Date: Sun, 17 May 1998 20:54:12 GMT
Reply-To: Richard F Ulrich <wpilib+@PITT.EDU>
Sender: "SPSSX(r) Discussion" <SPSSX-L@UGA.CC.UGA.EDU>
From: Richard F Ulrich <wpilib+@PITT.EDU>
Organization: University of Pittsburgh
Subject: Re: power models
Dave D. Waller (firstname.lastname@example.org) wrote:
: Hi. I seem to be having a conceptual difficulty with SPSS output --
: perhaps more generally with modeling data. Perhaps a kind and knowing
: person can offer some advice.
- "more generally, with modeling ...".
What are your assumptions about the distribution of the error?
Do you want to have error that is distributed nicely about "y",
or about "log y" ?
Your two solutions are minimizing different error functions, so
they are bound to be distinct. How different do the figures look
if you plot them on ordinary paper, compared to log-log paper?
Rich Ulrich, biostatistician email@example.com
http://www.pitt.edu/~wpilib/index.html Univ. of Pittsburgh
====================rest of the note
: I am fitting a power equation to psychophysical data. Typically, I
: regress the log of a person's responses onto the log of the physical
: quantity and use the resulting slope estimate as an estimate of the
: exponent of the power function.
: Now I am starting to fit some more general nonlinear models. As a
: comparison, I thought that I could express the power equation as a
: nonlinear model (using untransformed variables) and get the same results
: as the linear regression on the log variables.
: To my dismay, the parameter estimates and r^2 values for the
: log-transformed linear model and the un-transformed nonlinear model are
: not in agreement. What am I missing?
: For example, why don't the two regression procedures below produce the
: same estimate of the exponent? How are these two models different? Any
: insight you can provide would be greatly appreciated.
: DATA LIST FREE / x y.
: BEGIN DATA.
: 12 10
: 10 9
: 16 14
: 17 16
: 14 12.
: END DATA.
: COMPUTE logx = ln(x).
: COMPUTE logy = ln(y).
: /MISSING LISTWISE
: /STATISTICS COEFF OUTS R ANOVA
: /CRITERIA=PIN(.05) POUT(.10)
: /DEPENDENT logy
: /METHOD=ENTER logx .
: * NonLinear Regression.
: MODEL PROGRAM MODULUS=1 EXPONENT=1 .
: COMPUTE PRED_ = MODULUS*x**EXPONENT.
: NLR y
: /PRED PRED_
: /CRITERIA SSCONVERGENCE 1E-8 PCON 1E-8 .