Luigi Lombardi

Full Professor of Psychometrics,
Dept. of Psychology and Cognitive Sciences, University of Trento
Mail: Corso Bettini, 31 - 38068 Rovereto, TN, Italy
Phone: +39 0464 808642 (office) | luigi.lombardi at

freely available packages

The sgr package (ver. 1.3) is available on CRAN.

sgr is an R package developed for running fake data analysis according to the sample generation by replacement approach (SGR, Lombardi & Pastore, 2012). SGR is a data simulation procedure that allows to generate artificial samples of fake discrete/ordinal data. SGR can be used to quantify uncertainty in inferences based on possible fake data as well as to evaluate the implications of fake data for statistical results. For example, how sensitive are the results to possible fake data? Are the conclusions still valid under one or more scenarios of faking?

Download the sgr package: R package version 1.3 [CRAN site].
Reference: Lombardi L. & Pastore M. (2014). sgr: A package for simulating conditional fake ordinal data. The R Journal, 6(1), 164-177. (pdf)

The DYFRAT package (ver. 1.0).

DYFRAT is a new methodology for modeling human rating evaluations from a fuzzy-set perspective (Calcagni' & Lombardi, 2014).
Download the DYFRAT package (ver. 1.0) [DYFRAT webpage].

The EMOT package (ver. 1.0).

EMOT is a Matlab package implementing a new methodology for modeling computer-mouse trajectories in a data-driven perspective and allows researchers to analyse raw x-y trajectories in terms of dynamic and static components (Calcagni', Lombardi, & Sulpizio, 2017).
Download the EMOT package (ver. 1.0) [EMOT webpage].

The NP-RMI R functions.

We developed a new nonparametric testing procedure based on the truncated Kolmogorov-Smirnov test for evaluating the race model inequality (RMI; Miller, 1982) in single participant's data. The procedure is implemented using a simple R function which only requires the base R package (R Core Team, 2018) to be installed.
Download the R functions at [NP-RMI webpage].

research interests

My main research stream focuses on interrelated issues dealing with multivariate data analysis of discrete variables, fake data analysis, and new MC-type approaches to evaluate statistical models. Papers on this topic are denoted with [P].

I also like to study and propose new formal models of higher level cognition, such as decision strategies, induction, similarity evaluation, and classification. My current interest is on semantic memory and semantic representations in natural languages. In particular, I am focused on problems that are related to how people categorize and integrate semantic information as well as probabilistic cues in concept name retrieval tasks. I also try to compare results of my models with empirical data collected on healthy participants or neuropsychological patients suffering from semantic memory disorders. Papers on this topic are denoted with [C].

Finally, I work on the application of statistical models on psychological data. I am particularly interested in structural equation modeling and multivariate data analysis for discrete or categorical data. The fields of application include: psychology of decision, psychology of perception, and organizational psychology. Papers on this topic are denoted with [A].


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[P] Calcagni' A., Cao N., Rubaltelli E., & Lombardi L. (2022). A psychometric modeling approach to fuzzy rating data. Fuzzy Sets and Systems. DOI: 10.1016/j.fss.2022.01.008 (publisher web site)

[P] Calcagni' A. & Lombardi L. (2022). Modeling random and non-random decision uncertainty in ratings data: A fuzzy beta model. AStA Advances in Statistical Analysis, 106, 145-173. DOI: 10.1007/s10182-021-00407-7 (publisher web site)

[A] Avanzi L., Perinelli E., Bressan M., Balducci C., Lombardi L., Fraccaroli F., & van Dick R. (2021). The mediational effect of social support between organizational identification and employees' health: a three-wave study on the social cure model. Anxiety, Stress, & Coping. DOI: 10.1080/10615806.2020.1868443 (publisher web site)

[A] Valzolgher C., Verdelet G., Salemme R., Lombardi L., Gaveau V., Farne' A., & Pavani F. (2020). Reaching to sounds in virtual reality: A multisensory-motor approach to promote adaptation to altered auditory cues. Neuropsychologia, 149, 107665. (publisher web site)

[P/C] D'Alessandro M., Radev S., Voss A., & Lombardi L. (2020). A Bayesian brain model of adaptive behavior: an application to the Wisconsin Card Sorting Task. PeerJ, 8:e10316, 1-32. (publisher web site).

