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Dietro ogni problema c'e' un'opportunita'   Galileo Galilei

Research interests

My research mainly considered random effects models for multilevel analysis, with methodological advances concerning the specification and estimation of models in complex frameworks such as duration data, multivariate qualitative responses, informative sampling designs, and sample selection bias. I also investigated methods for causal inference in the potential outcomes framework, dealing with truncation and partial compliance. In the recent research activity, I considered a variety of statistical methods including IRT models, latent growth curve models, mixture models, and quantile regression. The methodological work is typically driven by applications on real data in different fields including economics, demography, medicine, and bibliometrics.


PAPERS BY YEAR (full-texts available on Research Gate)


Grilli L., Marino F.M., Paccagnella O., Rampichini C. (2020). Multiple imputation and selection of ordinal level 2 predictors in multilevel models. An analysis of the relationship between student ratings and teacher beliefs and practices. Statistical Modelling. DOI: 10.1177/1471082X20949710


Hasa E., Grilli L. (2019) Analysis of the prediction ability of a university self-evaluation test: statistical learning methods for predicting student performance. Statistica Applicata - Italian Journal of Applied Statistics, Vol. 31 (2), pp. 201-213. DOI: 10.26398/IJAS.0031-011

Grilli L., Rampichini C. (2019). Discussion of "The class of CUB models: statistical foundations, inferential issues and empirical evidence" by Domenico Piccolo and Rosaria Simone. To appear in Statistical Methods and Applications. DOI: 10.1007/s10260-019-00466-w    text view-only version


Grilli L., Rampichini C. (2018). A handful of critical choices in multilevel modelling. Boletin de Estadistica e Investigacion Operativa, Vol. 34, No. 1.

Grilli L., Panzera A., Rampichini C. (2018) Clustering Upper Level Units in Multilevel Models for Ordinal Data. In: Mola F., Conversano C., Vichi M. (Eds.) Classification, (Big) Data Analysis and Statistical Learning, Springer. pp 137-144. DOI: 10.1007/978-3-319-55708-3_15


Bacci S., Bartolucci F., Grilli L., Rampichini C. (2017) Evaluation of student performance through a multidimensional finite mixture IRT model. Multivariate Behavioral Research. 52(6): 732-746.  DOI: 10.1080/00273171.2017.1361803 Draft at

Grilli L., Innocenti F. (2017) Fitting logistic multilevel models with crossed random effects via Bayesian Integrated Nested Laplace Approximations: a simulation study. Journal of Statistical Computation and Simulation, 87:14, 2689-2707, DOI: 10.1080/00949655.2017.1341886

Barletta V., Profili F., Gini R., Grilli L., Rampichini C., Matarrese D., Francesconi P. (2017) Impact of Chronic Care Model on diabetes care in Tuscany: a controlled before-after study. European Journal of Public Health. 27(1):8-13. doi:10.1093/eurpub/ckw189


Grilli L., Pennoni F., Rampichini C., Romeo I. (2016) Exploiting TIMSS and PIRLS combined data: multivariate multilevel modelling of student achievement. The Annals of Applied Statistics, 10 (4), pp. 2405-2426.  Open access on the journal web page

Grilli L., Rampichini C. & Varriale R. (2016) Statistical modelling of gained university credits to evaluate the role of pre-enrolment assessment tests: an approach based on quantile regression for counts. Statistical Modelling. 16, pp 47-66, DOI: 10.1177/1471082X15596087    draft     Dataset and Stata code to replicate the analysis: Dataset   Stata do-file

Abramo G., D'Angelo C.A. & Grilli L. (2016) From rankings to funnel plots: The question of accounting for uncertainty when assessing university research performance. Journal of Informetrics. 10 (3), pp 854-862, DOI: 10.1016/j.joi.2016.07.005


Abramo G., D`Angelo C.A., Grilli L. (2015) Funnel plots for visualizing uncertainty in the research performance of institutions. Journal of Informetrics. 9 (4) pp 954-961. DOI:10.1016/j.joi.2015.08.006

Grilli L., Rampichini C. & Varriale R. (2015) Binomial mixture modelling of university credits. to appear in Communications in Statistics - Theory and Methods.  44(22), pp 4866-4879. DOI:10.1080/03610926.2013.804565    draft     Dataset and R code (using `flexmix`) to replicate the analysis: Dataset   R script (`flexmix` package)

Mauro V., Biggeri M., Grilli L. (2015) Does community-based rehabilitation enhance the multidimensional well-being of deprived persons with disabilities? A multilevel impact evaluation. World Development, 76, pp 190-202. DOI: 10.1016/j.worlddev.2015.07.004

Grilli L., Rampichini C. (2015) Specification of random effects in multilevel models: a review. Quality & Quantity, 49 (3), pp 967-976. DOI: 10.1007/s11135-014-0060-5    draft  

Grilli L., Metelli S., Rampichini C. (2015) Bayesian estimation with INLA for logistic multilevel models. Journal of Statistical Computation and Simulation.  85(13), pp 2718-2726. DOI: 10.1080/00949655.2014.935377    draft


