Adding an asymptote to a linear model of the kappa parameter of a von Mises distribution

[John Kirwan]

Dear google-group users,

I am trying to estimate both circular mean (mu) and the precision (kappa) of a circular outcome according to a von Mises distribution with respect to an effect on a linear scale.Both a slope and intercept are estimated for each of mu and kappa, as follows:

 

m1.formula <- bf(radians_error ~ polarization_logged,

kappa ~ polarization_logged) + von_mises()

 

 I am mostly interested in the kappa and I wish to introduce an asymptote parameter into the linear equation for kappa, as follows:

                             kappa ~ polarization_logged + lower_asymptote,

                             lower_asymptote ~ 1)

 

Is this possible for an auxiliary parameter in the brms framework?

Kind regards,

John Kirwan

[Paul Buerkner]

can you explain the purpose of such a parameter for your model?

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[John Kirwan]

I  think that the circular concentration should only scale with the predictor for a range of predictor values (above and below which it should be constant). I would like to add a lower limit to better model the lower values of the predictor. 

[Paul Buerkner]

So you want to use a non-linear model for kappa? That's possible. For this to work, you have to wrap the formula for kappa as well as the related formulas in a call to nlf().

2018-04-11 7:17 GMT+02:00 John Kirwan <jo...@jkirwan.org>:

I  think that the circular concentration should only scale with the predictor for a range of predictor values (above and below which it should be constant). I would like to add a lower limit to better model the lower values of the predictor. 

On Wed, Apr 11, 2018, 5:14 AM Paul Buerkner <paul.b...@gmail.com> wrote:

can you explain the purpose of such a parameter for your model?

John Kirwan <jo...@jkirwan.org> schrieb am Mo., 9. Apr. 2018, 14:48:

Dear google-group users,

I am trying to estimate both circular mean (mu) and the precision (kappa) of a circular outcome according to a von Mises distribution with respect to an effect on a linear scale.Both a slope and intercept are estimated for each of mu and kappa, as follows:

 

m1.formula <- bf(radians_error ~ polarization_logged,

kappa ~ polarization_logged) + von_mises()

 

 I am mostly interested in the kappa and I wish to introduce an asymptote parameter into the linear equation for kappa, as follows:

                             kappa ~ polarization_logged + lower_asymptote,

                             lower_asymptote ~ 1)

 

Is this possible for an auxiliary parameter in the brms framework?

Kind regards,

John Kirwan

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[John Kirwan]

Thank you very much for your kind help. One difficulty I have is that when I attempt use the non-linear formulation, as follows:

formula  <- bf( radians ~ polarization, 

                  kappa ~ gamma +  polarization ,

                  gamma ~ 1) + set_nl(TRUE) +

                  von_mises(link = "tan_half", link_kappa = "identity")

brm throws an error: "Error: Some non-linear parameters are missing in formula: 'gamma'" or ... " non-numeric argument to binary operator" if I use nlf()  Is there something obviously incorrect with my syntax?

Kind regards,

John

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[Paul Buerkner]

with you showing me the nlf() code i obviously cannot tell whats going wrong.

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[Paul Buerkner]

try out

bf (radians ~ polarization) + nlf(kappa ~ gamma + polarization, gamma ~ 1)

but keep in mind how nonlinear formulas are evaluate in brms.

John Kirwan <jo...@jkirwan.org> schrieb am Mi., 11. Apr. 2018, 08:08:

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[John Kirwan]

Thank you, this has worked.

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