I am exploring some data and and possibilities of quasibinomial GLM. The data is less than perfect. Nonetheless, the target variable can range from 0 till 1 and from my knowledge it seems okay (is it? perhaps there are other options?) to use a quasibinomial GLM. However, visualizing the predictions it seems that oversaturation of values 0.5 pull the model some down (Fig A solid line; if this is the right description). So, it is possible to weigh the values as weight=abs(values-0.5), seemingly improving the visual fit (Fig A dashed lines). Yet, then I am disregarding the 0.5 values and Base R does not return an AIC for the models. So, I am not really sure how to compare the models (besides the residuals Fig B-C). One other option would be to correlate the predicted versus the actual values. Which is higher for the weighted model. Yet, I am completely ignorant to any implications of weighing a quasibinomial model and the implications, and it is relatively difficult to find information on this, while for WLS is.
The questions are:
(1.) Is a quasibinomial GLM reasonable or are there better options?
(2.) Is weighing the GLM reasonable?
(3.) What are the implications of (2.) or are they similar to WLS?
(4.) Is it possible to compare the models by comparing the correlation between predicted and actual values?
Thank you in advance
What is the meaning of the colors in the figure? This may be the key to find an appropriate model.
Given most of values are 0.5 across the whole range of P-PO4, the solid line seems to be the better fit. Why do you want to exclude these (yellow) values?
Quasi-models dont have proper likelihoods. It's therefore impossible to calculate any statistics that is based on the (maximum) likelihood, this is including information criteria (ICs). If you need ICs, you may consider fitting a beta-regression model (library betareg, but as usual there are other way as well, e.g. mgcv or gamlss).
Jochen Wilhelm The topic is a bit confusing. In general and I am struggling with the fact the colours on the y-axis as represent a particular state. So a better option would be ordinal regression or direct classification, of which I prefer the latter. Even though the colours represent classes, regression is normally applied.
The 0.5 is so dominant, around 20%, it seems to reduce the magnitude of the estimate. Not that this is an issue, but I expected the model to follow a more sigmoid like curve, fitting better to the extremes (0 and 1) as it does not really seem to centralize between the points (if this is the correct wording).
In simplicity (the colours), an ecological manager/government goes outside takes samples (species composition) and calculates this EQR(-score) ranging from 0-1, 0-0.2 = "bad", 0.2-0.4="poor", 0.4-0.6="moderate", 0.6-0.8="good", 0.8-1.0="high". These are called ecological states. According to law, everything should be at least "good" or "high", thus > 0.6 (reaching the Good Ecological State; GES). In theory you have five classes, but the actual end goal is two (0.6). The estimates and correlation from a linear model are more convenient than a bit more black-box-like ML model. Yet, the accuracy or Cohen's kappa are also very convenient (e.g. for 5 states the accuracy is only ~25% and Cohen's kappa ~0.1). Indeed, there is a negative relation, but the discriminative power along the gradient is not satisfactory in relation to five states. It all depends a bit on the question managers/government want to answer, which is to me not really clear(???, which is rather funny as there are laws build around this).
Hence, either we are in a particular state, or not, I would like to have some coarse "hypothetical-theoretical" idea (educated guess at least), of how regression relates to classification; and how how this "hypothetical-theoretical" idea relates to practical applications, as the question from a management perspective is not really clear perhaps some pragmatic example might help. I find it always a bit sad most models are seen as a tool with a means to an end so I feel to somehow bring it a bit more pragmatic (perhaps wrong).
P.S. I also tried a beta regression, but the only way to perform this is by setting 0 = 0.01 and 1 = 0.99, which I don't think is correct. The intercept and estimate are the same as for the quasibinomial.
I see. I also think that a beta-regression (or quasi-binomial) is ok. And that there should not be any weighting, unless you have external grounds to down-weight. I don't think it is ok to down-weight values close to 0.5 just because they are close to 0.5.
Yes, the beta-regression model cannot handle 0 and 1 values. If such values are present, you could go for an inflated beta regression model (zero- and one-inflated) that can handel such values. This is provided in gamlss with the family BEINF. However, I think is is way too complicated just to get a likelihood. I'd stay with the quasi-binomial model. The result is, presumably, that the relation between P-PO4 and score is not conclusive (or very uncertain).
- Badges
- Science topic
- Similar topics
- Computer Communications (Networks)
- Simulators