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Problems of transforming scales of life satisfaction Euromodule workshop Berlin, 18-19 October 2002 Sergiu Bălţătescu University of Oradea Life satisfaction Defined as an overall, cognitive evaluation of one's life. A construct generally measured by single direct questions Single scales: two formulation of the questions: – referring to the 'satisfaction with the life one leads’ – referring to 'satisfaction with life-as-a-whole’ Scales with 3, 4, 5 points – with answer categories verbally labeled Scales with 10, 11 and 101 points – represented on a pseudo-graphic scales, – only the extreme values are represented verbally. (Veenhoven, 1993) Why we need knowledge about the transformation of life satisfaction scales ? PRACTICAL REASONS: To homogenize life satisfaction data, in order to compare levels of subjective well-being: – between nations – through time Examples: - compare national life satisfaction means of Euromodule and non-Euromodule countries – make compatible the time-trend of life satisfaction obtained with another survey program (Diagnosis of quality of life 1990-1999) with Euromodule Romania (2003? - Why we need knowledge about the transformation of life satisfaction scales ? THEORETICAL REASONS: – Assess the convergent validity of new measures • Example: results from new international programs (like Euromodule) can be compared with the results of other national surveys which are using different life satisfaction scales. – Analyze through conversion some characteristics of life satisfaction scale used. • Example: which level of measurement can be assessed to life satisfaction scale we use - ordinal or interval ? The initial scale Used in ‘Diagnosis of quality of life’ survey program (ICCV, 1990-1999) (for the analysis was used the 1999 data set) Sample: national, random, around 1200 cases A 5-point simple life satisfaction scale: “Considering the whole situation, how satisfied are you about your daily life? a. Very unsatisfied b.Unsatisfied c.Neither unsatisfied, nor satisfied d.Satisfied e.Very satisfied” See: Mărginean (1991), Zamfir (1992) See also: www.iccv.ro Distribution of the initial variable (Diagnosis of Quality of life 1999) 35,00% 33,30% 31% Mean: 2,71 (under the mean value of the scale) Slightly positively skewed See next the graphic representation of the distribution 30,00% 25,00% 23,40% 20,00% 15,00% 10,80% 10,00% 5,00% 1,30% 0,00% very unsatisfied unsatisfied neither unsatisfied nor satisfied satisfied very satisfied The target scale 11-point pseudo-interval scale Only the extremes are represented verbally Has graphic elements Used in the Euromodule questionnaire See: Delhey, J., P. Bohnke, et al. (2002). Goals for transforming life satisfaction scales A. Convert an ordinal scale into another – Ex: a 5-step life satisfaction scale into an 11-step life satisfaction scale B. Assigning interval values to an ordinal scale – Ex: assign scores for each answers on a 5-step life satisfaction scale, and assess the true (empirical) distance between the categories C. Combining the two approaches Methods for converting an ordinal scale into another 1. Linear (conventional) transformation – the simplest way to convert scales, using an unique formula – used implicitly for homogenizing means of life satisfaction scales in World Database of Happiness (Veenhoven, 1993) 2. Transformation by expert ratings – the analyst, a panel of expert researchers or typical respondents are assigning to each category of the original scale a value (or category) on the target variable • Ex: very unsatisfied-3, somehow satisfied 6, very satisfied - 9 Linear (conventional) transformation Formula used for converting into a 11 point scale Ai - A0 Bi = ___________ x 10 An - A0 where Bi = Transformed value (to 11-point scale) Ai = Value on original scale A0 = Lowest possible score on original scale An = Highest possible score on original scale (Veenhoven, 1993) Examples: For a 5-point Likert scale (assumed with equal intervals, with values from 1 to 5), the transformed values are: 0, 2.5, 5, 7.5, 10 Proprieties: a. formula is designed in such a way that the end-points of the original scale coincide after transformation with the endpoints of the target (010) scale. b. while stretching the scale, the linear transformation preserves the initial distances between the values. That is why it can be