Grilli L., Varriale R. (2014) Specifying Measurement Error Correlations in Latent Growth Curve Models with Multiple Indicators. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences. Vol 10(4), pp 117-125  DOI:10.1027/1614-2241/a000082  draft   Dataset and R scripts (`OpenMx` package) 

Grilli L. & Rampichini C. (2014) Ordered logit model. In: Michalos AC (Ed.). Encyclopedia of Quality of Life and Well-Being Research. Dordrecht, Netherlands: Springer, pp 4510-4513. ISBN 978-94-007-0752-8.    draft

Grilli L., Iannario M., Piccolo D., Rampichini C. (2014) Latent Class CUB Models. Advances in Data Analysis and Classification, 8(1), pp 105-119. DOI 10.1007/s11634-013-0143-5. link   draft


Bertaccini B., Grilli L., Rampichini C. (2013) An IRT-MIMIC model for the analysis of university student careers. QdS - Journal of Methodological and Applied Statistics, 15, pp. 95-110   draft

Visca M. et al. (2013) Group versus single handed primary care: A performance evaluation of the care delivered to chronic patients by Italian GPs. Health Policy, 113 (1) pp 188-198 doi:10.1016/j.healthpol.2013.05.016. (full list of authors: Modesta Visca, Andrea Donatini, Rosa Gini, Bruno Federico, Gianfranco Damiani, Paolo Francesconi, Leonardo Grilli, Carla Rampichini, Gabriele Lapini, Carlo Zocchetti, Francesco Di Stanislao, Antonio Brambilla, Fulvio Moirano, Donata Bellentani)

Francavilla F., Giannelli G.C. & Grilli L. (2013) Mothers` Employment and their Children`s Schooling: A Joint Multilevel Analysis for India. World Development, 41, pp. 183-195.     draft    gllamm code to fit the model  [this paper was previously published as DSE Working Paper 7/2010 and IZA Discussion Paper No. 3531 and ChilD Working Paper n. 07/2008]

Bini M., Grilli L., Rampichini C. (2011) Contextual factors of the external effectiveness of the university education: a multilevel approach. Statistica Applicata - Italian Journal of Applied Statistics.  23(1), pp. 51-65.  Download paper


Bartolucci F. , Grilli L., Pieroni L. (2012) Estimating dynamic causal effects with unobserved confounders: a latent class version of the inverse probability weighted estimator. MPRA Paper No. 43430.  

Grilli L. (2012) Un  paradosso statistico: l`effetto Will Rogers. Sis-Magazine - Online Magazine della Società Italiana di Statistica. Inserito il 24 ottobre 2012.

Grilli L. & Rampichini C. (2012) Multilevel models for ordinal data. In: Kenett R and Salini S (eds.) Modern Analysis of Customer Surveys: with Applications using R. Chapter 19. Wiley. ISBN: 978-0-470-97128-4.   draft   Dataset and R script (`ordinal` package)

Samuh M., Grilli L., Rampichini C., Salmaso L., Lunardon N. (2012) The use of permutation tests for variance components in linear mixed models. Communications in Statistics - Theory and Methods, Volume 41, Issue 16-17, pages 3020-3029. DOI:10.1080/03610926.2011.587933


Sani C. & Grilli L. (2011) Differential variability of test scores among schools: a multilevel analysis of the fifth-grade Invalsi test using heteroscedastic random effects. Journal of Applied Quantitative Methods  Volume 6, Issue 4.    slides   paper

Bartolucci F. & Grilli L. (2011) Modelling partial compliance through copulas in a principal stratification framework. Journal of the American Statistical Association, 106, pp. 469-479. DOI: 10.1198/jasa.2011.ap09094.   paper     slides

Grilli L. & Rampichini C. (2011) The role of sample cluster means in multilevel models: a view on endogeneity and measurement error issues. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences. Vol. 7(4):121-133. DOI: 10.1027/1614-2241/a000030    paper   [previously published as Working papers 6/2009]

Grilli L. (2011) Causal inference through principal stratification: a special type of latent class modelling. In: Fichet B, Piccolo D, Verde R, Vichi M (Eds) Classification and Multivariate Analysis for Complex Data Structures, Springer, pp. 265-270. ISBN: 978-3-642-13311-4. draft

Bini M., Grilli L. & Bertaccini B. (2011) L`over education dei dottori di ricerca in Italia. Riflessioni e proposte operative. Le nuove frontiere della Scuola. Periodico quadrimestrale di cultura, pedagogia e didattica. N. 26 anno IX- Maggio 2011, pp. 99-109. La Medusa editrice - Marsala. ISBN 978-88-89949-89-4


Grilli L. & Rampichini C. (2010) Selection bias in linear mixed models. Metron: International Journal of Statistics, vol. LXVIII, n. 3, pp. 309-329  [an extended version was published as a working paper]


Grilli L. & Rampichini C. (2009) Multilevel models for the evaluation of educational institutions: a review. In: Monari, P.; Bini, M.; Piccolo, D.; Salmaso, L. (Eds.) Statistical Methods for the Evaluation of Educational Services and Quality of Products, Physica-Verlag, pp 61-80.  paper  


