.TRI + P3GEND + P5RACEX + EMPLD + P13REASN +
METHFST + URGE.DI + WDRAW.DI + RX_30 + P7HR30

                               Value  Std.Error    DF   t-value p-value
(Intercept)                1.2235603 0.13153231 14288   9.30236  0.0000
QUADSouthEast              0.2100666 0.13200891    76   1.59131  0.1157
QUADMidWest                0.2760390 0.15709516    76   1.75715  0.0829
QUADWest                  -0.1655914 0.15536003    76  -1.06586  0.2899
BEAL_TRI250K-1M           -0.0264939 0.11724713    76  -0.22597  0.8218
BEAL_TRI<250K             -0.0965256 0.16399464    76  -0.58859  0.5579
log(RZIPAREA + 1)          0.2965304 0.00757138 14288  39.16463  0.0000
log(PZIPAREA + 1)         -0.0042061 0.04413826    76  -0.09529  0.9243
AGE.TRI30-43              -0.0309444 0.01789442 14288  -1.72927  0.0838
AGE.TRI43-83              -0.1281177 0.02168648 14288  -5.90772  0.0000
P3GENDFemale              -0.0195289 0.01632703 14288  -1.19611  0.2317
P5RACEXLatino             -0.3527584 0.02904416 14288 -12.14559  0.0000
P5RACEXBlack              -0.5485861 0.03306146 14288 -16.59292  0.0000
P5RACEXOther              -0.1580669 0.04811350 14288  -3.28529  0.0010
EMPLDYes                   0.0098856 0.01650635 14288   0.59890  0.5493
P13REASNYes               -0.0095057 0.01650128 14288  -0.57606  0.5646
METHFSTYes                 0.0073478 0.01672948 14288   0.43921  0.6605
URGE.DI Strong-VeryStrong -0.0272769 0.02400068 14288  -1.13651  0.2558
WDRAW.DISevere-VerySevere  0.0012054 0.01810067 14288   0.06659  0.9469
RX_30Yes                   0.0934411 0.02165389 14288   4.31521  0.0000
P7HR30Yes                 -0.0408189 0.02256842 14288  -1.80867  0.0705

Standardized Within-Group Residuals:
        Min          Q1         Med          Q3         Max
-4.17921640 -0.49875991  0.08672984  0.59020542  4.54644432

Number of Observations: 14385
Number of Groups: 83

  I would like to summarize the fixed effects in terms of miles rather
than log(miles + 1).  How can that be done?  Are there common
generalized linear mixed models for miles driven that would avoid the
transformation and allow effects to be presented in miles?

thanks,

Chuck

-- 
Chuck Cleland, Ph.D.
NDRI, Inc. (www.ndri.org)
71 West 23rd Street, 8th floor
New York, NY 10010
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