Logistic regression model using the non-linear modelling syntax

[John Kirwan]

Dear google-group users,

I have been attempting to apply a multilevel logistic regression with an estimated lower asymptote (and/or an upper asymptote), using the non-linear model formulation in brms. E.g.

fit_4 <- brm(bf(success ~ lower_asym + (1 - lower_asym) * inv_logit(eta), 

                  eta ~ 0 + arc.s + (1|animal), 

                   lower_asym ~ 1, nl = TRUE),

                   data = worms, family = bernoulli("identity"), 

                            prior = c(prior(normal(0, 5), nlpar = "eta") , prior(normal(0.2, 0.01), nlpar = "lower_asym")))

I notice that it is necessary to exclude the intercept of eta, when including the asymptote. This appears to have the consequence of predetermining the location of the inflection point. Is it possible to estimate both the asymptote and the eta intercept, for instance by making one additive upon the other, within brms?

P.S: Thank you to Paul Brükner for producing the non-linear modelling vignette and directing me to it. 

Kind regards,

John

[Paul Buerkner]

Why should it be necessary to exclude the intercept?

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[John Kirwan]

This was in reference to the part of the vignette reading: 'We did not estimate an intercept for eta, as this will lead to a bias in the estimated guessing parameter (try it out; this is an excellent example of how careful one has to be in non-linear models).'

(I was of the impression that Stan might not be able to identify the model if there was a potential overlap in these estimated parameters.)

On Monday, 19 March 2018 14:36:03 UTC+1, Paul Buerkner wrote:

Why should it be necessary to exclude the intercept?

2018-03-19 14:30 GMT+01:00 John Kirwan <jo...@jkirwan.org>:

Dear google-group users,

I have been attempting to apply a multilevel logistic regression with an estimated lower asymptote (and/or an upper asymptote), using the non-linear model formulation in brms. E.g.

fit_4 <- brm(bf(success ~ lower_asym + (1 - lower_asym) * inv_logit(eta), 

                  eta ~ 0 + arc.s + (1|animal), 

                   lower_asym ~ 1, nl = TRUE),

                   data = worms, family = bernoulli("identity"), 

                            prior = c(prior(normal(0, 5), nlpar = "eta") , prior(normal(0.2, 0.01), nlpar = "lower_asym")))

I notice that it is necessary to exclude the intercept of eta, when including the asymptote. This appears to have the consequence of predetermining the location of the inflection point. Is it possible to estimate both the asymptote and the eta intercept, for instance by making one additive upon the other, within brms?

P.S: Thank you to Paul Brükner for producing the non-linear modelling vignette and directing me to it. 

Kind regards,

John

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[Paul Buerkner]

I couldn't remember myself saying that... The reason is just that we didn't include the intercept in when simulating the data. Now, when estimating the model with an intercept, the other parameters will of course be changed. I might revise this part of the vignette in order to avoid confusion.

For your purpose, I don't see a problem with including the intercept.

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[John Kirwan]

OK, thank you for your help.