CNR - Institute of Neuroscience CNR
Institute of Neuroscience


Grade of membership model


The main aim of this study was to apply the Grade of Membership (GoM) model to the World Health Survey (WHS) data in order to summarize the full set of health and health-related variables into a set of easily understandable and meaningful health profiles; and to assign the degree to which an individual belongs to each profile.

The World Health Organization (WHO) conducted the WHS between 2002 and 2004 in 70 countries to provide cross-population comparable data on health, health-related outcomes and risk factors.


The Grade of Membership is a flexible, non-parametric, multivariate method whose aim is to identify K pure types, and it identifies latent health profiles and the degree to which an individual fits these profiles. Briefly, the GoM model presupposes there are K pure types (profiles) to be defined. The study population consists of I individuals with J categorical variables, where the jth variable has Lj response levels. Each Lj response is encoded as a binary variable xijl, so that if xijl is equal to 1 then the ith individual has the lth response to the jth variable. The GoM model estimates two coefficients:

  • λkjl: likelihood of a response l to the jth question by an individual belonging to the kth health pure type;
  • gik: weights quantifying the grade of similarity of the health characteristics of the ith individual with the characteristics of each K pure types.

Finally, assuming independence of individual observations, the likelihood function for the GoM model is:

The parameters are estimated iteratively: the L function is maximized first with λkjl fixed, producing an initial estimate of all gik; then using the obtained gik the L function is maximized to update the λkjl, This process is repeated until convergence, where the parameters are such that within-group homogeneity is maximized and between-group homogeneity is minimized.

Moreover, the optimal number of profiles is established by performing a likelihood ratio test on the change in explanatory power between K and K+1 model. This ratio is Χ2 distributed, with degrees of freedom equal to the difference in the number of parameters to be estimated between models.

Principal findings

The overall dataset (containing 217,472 respondents) was divided into four economic areas based on the World Bank categories: high income, upper middle income, lower middle income and low income. The table below provides a summary of the pure types/health profiles by World Bank category. The components of pure types I (ROBUST) and II (INTERMEDIATE) are very similar across all the categories. Moving from type I to type II resulted in increasing difficulty in some health domains, with respondents more likely reporting "moderate difficulty" (INTERMEDIATE) instead of "no difficulty" (ROBUST) for the given health domain. The third health profile, FRAIL, was again a distinctly lower level of health based on difficulties with the health domains and presence of one or more of the health conditions.

From the graph showed below, it can be noticed that the high and upper-middle economic categories had more respondents in the ROBUST pure type (gik>62%); while the lower-middle and the low income categories had more respondents in the FRAIL pure type (gik equal to 21.8% and 19.2%, respectively). Finally, in the INTERMEDIATE profile a more uniform distribution of the grade of membership scores (gik) across all categories was obtained.

*SRH = self-reported overall health status
**HS = health state determined by level of difficulty with each of the eight health domains
***CC = reported physical and mental health conditions: arthritis, angina pectoris, asthma and depression



Performing these GoM analyses has provided a robust method to reduce and summarize health variables from health surveys. The three obtained health profiles have described concrete levels of health and have identified characteristics of healthy and non-healthy individuals. Moreover, these GoM analyses provide a set of profiles which are easier to interpret and use for decision-making in health policy.


  • Andreotti A, Minicuci N, Kowal P, Chatterji S (2009) Multidimensional profiles of health status: an application of the grade of membership model to the world health survey. PLoS ONE 4:e4426.


WHO-Agreement for performance of work


  • Paul Kowal, Somnath Chatterji, WHO, Switzerland.


PI photo

Nadia Minicuci

Contact information

email  E-mail

email  049 8211226

Participating staff

Alessandra Andreotti