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Re: st: Bounded dependent variable by ordered categories of independent in survey setting


From   Steven Samuels <[email protected]>
To   [email protected]
Subject   Re: st: Bounded dependent variable by ordered categories of independent in survey setting
Date   Fri, 16 Jan 2009 15:30:46 -0500

 Ángel,

1. Your data are not just skewed, but very patchy, with most at 1.0. The patchiness and negative numbers make the data set a poor candidate for -betafit-, in my opinion. (The authors might disagree!)

I recommend -svy: reg- to estimate the mean score as a function of your ordered variable X. To find a good trend model, do standard plots and checks.

2. Over 77% of respondents had scores > 0.76, but there were no scores> 0.80 except 1.0. Thus 1.0 is separated from other scores by gap of nearly 20% of the range of scores. This raises the possibility that a score of 1.0 is qualitatively, not just quantitatively, different from lesser scores. Consider a separate analysis of the proportion of scores which were 1.0 (-svy: logit-) and of those < 1.0 (-svy: reg-).

3. You might even combine the separate analyses with -suest-. Let M(Y| X,*) be the predicted mean for category X from the regression of Y on X, for Y<1. Then, the predicted mean for category X would be: E(Y|X) = P(Y=1|X) + [(1-P(Y=1|X)) x M(Y|X,*).

-Steve

On Jan 15, 2009, at 6:57 AM, Ángel Rodríguez Laso wrote:

Dear Statalisters,

I'm working with survey data with strata, clusters and
finite-population-correction variables and Stata 9.1 version.

I want to compare a continuous variable (quol) across ordered levels
of a categorical variable. quol is a measure of health related quality
of life from the Euroquol scale (social tariff), where values are
bounded between 0 and 1 (in fact, some few can be negative). It is not
a proportion, but the highest score you can get in the scale is 1. I
copy the distribution of quol (sorry, I haven't been able to
copy-paste the histogram): It is very  left skewed, with a
discontinuity between 0.8 and 1.

tab quol

Calidad de	
vida	
(Euroquol-t	
arifa	
social)	Freq.	Percent	Cum.
			
