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I'm trying to fit a GLM on my dataset which consists of soil respiration data (RS), soil temperature (TEMP), soil water content (SWC), biomass (BIOM), day of the year when the sampling was done (DOY) and the vegetation type (grasslands, old fields, ploughland and oversewn grassland). The measurement was done along a 15 m long circular transsect of consecutive quadrats, in every 20 cm, so there are 75 measurements in a transsect.

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The question is the relationship between soil respiration (RS) and the other variables (SWC, TEMP, BIOM, DOY and type of vegetation) so how the changes of the related variables influence soil respiration (e.g. if the temperature is increasing, will soil respiration also increase?). I am thinking about a model like this: glm(RS~SWC+TEMP+DOY+type).

The values of RS, TEMP and DOY are all above zero, but SWC and BIOM have zero values, and there are NAs in the BIOM variable. None of the variables are normally distributed and there is an order of magnitude difference between the variables.

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How can I decide which family to use?

Thank you for the suggestions!

Edit: boxplot and histogram of the variables

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Related question: Do I need to transform my variables for GLM?

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    $\begingroup$ What is your research question? $\endgroup$ Nov 24, 2022 at 10:47
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    $\begingroup$ OK, so what does RS look like? What is its domain and distribution? Can you show some plots? $\endgroup$ Nov 24, 2022 at 10:59
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    $\begingroup$ The choice of family is much less crucial than the choice of link which here surely starts with trying logarithms. On the face of it your measurements are for a Northern Hemisphere summer or a Southern Hemisphere winter, but I agree with @StephanKolassa that using sines and cosines of something like (doy - 0.5) / (365 or 366) is natural to tackle seasonality. As a geographer I do know what a transect is; your present set-up implies that you are treating different sites on your transect as independent replicates, and whether that is a sound idea is an open question. $\endgroup$
    – Nick Cox
    Nov 24, 2022 at 11:52
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    $\begingroup$ The distributions of the predictors (covariates) have no bearing on choice of GLM family. Whether they need transformation on other grounds is a different question. $\endgroup$
    – Nick Cox
    Nov 24, 2022 at 11:54
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    $\begingroup$ Please add new information in comments as an edit to the post! Especially the research question should be prominent at the beginning of the post! We want posts to be self-contained, comments are easily overseen (especially when there are so many as with this post=, and they can be deleted $\endgroup$ Nov 24, 2022 at 13:16

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Your dependent variable RS could likely be handled with a log transformation or modeled as conditionally Gamma-distributed.

In this case, there would be a question with how to handle zero values. One thing to consider is if these values are actually zero, or if they are simply below some nominal detection level. I imagine that soil respiration in a natural system would unlikely to be precisely zero, but there could be situations where this is true. One approach for left-censored data is to simply substitute small values for zero values. It's clear that the zeros account for a relatively small proportion of your observations. You might see section 4.7 in the USEPA document below for some simple guidelines for substituting values for observations below the detection limit.

Also, ordinary least squares (OLS) regression may work for your situation. You might construct the model and examine the residuals. It may be that RS is close enough to conditionally normal for this to work fine.

The question as to whether to transform other variables is a separate question.

USEPA. 2000. Guidance for Data Quality Assessment: Practical Methods for Data Analysis, EPA QA/G-9, QA00 Update. https://www.epa.gov/sites/default/files/2015-06/documents/g9-final.pdf

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