I am looking for advice/input on how to report results from a beta regression output. My data is bound between 0 and 1, as ratios, and I am looking at a simple relationship between the response variable (D_Ratio), and predictor (body length, or BL) variable which is continuous. I used the betareg function from the betareg package in R.
For example, here is my R output:
Call: betareg(formula = D_Ratio ~ BL, data = wild, link = c("cloglog")) Standardized weighted residuals 2: Min 1Q Median 3Q Max -1.4137 -0.6463 -0.1782 0.3970 2.6160 Coefficients (mean model with cloglog link): Estimate Std. Error z value Pr(>|z|) (Intercept) -2.14147 0.51930 -4.124 3.73e-05 *** BL 0.05252 0.01673 3.139 0.00169 ** Phi coefficients (precision model with identity link): Estimate Std. Error z value Pr(>|z|) (phi)1.9522 0.2969 6.576 4.82e-11 *** Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Type of estimator: ML (maximum likelihood) Log-likelihood: 8.766 on 3 Df Pseudo R-squared: 0.2058 Number of iterations: 13 (BFGS) + 1 (Fisher scoring)
Firstly, I noticed that there are two tables to consider; the coefficients from the mean model link and the coefficients from the precision model. Which coefficients do I report? I am finding different answers in other threads... Right now I am thinking it should be the pseudo R squared, Z value, P value from the mean model...Or does the "Estimate" coefficient term mean something significant, like slope? I ask because I am under the impression that this relationship is not a straight line.
Unfortunately, I am a relatively new R user so if there is a coding issue here, please let me know.