Hi,
I am seeking your kind advice on the possible statistical distribution of temporal variability of the total biomass measured in the field sites.
Let's say I have 50 grassland plots, whose total biomass were monthly estimated. And then I calculated the temporal variation (by coefficient of variation) of the total biomass in each of the 50 plots. I want to conduct a GLM to explore how environmental variables regulate the temporal variation of the total biomass. Now, I want to know what type of statistical distribution is proper for the response (i.e. temporal variability) in my GLM model. Most of my temporal variability is within the range [0, 1]. Very occasionally, the value will be larger than 1.
Many thanks!
Hi,
In the study of temporal variability is usually estimated seasonal (summer-autumn-winter-spring), interannual or other trends. Time Series Analysis is this a statistical method for solving such problems, but the length of the series should be longer than 15-20 date. If the purpose to assess the dependence on other parameters, you can apply Crosscorrelations - Time Series Analysis.
Answering your question, I think that the law of statistical distribution of temporal variation can be checked in the same way as for any samples. Normality distribution – Shapiro-Wilks test (for sample valid n=3-50), Chi-Square test (for sample valid n>100), Kolmogorov-Smirnov & Lilliefors test and other. If the normal law is not approximated, tests can be performed for other distribution laws (Lognormal, Exponential, Rectangular and other). variability is within the range [0, 1] - that the coefficients of variation were 0-100% ? I think, then on many sites normal distribution will be applicable. However, it is necessary to check with Normality tests.
In addition, this type of data that you describe is a spatial&temporal study. Some patterns can be identified by the results of spatial variation on 50 plots and between them. ANOVA/MANOVA or other statistical methods can be used to jointly analyze temporal and spatial variability.
Hi Denis,
Thank you very much for your kind reply, which is very helpful. I actually calculated the inter-annual temporal variability of the total biomass for each of my field plots (N is around 1000). Then I have the explanatory variable for the field plots. I want to do a Generalized linear (mixed) regression, and the temporal variability will be the response. Although I can examine the normality of my data, the temporal variability is bonded within the range [0, 1], so a normal distribution may be not good for my case. Now, for my model residuals, I think I will try the binomial distribution first, which is always used for proportional data. But anyway, I will try to explore the method you mentioned to test the distribution (binomial or others) of my data.
Cheers,
Qiang
Andrew Paul McKenzie Pegman Many thanks, Andrew. But I cannot figure out how to do it. Could you please tell a little more details.
Dear Qiang,
I just saw your questions today. But I feel you have solved your stuff already.
If the data is not normal and belongs to [0,1], should be "beta distribution". You can check them. By the way, there are some R packages to check data distribution for GLM(or GLMM). One example is tdistrplus package. you can download PDF with title ( tdistrplus: An R Package for Fitting Distributions). Hope it is useful.
Below are some suggestions:
"values must be positive to fit a lognormal distribution"
"values must be positive to fit an gamma distribution"
"values must be in [0-1] to fit a beta distribution"
"values must be positive to fit an Weibull distribution"
"values must be positive to fit an inverse gamma distribution"
"values must be positive to fit a log-logistic distribution"
"values must be positive to fit an inverse Weibull distribution"
"values must be positive to fit a Pareto distribution"
"values must be positive to fit a Pareto distribution"
"values must be positive to fit a log-gamma distribution"
"values must be positive to fit an inverse trans-gamma distribution"
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