[R-sig-ME] Assessing linearity

[Mike Lawrence]

Ah, this looks promising! So how does this sound:

I typically assess the evidence for a relationship between the
predictor and response variables by comparing the AIC values for a
model including the predictor to a model without it. In the case of
grade_as_numeric, I'd do:

fit_null = lmer(
    formula = response ~ (1|individual)
    data = my_data
)
fit_null_AIC = AIC(fit_null)

fit_alt = lmer(
    formula = response ~ (1|individual) + grade_as_numeric
    data = my_data
)
fit_alt_AIC = AIC(fit_alt)

grade_loglikratio = fit_null_AIC - fit_alt_AIC

Now, if I wanted to check whether there is a quadratic component to
the grade effect, I'd first compute an analogous likelihood ratio for
the quadratic fit compared to the null:
fit_alt_quad = lmer(
    formula = response ~ (1|individual) + poly(grade_as_numeric)^2
    data = my_data
)
fit_alt_quad_AIC = AIC(fit_alt_quad)
grade_quad_loglikratio = fit_null_AIC - fit_alt_quad_AIC

Then compute a final log likelihood ratio between the improvement over
the null caused by grade versus the improvement over the null caused
by grade as a quadratic:

grade_lin_vs_quad_LLR = grade_loglikratio - grade_quad_loglikratio

I could repeat this for higher-order polynomials of grade, each
compared to the order directly below it, to develop a series of
likelihoood ratios that describe the relative improvement of the fit.

Does this sound appropriate?

Cheers,

Mike

--
Mike Lawrence
Graduate Student
Department of Psychology
Dalhousie University

Looking to arrange a meeting? Check my public calendar:
http://tr.im/mikes_public_calendar

~ Certainty is folly... I think. ~



On Sun, Oct 24, 2010 at 6:41 AM, Jarrod Hadfield <j.hadfield at ed.ac.uk> wrote:
> Hi Mike,
>
> You would be better off trying out something like polynomials or splines,
> For example:
>
>  fit1 = lmer(
>     formula = response ~ (1|individual)+poly(grade_as_numeric,n),
>     , data = my_data
>     , family = gaussian
>  )
>
> where n is the order of the polynomial. n=1 would fit the same model as your
> original fit1, although the covariate (and the regression parameter) would
> be scaled by some number. When n=6 the model would be a reparameterised
> version of your model fit2. When 1<n<6 you would be working with a
> non-linear relationship in between these two extremes, although the model is
> still linear in the parameters.
>
> Cheers,
>
> Jarrod
>
>
>
>
>
>
>
>
> Quoting Mike Lawrence <Mike.Lawrence at dal.ca>:
>
>> Hi folks,
>>
>> I have developmental data collected across several grades (1-6). I
>> would like to be able to assess whether there are any linear or
>> non-linear trends across grade. Does it make sense to run a first lmer
>> treating grade as continuous, obtain the residuals, then run a second
>> lmer treating grade as a factor? That is:
>>
>> fit1 = lmer(
>>    formula = response ~ (1|individual)+grade_as_numeric
>>    , data = my_data
>>    , family = gaussian
>> )
>> my_data$resid = residuals(fit1)
>> fit2 = lmer(
>>    formula = resid ~ (1|individual)+grade_as_factor
>>    , data = my_data
>>    , family = gaussian
>> )
>>
>>
>> As I understand it, fit1 will tell me if there are any linear trends
>> in the data, while fit2 will tell me if there are any non-linear
>> trends in the data in addition to the linear trends obtained in fit1.
>>
>> If this is sensible, how might I apply it to a second binomial
>> response variable given that the residuals from a binomial model are
>> not 0/1?
>>
>> Cheers,
>>
>> Mike
>>
>> --
>> Mike Lawrence
>> Graduate Student
>> Department of Psychology
>> Dalhousie University
>>
>> Looking to arrange a meeting? Check my public calendar:
>> http://tr.im/mikes_public_calendar
>>
>> ~ Certainty is folly... I think. ~
>>
>> _______________________________________________
>> R-sig-mixed-models at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>
>>
>
>
>
> --
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> Scotland, with registration number SC005336.
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