[P/C] D'Alessandro M., Gallitto G., Greco A., & Lombardi L. (2020). A Joint modelling approach to analyze risky decisions by means of diffusion tensor imaging and behavioural data. Brain Sciences, 10(3), 138, 1-16. doi:10.3390/brainsci10030138 (publisher web site).

[C] Tagliabue C. F., Lombardi L., & V. Mazza (2020). Individuation of object parts in aging. Attention, Perception, & Psychophysics. doi: 10.3758/s13414-020-01996-2 (publisher web site)

[P/C] Calcagni' A., Lombardi L., D'Alessandro M., & Freuli F. (2019). A state space approach to dynamic modeling of mouse-tracking data. Frontiers in Psychology. doi: 10.3389/fpsyg.2019.02716 (publisher web site).

[P/C] D'Alessandro M. & Lombardi L. (2019). A Dynamic Framework for modelling set-shifting performances. Behavior Sciences, 9, 79, 1-13. doi:10.3390/bs9070079 (publisher web site).

[P/C] Lombardi L., D'Alessandro M., & Colonius H. (2019). A nonparametric test for the race model inequality. Behavior Research Methods, 51, 5, 2290-2301. (publisher web site).

[P] Bressan M., Rosseel Y., & Lombardi L. (2018). The effect of faking on the correlation between two ordinal variables: some population and Monte Carlo results. Frontiers in Psychology, 9:1876. doi: 10.3389/fpsyg.2018.01876 (publisher web site).

[P] Calcagni' A., Lombardi L., Avanzi L., & Pascali E. (2017). Multiple mediation analysis for interval-valued data. Statistical Papers, 1-23. Online first article. (publisher web site).

[P/C] Calcagni' A., Lombardi L., & Sulpizio S. (2017). Analysing spatial data from mouse tracker methodology: An entropic approach. Behavior Research Methods, 49, 2012-2030. (publisher web site).

[P] Pastore M., Nucci M., Bobbio A., & Lombardi L. (2017). Empirical scenarios of fake data analysis: The Sample Generation by Replacement (SGR) approach. Frontiers in Psychology, 8:482. doi: 10.3389/fpsyg.2017.00482 (publisher web site).

[P] Lombardi L. & Pastore M. (2016). Robust evaluation of fit-indices to fake-good perturbation of ordinal data. Quality & Quantity, 50, 2651-2675. (publisher web site).

[P] Calcagni' A., Lombardi L., & Pascali E. (2016). A dimension reduction technique for two-mode non-convex fuzzy data. Soft Computing, 20, 749-762. (publisher web site).

[P] Lombardi L., Pastore M., Nucci M., & Bobbio A. (2015). SGR modeling of correlational effects in fake good self-report measures. Methodology and Computing in Applied Probability, 17, 1037-1055. (publisher web site).

[C] Lombardi L., Bazzanella B., & Calcagni' A. (2014). A probabilistic model for integration of strong dependent cues in category identification. TPM - Testing, Psychometrics, Methodology in Applied Psychology, 21, 407-419, DOI: 10.4473/TPM21.4.3 (publisher web site).

[C] Didino D., Lombardi L., & Vespignani F. (2014). Operand-order effect in multiplication and addition: the long-term effects of reorganization process and acquisition sequence. Experimental Psychology, 61, 470-479. [DOI: 10.1027/1618-3169/a000264] (publisher web site).

[P/C] Calcagni' A. & Lombardi L. (2014). Dynamic Fuzzy Rating Tracker (DYFRAT): A novel methodology for modeling real-time dynamic cognitive processes in rating scales. Applied Soft Computing, 24, 948-961. (publisher web site).

[P] Lombardi L. & Pastore M. (2014). sgr: A package for simulating conditional fake ordinal data. The R Journal, 6(1), 164-177. (pdf)

[C] Pagano S., Lombardi L., & Mazza V. (2014). Brain dynamics of attention and working memory engagement in subitizing. Brain Research, 1543, 244-252. (pdf)

[P] Pastore M. & Lombardi L. (2014). The impact of faking on Cronbach's Alpha for dichotomous and ordered rating scores. Quality & Quantity, 48, 1191-1211, (publisher web site).

