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

[Steven Samuels <sjhsamuels@earthlink.net>]

 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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