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Re: st: types and codes of the non-linear models


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: types and codes of the non-linear models
Date   Thu, 21 Feb 2013 15:25:15 +0000

With a function like this, the parameters usually no longer have
simple interpretations.

There is an exception for -b3-. -b3- is in effect a kind of origin on
the time axis for your model and it is estimated as about 2010. In
this case, the very high t statistic and very low P-value are just a
side-effect of the usual null hypothesis that the origin is "really
zero", i.e. 0 AD. That hypothesis is not of scientific interest, or so
I presume.

This kind of modelling is usually lose-lose, unfortunately. One or
two-parameter models miss important features of the data. More
complicated models are more difficult to fit, or converge
unsatisfactorily.

Nick

On Thu, Feb 21, 2013 at 2:00 PM, BASSILI, Dr Amal     STB/TDR
<bassilia@emro.who.int> wrote:

> Further to my below mail, I have done the below non-linear regression to predict incidence of a disease over years and would like to know how to interpret the trend. Is it b1? And if b1= 1.6, does this mean that the average trend is 1.6% per year?
>
>
> -----------------------------
>
> Thanks, . predict incidence1_rate_hat
> (option yhat assumed; fitted values)
>
> . twoway (fpfitci incidence1_rate_hat year)
>
> . nl log4 : incidence_rate year
> (obs = 7)
>
> Iteration 0:  residual SS =  .1728985
> Iteration 1:  residual SS =  .1640116
> Iteration 2:  residual SS =  .1594486
> Iteration 3:  residual SS =  .1555352
> Iteration 4:  residual SS =  .1518877
> Iteration 5:  residual SS =  .1480812
> Iteration 6:  residual SS =  .1451413
> Iteration 7:  residual SS =  .1317394
> Iteration 8:  residual SS =  .1305299
> Iteration 9:  residual SS =  .1265793
> Iteration 10:  residual SS =  .1206557
> Iteration 11:  residual SS =  .1068023
> Iteration 12:  residual SS =  .1019377
> Iteration 13:  residual SS =  .0991159
> Iteration 14:  residual SS =  .0414042
> Iteration 15:  residual SS =  .0314478
> Iteration 16:  residual SS =  .0299035
> Iteration 17:  residual SS =  .0299035
> Iteration 18:  residual SS =  .0299035
> Iteration 19:  residual SS =  .0299035
>
>       Source |       SS       df       MS
> -------------+------------------------------         Number of obs =         7
>        Model |   .92438218     3 .308127393         R-squared     =    0.9687
>     Residual |  .029903534     3  .009967845         Adj R-squared =    0.9373
> -------------+------------------------------         Root MSE      =  .0998391
>        Total |  .954285714     6 .159047619         Res. dev.     = -18.32468
>
> 4-parameter logistic function, incidence_rate = b0 + b1/(1 + exp(-b2*(year - b3)))
> ------------------------------------------------------------------------------
> incidence_~e |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>          /b0 |   2.656667   .0695158    38.22   0.000     2.435436    2.877897
>          /b1 |   1.619345   1.376313     1.18   0.324    -2.760698    5.999388
>          /b2 |   1.240626   .8727815     1.42   0.250    -1.536954    4.018206
>          /b3 |   2010.526   1.460316  1376.77   0.000     2005.878    2015.173
> ------------------------------------------------------------------------------
>   Parameter b0 taken as constant term in model & ANOVA table
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