[P] Calcagni' A., Lombardi L., & Pascali E. (2014). Non-convex fuzzy data and fuzzy statistics: A first descriptive approach to data analysis. Soft Computing, 18, 1575-1588, (publisher web site).

[P] Lombardi L., Pastore M., Nucci M., & Bobbio A. (2013). SGR modeling of fake ordinal data with correlational structures. Proceedings, 15th Applied Stochastic Models and Data Analysis (ASMDA2013), 589-596.

[P] Calgagni' A. & Lombardi L. (2013). A fuzzy regression model for non-convex fuzzy numbers: The crisp input fuzzy output case. Proceedings, 15th Applied Stochastic Models and Data Analysis (ASMDA2013), 203-210.

[C] Pagano S., Lombardi L. & Mazza V. (2013). An electrophysiological assessment of the involvement of working memory in subitizing. Psychophysiology, 50, (Special Issue, Supplement 1, S62-S62).

[P] Lombardi L. & Pastore M. (2012). Sensitivity of fit indices to fake perturbation of ordinal data: A sample by replacement approach. Multivariate Behavioral Research, 47, 519-546. (publisher web site)

[A] Camperio Ciani A., Fontanesi L., Iemmola F., Giannella E., Ferron C., & Lombardi L. (2012). Factors associated with higher fecundity in female maternal relatives of homosexual men. The Journal of Sexual Medicine, 9 , 2878-2887, (pdf)

[P] Lombardi L., Ceulemans E., & Van Mechelen I. (2011). K-centroids hierarchical classes analysis. Proceedings AMSDA 2011, pp. 850-857, ETS Ed.

[P] Pastore. M, & Lombardi L. (2011). On the sensitivity of Cronbach's alpha to fake data. Proceedings AMSDA 2011, pp. 1080-1087, ETS Ed.

[C] Kemp C., Chang K-M. & Lombardi L. (2010). Category and feature identification. Acta Psychologica, 133, 216-233. (pdf)

[A] Palmieri A., Soraru' G., Lombardi L., D'Ascenzo C., Baggio L., Ermani M., Pegoraro E. & Angelini C (2010). Quality of life and motor impairment in ALS: Italian validation of ALSAQ. Neurological Research, 32 , p. 32-40. (pdf)

[P] Lombardi L., & Pastore. M (2009). A probabilistic approach for evaluating the sensitivity to fake data in structural equation modeling. L. Sakalauskas, C. Skiadas, E. K. Zavadskas (Eds.). Applied stochastic models and data analysis 2009, selected papers, pp. 27-32, Institute of Mathematics and Informatics, Vilnius Gediminas University. (pdf)

[C] Crupi V., Tentori K. & Lombardi L. (2009). Pseudodiagnosticity revisited. Psychological Review, 116, 971-983. (pdf)

[A] Palmieri A., Soraru' G., Lombardi L., D'Ascenzo C., Lazzarini L., Baggio L., Ermani M., Pegoraro E., & Angelini C. (2009). Validity of the Italian adaptation of ALSAQ-40 and ALSAQ-5. Basic Applied Myology, 19 (5-6) , p. 217-223.

[C] Lombardi L. (2008). Strong dependence and relevant cues in name retrieval. In Arcuri L., Boscolo P., Peressotti F. (Eds). Cognition and language: a long story. Padova: Cleup.

[A] Atzori M., Lombardi L., Fraccaroli F. & Battistelli A. (2008). Organizational socialization of women in the Italian army: learning processes and proactive tactics. Journal of Workplace Learning, 20 , p. 327-347. (pdf)

[A] Savadori L., Graffeo M., Bonini N., Lombardi L., Tentori K., & Rumiati R. (2007). Rebuilding consumer trust in the context of a food crisis. In Siegrist M., Earle T. C., Gutscher H. (Eds.). Trust in cooperative risk management, uncertainty and scepticism in the public mind. London: Earthscan.

[P] Van Mechelen I., Lombardi L., & Ceulemans E., (2007). Hierarchical classes modeling of rating data. Psychometrika, 72, 475-488. (pdf)

[P] Pastore M., Lombardi L., & Mereu F. (2007). Effects of malingering in self-report measures: A scenario analysis approach. In C. H. Skiadas (Ed.). Recent Advances in Stochastic Modelling and Data Analysis. Singapore: World Scientific Pub. Co. (Personal copy pdf) (publisher web site).