used also for transforming scales whose categories are at non-equal distances. See later how useful can be this feature. Ratings of typical respondents Typical respondents: Sample of students from the University of Oradea (N=116) – – – Specialization: Sociology, Social work Sex: Males 14 %, Females: 86 % Age mean: 22 They were asked to rate the categories of the 5-step life satisfaction scale: a. On a graphic scale (10 cm. long). The distance of the signs to the left extremity was measured in cm. b. On a pseudo-interval scale (with graphic elements), as used in the Euromodule questionnaire See right the original questionnaire, in Romanian language 1. În ce loc, pe scala de mai jos, s-ar afla cineva care dă unul din cele 5 răspunsuri la următoarea întrebare? Puneţi câte un x pe scală, acolo unde credeţi că ar corespunde cele 5 răspunsuri. LUÂND ÎN CONSIDERARE ÎNTREAGA SITUATIE, CÂT DE MULŢUMIT SUNTETI DE VIATA DVS. DE ZI CU ZI ? Foarte nemulţumit Nemulţumit Nici nemulţumit, nici mulţumit Mulţumit Foarte mulţumit Total nemulţumit de viaţa de zi cu zi Total mulţumit de viaţa de zi cu zi 2. La ce număr, pe scara de mai jos, s-ar afla cineva care dă unul din cele 5 răspunsuri la următoarea întrebare? Încercuiţi numărul din dreptul scalei care i s-ar potrivi cel mai bine: LUÂND ÎN CONSIDERARE ÎNTREAGA SITUATIE, CÂT DE MULŢUMIT SUNTETI DE VIATA DVS. DE ZI CU ZI ? Total mulţumit Foarte mulţumit Mulţumit Nici nemulţumit, nici mulţumit Nemulţumit Foarte nemulţumit Total nemulţumit Means of the ratings have been calculated and plotted (line from every point to centroid point and regression line included) 8 outliers (7% of ratings excluded from the analysis) The resulted correlation between the mean of ratings on the two scales is high (r = 0.72) Mean ratings on pseudo-interval scale was higher m(Xp)=5.19 m(Xg)=4.94 The assigned values for the categories were calculated as the mean of ratings of each category The resulted ratings: Xp=(0.8; 2.440; 4.628; 6.973; 9.098) on the pseudo-interval scale Xs=(1.16; 2.94; 5.03; 7.15; 9.00) on the graphic scale means of estimations on the peudo-interval scale Ratings of the typical respondents 8,00 m ean_s = 2.01 + 0.64 * m ean_l R-Square = 0.52 7,00 6,00 5,00 4,00 3,00 2,00 3,00 4,00 5,00 6,00 Linear Regression 7,00 means of estimations on the graphic scale Assigning interval values to an ordinal scale 1. 2. Estimation from the observed frequencies and distributional assumption Optimal scoring Estimation from the observed frequencies and distributional assumption Used when researchers assumes that the latent variable has a particular distribution (ex: rectangular, normal) We can consider that observed categories correspond to separate segments under the density function of the latent variables For normal curve, we use a table of areas under the normal curve to estimate the upper & lower boundaries of each segment under the density function. After that, we calculate (or use a table of) the ordinates of the normal curve for the upper and lower boundaries. We substract the valueas and divides the results by a propostion of this category See: Hensler & Stipak (1979) Computing of the estimation from the observed frequencies and distributional assumption 10,8% 33.4% x1 x2 z1 23.4% 31,0% x3 z2 1,3% x4 z3 x5 z4 Z values corresponding areas under the normal curve (-1,61; -0,77; 1,16; 2,49) Ordinates on the normal curve of Z values f(Z)=(0,1092; 0,2966; 0,2036; 0,018) Values of estimates calculated by subtracting ordinate of the lower boundary from the ordinate of the upper boundary and dividing by the proportion of each category xj=(-1,01111; -0,56276; 0,3; 0,793162; 1,384615) Scores linearly transformed to 0-10 scale (0; 1,87145; 5,472708; 7,531217; 10) The optimal scoring method (OSM) The algorithm is rather new (Young et al., 1981). Precursors: Cattell (1962), Allen (1976), Hensler & Stipak (1979) OSM begins with the premise that the problem of obtaining latent interval scores for ordinal variables is inherently insoluble. Thus, we should use scoring systems which maximally simplify the empirical relationship within a set of variable. "Specifically, optimal scores are those which maximize the average inter-item correlation within a set of variables." (Allen, 1976) The problem looks similar to that of maximizing the internal consistency of a set of variables. (calculating the Crombach - coefficient) Regression