[R-sig-ME] Model specification/family for a continuous/proportional response with many zeros
Michael Lawson
mrm|500 @end|ng |rom york@@c@uk
Wed May 19 10:31:46 CEST 2021
Hi Thierry,
I understood after your previous message that a high dispersion parameter
in beta models does not signify overdispersion. Both answers addressed this
misconception in those two links I provided.
I suppose the real answer I am now looking for is - how do I assess the
validity and fit of the model? Are there specifics or assumptions I must
take into account with zero-inflated beta glmms?
Thanks for your help,
Mike
On Tue, 18 May 2021 at 13:57, Thierry Onkelinx <thierry.onkelinx using inbo.be>
wrote:
> Dear Mike,
>
> I think you misread my reply. I never stated that there's something wrong
> with the model. The only "problem" I highlighted was your misconception
> about the "high overdispersion". In this case, a high parameter value
> indicates a low variance, which is what we mostly want to see.
>
> Best regards,
>
> ir. Thierry Onkelinx
> Statisticus / Statistician
>
> Vlaamse Overheid / Government of Flanders
> INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
> FOREST
> Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
> thierry.onkelinx using inbo.be
> Havenlaan 88 bus 73, 1000 Brussel
> www.inbo.be
>
>
> ///////////////////////////////////////////////////////////////////////////////////////////
> To call in the statistician after the experiment is done may be no more
> than asking him to perform a post-mortem examination: he may be able to say
> what the experiment died of. ~ Sir Ronald Aylmer Fisher
> The plural of anecdote is not data. ~ Roger Brinner
> The combination of some data and an aching desire for an answer does not
> ensure that a reasonable answer can be extracted from a given body of data.
> ~ John Tukey
>
> ///////////////////////////////////////////////////////////////////////////////////////////
>
> <https://www.inbo.be>
>
>
> Op di 18 mei 2021 om 12:49 schreef Michael Lawson <mrml500 using york.ac.uk>:
>
>> Dear Thierry,
>>
>> Thanks for the help. So if the dispersion parameter in this model doesn't
>> fit with the beta distribution, are there any alternative approaches I can
>> use?
>>
>> I can't seem to find much information on this elsewhere other than these
>> two threads:
>> https://stats.stackexchange.com/a/451453/233414
>> https://stats.stackexchange.com/a/466951/233414
>>
>> All the best,
>> Mike
>>
>> On Tue, 18 May 2021 at 08:12, Thierry Onkelinx <thierry.onkelinx using inbo.be>
>> wrote:
>>
>>> Dear Mike,
>>>
>>> The zero-inflation is specified on the logit scale. plogis(-1.18) =
>>> 0.235 23.5% zero seems reasonable when reading your story. (Didn't look at
>>> the data).
>>>
>>> You need to look at the definition for the "over"dispersion parameter.
>>> For a beta distribution is \phi with Var(y) = \mu * (1 - \mu) / (\phi + 1)
>>> (see ?glmmTMB::beta_family) Hence a large value of \phi implies a low
>>> variance.
>>>
>>> Best regards,
>>>
>>> ir. Thierry Onkelinx
>>> Statisticus / Statistician
>>>
>>> Vlaamse Overheid / Government of Flanders
>>> INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE
>>> AND FOREST
>>> Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
>>> thierry.onkelinx using inbo.be
>>> Havenlaan 88 bus 73, 1000 Brussel
>>> www.inbo.be
>>>
>>>
>>> ///////////////////////////////////////////////////////////////////////////////////////////
>>> To call in the statistician after the experiment is done may be no more
>>> than asking him to perform a post-mortem examination: he may be able to say
>>> what the experiment died of. ~ Sir Ronald Aylmer Fisher
>>> The plural of anecdote is not data. ~ Roger Brinner
>>> The combination of some data and an aching desire for an answer does not
>>> ensure that a reasonable answer can be extracted from a given body of data.
>>> ~ John Tukey
>>>
>>> ///////////////////////////////////////////////////////////////////////////////////////////
>>>
>>> <https://www.inbo.be>
>>>
>>>
>>> Op ma 17 mei 2021 om 15:45 schreef Michael Lawson <mrml500 using york.ac.uk>:
>>>
>>>> Hi Thierry,
>>>>
>>>> Thank you for your advice and speedy response.
>>>>
>>>> Most of the data is closer to the lower bound (0). e.g. the mean time
>>>> for group A in zone A = 15.1 seconds and group A in zone B = 3.8 seconds.
>>>> However there are a very small number of outliers near the upper bound, the
>>>> largest being 294 out of the 300 seconds (see the attached file if you want
>>>> to look at the data).
>>>>
>>>> I have taken a stab at running a Zero-inflated Beta GLMM using glmmTMB
>>>> in R like so:
>>>>
>>>> betta_mod <- glmmTMB(prop_time ~ group*zone + (1|id),
>>>> family = beta_family(),
>>>> ziformula=~1,
>>>> data = glmm_zone_data)
>>>>
>>>> summary(beta_mod)
>>>>
>>>> *Family: beta ( logit )*
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> *Formula: prop_time ~ group * zone + (1 | id)Zero inflation:
>>>> ~1Data: glmm_zone_data AIC BIC logLik deviance
>>>> df.resid -763.6 -736.3 388.8 -777.6 359Random
>>>> effects:Conditional model: Groups Name Variance Std.Dev. id
>>>> (Intercept) 2.386e-09 4.885e-05Number of obs: 366, groups: id,
>>>> 14Overdispersion parameter for beta family (): 13.1Conditional model:
>>>> Estimate Std. Error z value Pr(>|z|) (Intercept)
>>>> -2.7685 0.1031 -26.844 < 2e-16 ***groupB -0.4455
>>>> 0.1498 -2.975 0.002932 **zonezone_B -0.4179 0.1524 -2.741
>>>> 0.006124 **groupB:zonezone_B 0.8443 0.2190 3.855 0.000116
>>>> ***---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’
>>>> 1Zero-inflation model: Estimate Std. Error z value Pr(>|z|)
>>>> (Intercept) -1.1804 0.1233 -9.575 <2e-16 ***---Signif. codes: 0
>>>> ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1*
>>>>
>>>> Does this look like the correct way of specifying the model? I am a
>>>> little confused about specifying and interpreting the zero-inflation
>>>> component - I have only just begun reading about this.
