# What causes the parameter phi (precision) to be very small in beta regression (by betareg in R)?

I tried to do a beta regression for a variable affected by age and intimacy, but it did not work well. The value of phi (precision) estimated by maximum likelihood method is very small, and when I actually draw the estimated distribution, I don't think it is modeling well. What could be the cause? Or is there any other better regression model?

I am thinking that maybe it is because there are too few variations in the explanatory variables, but I am not sure.

Here is a summary of my trial.

data(n=128):

y: the dependent variable

x_1: an explanatory variable of "age-group"

x_2: an explanatory variable of "Intimacy-level"

(the full data shown at the bottom)

code:

betareg(y ~ x_1 + x_2, data = data)

result:

Mu Coefficients (mean model with logit link):

Estimate
(intercept) -3.17
x_1 1.12
x_2 0.12

Phi coefficients (precision model with identity link):

Estimate
(phi) 0.74

data(full):

        y x_1 x_2
1   0.999   4   0
2   0.999   4   0
3   0.500   4   0
4   0.999   4   0
5   0.999   4   0
6   0.999   4   0
7   0.999   4   0
8   0.999   4   0
9   0.999   4   0
10  0.999   4   0
11  0.500   4   0
12  0.999   4   0
13  0.999   4   0
14  0.999   4   0
15  0.500   4   0
16  0.500   4   0
17  0.999   4   1
18  0.999   4   1
19  0.500   4   1
20  0.999   4   1
21  0.999   4   1
22  0.999   4   1
23  0.999   4   1
24  0.999   4   1
25  0.999   4   1
26  0.999   4   1
27  0.999   4   1
28  0.999   4   1
29  0.999   4   1
30  0.999   4   1
31  0.500   4   1
32  0.999   4   1
33  0.500   3   1
34  0.999   3   1
35  0.001   3   1
36  0.999   3   1
37  0.999   3   1
38  0.001   3   1
39  0.999   3   1
40  0.999   3   1
41  0.500   3   1
42  0.500   3   1
43  0.500   3   1
44  0.500   3   1
45  0.999   3   1
46  0.500   3   1
47  0.001   3   1
48  0.500   3   1
49  0.500   3   1
50  0.999   3   1
51  0.500   3   1
52  0.999   3   1
53  0.999   3   1
54  0.001   3   1
55  0.999   3   1
56  0.999   3   1
57  0.500   3   1
58  0.500   3   1
59  0.999   3   1
60  0.999   3   1
61  0.999   3   1
62  0.999   3   1
63  0.001   3   1
64  0.999   3   1
65  0.001   2   1
66  0.500   2   1
67  0.001   2   1
68  0.001   2   1
69  0.001   2   1
70  0.001   2   1
71  0.500   2   1
72  0.001   2   1
73  0.001   2   1
74  0.001   2   1
75  0.001   2   1
76  0.001   2   1
77  0.001   2   1
78  0.001   2   1
79  0.001   2   1
80  0.001   2   1
81  0.001   2   1
82  0.500   2   1
83  0.001   2   1
84  0.001   2   1
85  0.001   2   1
86  0.001   2   1
87  0.500   2   1
88  0.001   2   1
89  0.001   2   1
90  0.001   2   1
91  0.001   2   1
92  0.001   2   1
93  0.001   2   1
94  0.001   2   1
95  0.001   2   1
96  0.001   2   1
97  0.001   1   1
98  0.500   1   1
99  0.001   1   1
100 0.001   1   1
101 0.001   1   1
102 0.001   1   1
103 0.001   1   1
104 0.001   1   1
105 0.001   1   1
106 0.001   1   1
107 0.001   1   1
108 0.001   1   1
109 0.001   1   1
110 0.001   1   1
111 0.001   1   1
112 0.001   1   1
113 0.001   1   1
114 0.500   1   1
115 0.001   1   1
116 0.001   1   1
117 0.001   1   1
118 0.001   1   1
119 0.001   1   1
120 0.001   1   1
121 0.001   1   1
122 0.001   1   1
123 0.001   1   1
124 0.001   1   1
125 0.001   1   1
126 0.001   1   1
127 0.001   1   1
128 0.001   1   1

• How is y measured?
– whuber
Apr 18 at 15:46
• Y is the value of the grammaticality judgment for a given language form. As in my reply to Luka, actually, it was originally a 3-step count data, and now I was able to get good results with the normal logistic model (binominal-logit). Apr 18 at 22:12

Your $$Y$$ only takes the value $$0.001, 0.5$$ and $$0.999$$. That is not a good fit a beta-Regression which models a continuum of proportions. Also 0.5 to 0.999 is a huge spread, so the precision has to be low.
• @TomoChang So you have 3 binomial measures for each of your 128 "language forms"? If so you should probably introduce a random effect (1|form) to account for the correlation among those 3 measures. Relevant help: bbolker.github.io/mixedmodels-misc/glmmFAQ.html Apr 19 at 9:28