Grilli L. & Mealli F. (2008) Nonparametric Bounds on the Causal Effect of University Studies on Job Opportunities Using Principal Stratification. Journal of Educational and Behavioral Statistics, 33(1), pp 111-130 (Abstract on the journal web site) DOI: 10.3102/1076998607302627 


Grilli L. & Rampichini C. (2007) Sample selection in linear mixed models. Electronic Working Papers 10/2007, Department of Statistics - University of Florence. [A compact version is published in Metron 2010]

Grilli L. & Rampichini C. (2007) Multilevel factor models for ordinal variables. Structural Equation Modeling, 14 (1), pp 1-25 (Paper on the journal web site). DOI:10.1080/10705510709336734      draft 

Grilli L. & Rampichini C. (2007) A multilevel multinomial logit model for the analysis of graduates` skills. Statistical Methods and Applications, 16(3), pp 381-393 (Abstract on the journal web site).

Grilli L. & Rampichini C. (2007) A Multilevel Analysis of Graduates’ Job Satisfaction. In Effectiveness of University Education in Italy: Employability, Competences, Human Capital (L. Fabbris ed.), pp 29-42. Physica Verlag.

Grilli L. & Mealli F. (2007) University Studies and Employment. An Application of the Principal Strata Approach to Causal Analysis. In Effectiveness of University Education in Italy: Employability, Competences, Human Capital (L. Fabbris ed.), pp 219-232. Physica Verlag.

Gottard A., Grilli L. & Rampichini C. (2007) A chain graph multilevel model for the analysis of graduates` employment. In Effectiveness of University Education in Italy: Employability, Competences, Human Capital (L. Fabbris ed.), pp 169-182. Physica Verlag.


Grilli L. & Rampichini C. (2006) A review of random effects modelling using gllamm in Stata. Review written for the Multilevel Modelling Software Reviews of The Centre for Multilevel Modelling.

Testa M.R. & Grilli L. (2006) The Influence of Childbearing Regional Contexts on Ideal Family Size in Europe. Population, 61 (1-2), pp 109-138. [previous version published in European Demographic Research Papers 2004 No. 4. (Full text)]


Grilli L. (2005) The random-effects proportional hazards model with grouped survival data: a comparison between the grouped continuous and continuation ratio versions. Journal of the Royal Statistical Society - Series A, Vol. 168, n. 1, pp. 83-94.(Abstract on the journal web site) (Previous working paper)

Grilli L. & Rampichini C. (2005) Selection bias in random intercept models. Multilevel Modelling Newsletter, Vol. 17 (1). (Full text)


Grilli L. & Pratesi M. (2004) Weighted estimation in multilevel ordinal and binary models in the presence of informative sampling designs. Survey Methodology, Vol. 30,  n. 1, 93-103. (Abstract on the journal web site) (Previous working paper)

Rampichini C., Grilli L. & Petrucci A. (2004) Analysis of university course evaluations: from descriptive measures to multilevel models. Statistical Methods and Applications, Vol. 13, n. 3, pp. 357-373. (Abstract on the journal web site)  

Grilli L. & Rampichini C. (2004) Book review: Methodology and Epistemology of Multilevel Analysis (Daniel Courgeau ed.). European Journal of Population, Vol. 20. n. 3, pp. 289-291. (Abstract on the journal web site)  


 Grilli L. & Rampichini C. (2003) Alternative specifications of multivariate multilevel probit ordinal response models. Journal of Educational and Behavioral Statistics, Vol. 28, pp. 31-44. (Abstract on the journal web site) (Previous working paper)


Grilli L. & Rampichini C. (2002) Scomposizione della dispersione per variabili statistiche ordinali. Statistica, anno LXII, n. 1, pp. 111-116.

Grilli L. & Rampichini C. (2002) Specification issues in stratified variance component ordinal response models. Statistical Modelling, Vol. 2, pp. 251-264. (Abstract on the journal web site)


Biggeri L., Bini M. & Grilli L. (2001) The transition from university to work: a multilevel approach to the analysis of the time to obtain the first job. Journal of the Royal Statistical Society - Series A, Vol. 164 (2), pp 293-305 (Abstract on the journal web site)

2000 and before

Grilli L. (2000) La valutazione della didattica da parte degli studenti attraverso un questionario unico: l'esperienza dell`ateneo fiorentino. In Valutazione della didattica con sistemi computer-assisted, a cura di M. Civardi e L. Fabbris. Cleup, Padova.

Grilli L. (1999) Sbocchi occupazionali e scelte formative dei diplomati: un'analisi multilivello. Tesi di dottorato di ricerca in Statistica Applicata (relatore L. Biggeri). Dipartimento di Statistica dell'Universita' di Firenze.

Grilli L. & Gori E. (1996) L'approccio dei processi di conteggio ai modelli di regressione per dati di durata. Working Paper n. 69 del Dipartimento di Statistica dell'Universita' di Firenze. Editrice 2P. Luglio 1996, Firenze.

Grilli L. (1996) L'approccio dei processi di conteggio all'analisi dei dati di durata. Tesi di laurea (relatore E. Gori). Facolta' di Economia dell'Universita' di Firenze.