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by Marco Fortini and Gerardo Gallo The National Institute of Statistics, Italy

European Conference on Quality in Official Statistics 3-6 May, 2010 - Helsinki A mixture model for estimating under-coverage rate in Italian municipal population registers. by Marco Fortini and Gerardo Gallo The National Institute of Statistics, Italy. Q2010 Helsinky 3-6 May 2010.

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by Marco Fortini and Gerardo Gallo The National Institute of Statistics, Italy

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  1. European Conference on Quality in Official Statistics 3-6 May, 2010 - Helsinki A mixture model for estimating under-coverage rate in Italian municipal population registers by Marco Fortini and Gerardo Gallo The National Institute of Statistics, Italy

  2. Q2010 Helsinky 3-6 May 2010 Content of presentation Relationship between Population Census and Population register in Italy Quality and accuracy of population Census results and Population Register (PR) data Analysis of 2001 Population Register’s Undercount (PRU events) at municipality level by using administrative data Findings and solution for next Population Census rounds

  3. Q2010 Helsinky 3-6 May 2010 Census returns and update of population register (1) • Census provides valuable data at a reference day on population size by socio-economic characteristics of usual residents • Population register (PR) is managed at municipality level according to legal framework and it continuously records personal data for administrative use (i.e. to establish identity of individuals or change of legal residence) • Both data sources are affected by coverage and quality problems

  4. Q2010 Helsinky 3-6 May 2010 Census returns and update of population register (2) • Census data could be incorrect due to (undercount) missed people and by duplicates or other erroneous enumerations (over count) • PR is affected by over coverage whenever events of emigrations and deaths do not cause a deletion and by under coverage as far as immigration events and births do not produce a formal registration • Census returns play an important role for PR coverage evaluation and control, since PR can be updated extensively every 10 years as results of the comparison with Census records

  5. Q2010 Helsinky 3-6 May 2010 Register-supported Census: involvements and Proposals Key operational assumptions of register-supported Census: • Over coverage events can be amended during fieldwork operation of the 2011 Census • PR is affected by undercount for those people who usually reside on the territory at the Census reference day without being enlisted into PR • The goal is to evaluate at municipal level an approximate amount of Population Register Undercount (PRU events) on the basis of 2001 Census returns

  6. Q2010 Helsinky 3-6 May 2010 Data description • Data on PRU events are provided by the 8,101 municipal Register Offices (from Oct. 2001 to Dec. 2006) • Local authorities verify and finalise the administrative procedures about persons who were enumerated as usual residents at the Census date being not included into the municipal archive • PRU events refer to people who moved to a current municipality without applying for a formal change of place of residence

  7. Q2010 Helsinky 3-6 May 2010 PRU events according to 2001 Census returns 1,175 Municipalities reporting zero PRU events

  8. Q2010 Helsinky 3-6 May 2010 Immigration rate and population register’s undercount ratio of the larger-size Italian municipalities(over 250,000 inh.)

  9. Q2010 Helsinky 3-6 May 2010 The assumption based on the available evidence!!!! The observed 2001 PRU events could be considered only an underestimate of the whole figure It is unknown the number of municipalities which have updated their PR with accuracy, in efficient manner and quickly • Two sets of municipalities can be expected: • Those updating the PR with accuracy • Those not achieving this task or • fulfilling it only in part and in delay

  10. Q2010 Helsinky 3-6 May 2010 Why do we use Mixture regression modelling? In order to correct the observed PRU events To take into account for underreporting made by municipalities which didn’t properly update their population register (undercount)

  11. Q2010 Helsinky 3-6 May 2010 How Finite Mixture regression models work…? • Average probability density function weighted by distribution functions of the same or different type pg>0 and pg=1 are weights or prior probabilities. By introducing a linear regression model relating to a dependent variable and one or more explicative variables By defining a log-likelihood that can be written as g,g, 2g e pg ….and can be maximized by EM algorithm The best fitting model is selected by means of the Bayesian Information Criterion (BIC)…max of the model likelihood penalised with the product of the model degrees of freedom by the number of municipalities

  12. Q2010 Helsinky 3-6 May 2010 The relationship between PRU events and the explicative variables Municipality population size (POP) and Average annual number of immigrants from 2002 to 2005 (AI0205) are the mostexplicative variables of PRU events (other promising variables have been discarded after preliminary analysis)

  13. Q2010 Helsinky 3-6 May 2010 Best fitting models results in 3 components mixture regression

  14. Q2010 Helsinky 3-6 May 2010 Expected PRU events according to municipal population size

  15. Q2010 Helsinky 3-6 May 2010 Expected PRU events according to geographical area

  16. Q2010 Helsinky 3-6 May 2010 Final remarks This figure remains lower than 2001 Census under coverage survey which estimated 800,000 individuals So the strategy based on register-supported Census could be accomplish without causing trouble for Each municipal Office should provide to Italian National Institute of Statisticsa final balance sheet reporting quality and accuracy information on the maintenance of population archive

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