-,0757	6	0,05	0,05
-,0245	4	0,03	0,08
-,0161	3	0,02	0,11
,014	3	0,02	0,13
,0255	1	0,01	0,14
,0267	10	0,08	0,22
,0351	5	0,04	0,27
,0435	1	0,01	0,27
,0652	8	0,07	0,34
,0767	2	0,02	0,36
,0806	2	0,02	0,37
,0863	7	0,06	0,43
,0947	7	0,06	0,49
,1037	1	0,01	0,50
,1152	2	0,02	0,51
,1164	10	0,08	0,60
,1203	2	0,02	0,61
,1248	13	0,11	0,72
,1279	1	0,01	0,73
,1318	3	0,02	0,75
,1332	1	0,01	0,76
,1413999	1	0,01	0,77
,1459	12	0,10	0,87
,1664001	8	0,07	0,94
,1703	49	0,41	1,34
,1715	1	0,01	1,35
,1748	1	0,01	1,36
,176	6	0,05	1,41
,1799	4	0,03	1,44
,1838	1	0,01	1,45
,1844	1	0,01	1,46
,1869	1	0,01	1,47
,1875	1	0,01	1,48
,1959	1	0,01	1,48
,2009999	1	0,01	1,49
,2049	2	0,02	1,51
,2061	1	0,01	1,52
,2176	15	0,12	1,64
,2215	46	0,38	2,02
,2229	1	0,01	2,03
,2254	2	0,02	2,05
,2260001	6	0,05	2,10
,2299	7	0,06	2,16
,2311	1	0,01	2,16
,233	1	0,01	2,17
,235	1	0,01	2,18
,2356	10	0,08	2,26
,2369	1	0,01	2,27
,2426	2	0,02	2,29
,2471	1	0,01	2,30
,2561	1	0,01	2,31
,26	3	0,02	2,33
,2645	3	0,02	2,36
,2657	1	0,01	2,36
,2676001	3	0,02	2,39
,2715	23	0,19	2,58
,2727	43	0,36	2,94
,2766001	2	0,02	2,95
,2772	11	0,09	3,04
,2842	1	0,01	3,05
,2856001	3	0,02	3,08
,2881	2	0,02	3,09
,2895	1	0,01	3,10
,2946	1	0,01	3,11
,2965	1	0,01	3,12
,3022	1	0,01	3,13
,3061	5	0,04	3,17
,3112	7	0,06	3,23
,3157001	2	0,02	3,24
,3188	4	0,03	3,28
,3196	1	0,01	3,28
,3227	52	0,43	3,72
,3253	2	0,02	3,73
,3266	15	0,12	3,86
,3272001	2	0,02	3,87
,3278	8	0,07	3,94
,3292	1	0,01	3,95
,3311	6	0,05	4,00
,3368	8	0,07	4,06
,3393	3	0,02	4,09
,3477	1	0,01	4,10
,3573	1	0,01	4,10
,3612	12	0,10	4,20
,3624	3	0,02	4,23
,3663	1	0,01	4,24
,3739	55	0,46	4,69
,3747	1	0,01	4,70
,3753	2	0,02	4,72
,3778	52	0,43	5,15
,3784	2	0,02	5,17
,3862	17	0,14	5,31
,3907	3	0,02	5,33
,3989	1	0,01	5,34
,4085	1	0,01	5,35
,4124	19	0,16	5,51
,4163	40	0,33	5,84
,4175	4	0,03	5,87
,4208	7	0,06	5,93
,4253	1	0,01	5,94
,4265	1	0,01	5,95
,429	84	0,70	6,64
,4355	1	0,01	6,65
,438	1	0,01	6,66
,4458	3	0,02	6,68
,4585	13	0,11	6,79
,4636	13	0,11	6,90
,4675	90	0,75	7,65
,4681	3	0,02	7,67
,4759	55	0,46	8,13
,4765	2	0,02	8,14
,493	64	0,53	8,67
,5187	182	1,51	10,18
,5277	2	0,02	10,20
,5355	37	0,31	10,51
,5442	78	0,65	11,15
,5481001	5	0,04	11,19
,5526	16	0,13	11,33
,5827	8	0,07	11,39
,5942	68	0,56	11,96
,5993	17	0,14	12,10
,6038	31	0,26	12,36
,6077	2	0,02	12,37
,6339	12	0,10	12,47
,6378	3	0,02	12,50
,6423	2	0,02	12,51
,6454	104	0,86	13,38
,6493	116	0,96	14,34
,6538	8	0,07	14,40
,6589	9	0,07	14,48
,6839	30	0,25	14,73
,689	8	0,07	14,79
,6935	9	0,07	14,87
,6974	1	0,01	14,88
,7005	307	2,55	17,42
,705	26	0,22	17,64
,7089	26	0,22	17,85
,7351	50	0,41	18,27
,739	406	3,37	21,64
,7435	5	0,04	21,68
,7486	18	0,15	21,83
,7601	149	1,24	23,06
,7902	1.459	12,10	35,16
,7947	44	0,36	35,53
,7986	434	3,60	39,12
1	7.341	60,88	100,00
			
Total	12.059	100,00


Initially, the analysis would ask for one-way ANOVA (unless skewness
and non-homogeneity of variances can be a problem here) but, in any
case, I don't see tha ANOVA or -kwallis- is supported by -svy-
commands.

-Svy: regress- could be an alternative, inserting the independent
variable without dummies and assessing its significance (strong
skewness can be problematic, too). Nevertheless,  I've read in
previous posts (http://www.stata.com/statalist/archive/2004-10/ msg00169.html)
that for bonded 0-1 dependent variables, -glm family(binomial)- or
-betafit- are recommended (although I'm not sure if this applies only
to dependent variables which are proportions, which is not the case).

My questions are:

1) In a non-survey setting, do -glm- or -betafit- have to be used when
the dependent variable is not a proportion but is bounded between 0
and 1? By the way, would you recommend any introductory text
explaining this approach?

2) Can these two approaches be used in survey settings?

3) Any recommendation in case the answer to 1 or 2 is "no"?

Many thanks,

Angel Rodriguez-Laso
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