[C] Lombardi L. & Sartori G. (2007). Models of relevant cue integration in name retrieval. Journal of Memory and Language, 57, 101-125. (pdf)

[C] Sartori G., Gnoato F., Mariani I., Prioni S., & Lombardi L. (2007). Semantic relevance, domain specificity and the sensory/functional theory of category specificity. Neuropsychologia, 45, 966-976. (pdf)

[P] Lombardi L., Ceulemans E., & Van Mechelen I. (2006). K-centroids hierarchical classes analysis. Technical Report 0352, IAP Statistics Network - Interuniversity Attraction Pole ( (pdf)

[C] Sartori G., Polezzi D., Mameli F., & Lombardi L. (2006). An ERP study of low and high relevance semantic features. Brain Research Bulletin, 69, 182-186. (pdf)

[C] Lombardi L., & Sartori G. (2006). Concept similarity: an abstract relevance classes approach. Proceedings of the 7th International conference on cognitive modeling, 190-195. (pdf)

[A] Graffeo M., Savadori L., Bonini N., Lombardi L., Tentori K., & Rumiati R. (2006). Food choice in the context of a food hazard: insights from psychological experiments. In Romano D., Stefani G. (Eds.). How safe is eating chicken? A study on the impact of trust and food risk communication on consumer behaviour in the European Union. Firenze: University Press.

[P] Lombardi L. & Van Mechelen I. (2005). Conjunctive prediction of an ordinal criterion variable on the basis of binary predictors. Discrete Applied Mathematics, 147, 91-100. (pdf)

[P] Pastore M., & Lombardi L. (2005). Evaluating the sensitivity of goodness-of-fit indices to data perturbation: An integrated MC-SGR approach. In: J. Janssen and P. Lenca (Eds). Applied stochastic models and data analysis, Brest: ENST. (pdf)

[C] Sartori G., Lombardi L., & Mattiuzzi L. (2005). Semantic relevance best predicts normal and abnormal name retrieval. Neuropsychologia, 43, 754-770. (pdf)

[C] Sartori G., Polezzi D., Mameli F., & Lombardi L. (2005). Feature type effects in semantic memory: An event related potentials study. Neuroscience letters, 390, 139-144. (pdf)

[C] Sartori G. & Lombardi L. (2005). Double dissociations on the same stimuli. Cortex, 41, 867-868. (pdf)

[P] Lombardi L., Pastore M., & Nucci M. (2004). Evaluating uncertainty of model acceptability in empirical applications: a replacement approach. In Monfort K., Oude H., Satorra A. (Ed.). Recent developments in structural equation modeling: theory and applications. Amsterdam, Kluwer academic publishers.

[C] Sartori G., & Lombardi L. (2004). Semantic relevance and semantic disorders. Journal of Cognitive Neuroscience, 16 439-452. (pdf)

[A] Graffeo M., Savadori L., Lombardi L., Tentori K., Bonini N., & Rumiati R. (2004). Trust and attitude in consumer food choices under risk. Agrarwirtschaft : Zeitschrift fur Betriebswirtschaft, Marktforschung und Agrarpolitik, 53, 319-327.

[P] Lombardi L., Ceulemans E., & Van Mechelen I. (2003). A hierarchical classes approach to discriminant analysis. In Schader M., Gaul W., Vichi M. (Eds). Between data science and applied data analysis. Heidelberg: Springer. (pdf)

[P] Lombardi L. (2000). Sviluppo di un modello formale del cambiamento comportamentale. In Vidotto G., Marchesini C. (Eds). La realizzazione professionale: risorse personali e processi decisionali per l'orientamento scolastico-professionale. Milano: Franco Angeli.

[A] Pagani D. & Lombardi L. (2000). An intercultural examination of facial features communicating surprise. In Birnbaum M. (Ed), p. 169-194. Psychological Experiments on the Internet. New York: Academic press. (pdf)

[C] Lombardi L., Burigana L. (2000). MSA (Model of Structural Analysis): an example of formal analysis on the emotion of surprise. In Zanforlin M., Tommasi L. (Eds). Research in perception. Padova: Logos press.