>>>>
>>>> I noticed that the dispersion parameter is quite high at 13.1. I'm not
>>>> sure if this matters for beta models?. I tried running DHARMa
>>>> simulateResiduals on the model output and got significant deviations in the
>>>> dispersion (<2.2e-16) and KS tests. e.g.
>>>>
>>>> DHARMa::testDispersion(beta_mod)
>>>>
>>>> *DHARMa nonparametric dispersion test via sd of residuals fitted vs.
>>>> simulated*
>>>>
>>>> *data: simulationOutput*
>>>> *ratioObsSim = 1.3612, p-value < 2.2e-16*
>>>> *alternative hypothesis: two.sided*
>>>>
>>>>
>>>>
>>>> Many thanks,
>>>> Mike
>>>>
>>>> On Mon, 17 May 2021 at 13:22, Thierry Onkelinx <
>>>> thierry.onkelinx using inbo.be> wrote:
>>>>
>>>>> Dear Michael,
>>>>>
>>>>> Your data has bounds (lower bound at 0 and upper bound at 300) and you
>>>>> have a lot of data close to a boundary. In such a case, a continuous
>>>>> distribution which ignores those bound is not a good idea. If the time
>>>>> spent outside of both zones is limited, then a long time in zone A excludes
>>>>> a long time in zone B by definition. Then I'd look towards a multinomial
>>>>> distribution. If the time spent outside both zones is dominant, then you
>>>>> can use a zero-inflated beta as you suggested. A zero-inflated gamma might
>>>>> be OK if the data is not too close to the upper boundary. If you are
>>>>> considering zero-inflated beta vs zero-inflated gamma, then you should
>>>>> choose zero-inflated beta IMHO.
>>>>>
>>>>> Best regards,
>>>>>
>>>>> ir. Thierry Onkelinx
>>>>> Statisticus / Statistician
>>>>>
>>>>> Vlaamse Overheid / Government of Flanders
>>>>> INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE
>>>>> AND FOREST
>>>>> Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
>>>>> thierry.onkelinx using inbo.be
>>>>> Havenlaan 88 bus 73, 1000 Brussel
>>>>> www.inbo.be
>>>>>
>>>>>
>>>>> ///////////////////////////////////////////////////////////////////////////////////////////
>>>>> To call in the statistician after the experiment is done may be no
>>>>> more than asking him to perform a post-mortem examination: he may be able
>>>>> to say what the experiment died of. ~ Sir Ronald Aylmer Fisher
>>>>> The plural of anecdote is not data. ~ Roger Brinner
>>>>> The combination of some data and an aching desire for an answer does
>>>>> not ensure that a reasonable answer can be extracted from a given body of
>>>>> data. ~ John Tukey
>>>>>
>>>>> ///////////////////////////////////////////////////////////////////////////////////////////
>>>>>
>>>>> <https://www.inbo.be>
>>>>>
>>>>>
>>>>> Op ma 17 mei 2021 om 13:52 schreef Michael Lawson via
>>>>> R-sig-mixed-models <r-sig-mixed-models using r-project.org>:
>>>>>
>>>>>> Hello,
>>>>>>
>>>>>> I am new to GLMMs and have a dataset where I have two distinct groups
>>>>>> (A
>>>>>> and B) of 7 individuals each. The data consists of repeated
>>>>>> measurements of
>>>>>> each individual where the amount of time spent at either zone_A or
>>>>>> zone_B
>>>>>> is recorded (out of a total time of 300s/observation period). For
>>>>>> most of
>>>>>> the time period the individuals are in neither zone.
>>>>>>
>>>>>> I want to test if group A and group B spend more time in zone A
>>>>>> compared to
>>>>>> zone B (and vice versa).
>>>>>>
>>>>>> Speaking to someone else, they said I should use a Binomial GLMM using
>>>>>> cbind. i.e.
>>>>>> cbind(time_at_zone_A, time_at_zone_B) ~ group + (1| id).
>>>>>>
>>>>>> However, the response variable is continuous (albeit with an upper
>>>>>> bound of
>>>>>> 300 seconds per observation period), so I'm not sure if this is
>>>>>> appropriate?
>>>>>>
>>>>>> Should I convert the response into a proportion and use something
>>>>>> like a
>>>>>> Beta GLMM or else use a continuous (Gamma) GLMM? e.g. something like:
>>>>>> prop_time ~ zone*group + (1|id)
>>>>>>
>>>>>> The data is quite heavily right-skewed and contains a lot of 0's, so
>>>>>> reading around it also looks like I may need to convert these into a
>>>>>> zero-inflated/hurdle model?
>>>>>>
>>>>>> Thank you for any suggestions,
>>>>>> Mike
>>>>>>
>>>>>> [[alternative HTML version deleted]]
>>>>>>
>>>>>> _______________________________________________
>>>>>> R-sig-mixed-models using r-project.org mailing list
>>>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>>>>
>>>>>
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