with optimal scaling Is a version of the optimal scoring method Implemented in SPSS (CATREG algorithm) See Nichols (1995) Represents a variant of linear regression in which the scores for the variables are not given before, but calculated after, in such a way that assures the best fit of the model (maximizing r square) Practically, it stretches the measurement scales of the variables, assigning scores for their categories, to obtain a maximal fitness of the linear regression model, the only constraint being that of the monotonicity of variables. Allows the theoretical model to prevail: if the researcher assumes that one of the variables is interval-level, this variable will be entered in the model as such, and its values will not be changed Used recently for analyzing life satisfaction data (Shen & Lai, 1998) Regression with optimal scaling as a method for transforming life satisfaction scales Source data: Diagnosis of quality of life survey program (ICCV, 1990-1999) (for the analysis was used the 1999 data set) Sample: national, random, 1198 cases Dependent variable: life satisfaction Independent variables: 19 domain satisfaction indicators (ex: satisfaction with family, with the political situation, neighborhood, etc.) Theoretical model: bottom-up Results: The goodness of fit (r square) increases from 0,34 to 0,38 New scores were assigned to life satisfaction indicator categories: (-1,827; -0,665; 0,186; 1,221; 3,729) Scores linearly transformed to 0-10 scale (0; 2,091; 3,623; 5,485; 10) Quantification of life satisfaction (By CATREG algorithm) The algorithm dramatically increases the distance between scores assigned to “satisfied” and “very unsatisfied” categories - to about a half of the amplitude on the target scale (see figure) As a result, the computed mean on 0-11 scale is lower than the means calculated by other methods (see next slide) Possible interpretation: it is very hard (or unusual) to be very satisfied in Romania Indeed, the percent of those who declared themselves being very satisfied is about 1,3 % Transformation results neither very unsatisfied very unsatisfied satisfied unsatisfied nor satisfied satisfied Linear calculation (equalinterval 0-10 scale) Equal-interval 1-9 scale Expert rating-graphic scale Expert rating - pseudo-interval scale Values calculatted assuming normal distribution Quantification by regression with optimal scaling Mean 0 2,5 5 7,5 10 4,27 1 0,8 3 2,4 5 4,6 7 7,0 9 9,1 4,41 4,08 1,2 2,9 5,0 7,1 9 4,45 0 1,9 5,5 7,5 10 4,21 0 2,1 3,6 5,5 10 3,23 Evaluation of the methods: linear transformation Preserves the ratio of initial distances between categories Can be used to transform values assigned to rank-order categories May cause problems because is thus designed that the end-point of the original scale coincide after transformation to the end-points of the target (0-10) scale, when in fact: – The panel of typical respondents assigned the end-points to 1 and 9 – In the surveys using 0-10 scales, the extreme categories are in very few cases chosen It might be recommended to transform values to 1-9 scale, and use scores as if they are on a 0-10 scale Evaluation of the methods: rating by experts Is more complicated to use: we need a separate research to asses the value The ratings tend to be close to the equalinterval assigning on a 0-9 scale (1,3,5,7,9) It is recommended to be used for recent data (we cannot be sure the meaning of categories of life satisfaction is not changing in time) Evaluation of the methods: estimation from the observed frequencies and distributional assumption We cannot always assumes a normal distribution of the life satisfaction variable This works in the case of Romania 1990-1999, where the distribution is close to normal In western European countries, life satisfaction scores are markedly positively skewed (Cummins, 1998) Evaluation of the methods: regression with optimal scaling The value is very dissimilar with the other calculations (in our sample) The calculated optimal scores may differ from a sample to another, as the structure of subjective well being differs There is no guarantee that the final scoring reflects the true measurement level of the dependent variable, or the functional relationship between variables The method is rather new and deserves further tests Limitations The analysis is not exhaustive. 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