12,340
Views
67
CrossRef citations to date
0
Altmetric
Original Articles

Latent Variable Models and Networks: Statistical Equivalence and Testability

, , , , &

References

  • Bates, D., & Maechler, M. (2014). Matrix: Sparse and dense matrix classes and methods [Computer software manual]. Retrieved from http://CRAN.R-project.org/package=Matrix (R package version 1.1-4).
  • Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee’s ability. In F. M. Lord & M. R. Novick (Eds.), Statistical theories of mental test scores (pp. 397–479). Reading, MA: Addison-Wesley.
  • Bollen, K. A. (1989). Structural equations with latent variables. New York, NY: John Wiley and Sons. doi:10.1002/9781118619179
  • Bollen, K. A., & Lennox, R. (1991). Conventional wisdom on measurement: A structural equation perspective. Psychological Bulletin, 110(2), 305–314. doi:10.1037/0033-2909.110.2.305
  • Bollen, K. A., & Pearl, J. (2013). Eight myths about causality and structural equation models. In. S. L. Morgan (Ed.), Handbook of causal analysis for social research (pp. 301–328). Dordrecht, The Netherlands: Springer. doi:10.1007/978-94-007-6094-3.
  • Bond, T. G., & Fox, C. M. (2001). Applying the Rasch model: Fundamental measurement in the human sciences. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Borsboom, D. (2017). A network theory of mental disorders. World Psychiatry, 16(1), 5–13. doi:10.1002/wps.20375
  • Borsboom, D., & Cramer, A. O. J. (2013). Network analysis: An integrative approach to the structure of psychopathology. Annual Review of Clinical Psychology, 9(1), 91–121. doi:10.1146/annurev-clinpsy-050212-185608
  • Borsboom, D., Mellenbergh, G. J., & van Heerden, J. (2003). The theoretical status of latent variables. Psychological Review, 110(2), 203–219. doi:10.1037/0033-295X.110.2.203
  • Borsboom, D., Mellenbergh, G. J., & van Heerden, J. (2004). The concept of validity. Psychological Review, 111(4), 1061–1071. doi:10.1037/0033-295X.111.4.1061
  • Caspi, A., Houts, R. M., Belsky, D. W., Goldman-Mellor, S. J., Harrington, H., Israel, S., … Moffitt, T. E. (2014). The p factor: One general psychopathology factor in the structure of psychiatric disorders? Clinical Psychological Science, 2(2), 119–137. doi:10.1177/2167702613497473
  • Chen, B., & Pearl, J. (2014). Graphical tools for linear structural equation modeling. Technical Report R-432, Department of Computer Science, University of California, Los Angeles, CA. Psychometrika, forthcoming. Retrieved from http://ftp.cs.ucla.edu/pub/stat ser/r432.pdf
  • Costantini, G., Epskamp, S., Borsboom, D., Perugini, M., Mõttus, R., Waldorp, L. J., & Cramer, A. O. J. (2015). State of the aRt personality research: A tutorial on network analysis of personality data in R. Journal of Research in Personality, 54, 13–29. doi:10.1016/j.jrp.2014.07.003
  • Cramer, A. O. J., Borkulo, C. D., van, Giltay, E. J., Maas, H. L. J., van der, Kendler, K. S., Scheffer, M., & Borsboom, D. (2016). Major depression as a complex dynamical system. PLoS One, 11(12). doi:10.1371/journal.pone.0167490
  • Cramer, A. O. J., van der Sluis, S., Noordhof, A., Wichers, M., Geschwind, N., Aggen, S. H., … Borsboom, D. (2012). Dimensions of normal personality as networks in search of equilibrium: You can’t like parties if you don’t like people. European Journal of Personality, 26(4), 414–431. doi:10.1002/per.1866
  • Cramer, A. O. J., Waldorp, L. J., van der Maas, H. L. J., & Borsboom, D. (2010). Comorbidity: A network perspective. Behavioral and Brain Sciences, 33(2-3), 137–150. doi:10.1017/S0140525X10000920
  • Cramér, H. (1946). Mathematical methods of statistics (Vol. 9). Princeton, NJ: Princeton University Press. doi: 10.1515/9781400883868.
  • Cronbach, L. J., & Meehl, P. E. (1955). Construct validity in psychological tests. Psychological Bulletin, 52(4), 281–302. doi:10.1037/h0040957
  • Dalege, J., Borsboom, D., van Harreveld, F., van den Berg, H., Conner, M., & van der Maas, H. L. J. (2016). Toward a formalized account of attitudes: The causal attitude network (CAN) model. Psychological Review, 123(1), 2–22. doi:10.1037/a0039802
  • Deserno, M. K., Borsboom, D., Begeer, S., & Geurts, H. (2017). Relating ASD symptoms to well-being: Moving across different construct levels. Psychological Medicine, 48, 1–14. doi:10.1017/S0033291717002616
  • Edwards, A. W. F. (1972). Likelihood. London: Cambridge University Press.
  • Edwards, J. R., & Bagozzi, R. P. (2000). On the nature and direction of relationships between constructs and measures. Psychological Methods, 5(2), 155–174. doi:10.1037//1082-989X.5.2.155
  • Epskamp, S., Cramer, A. O. J., Waldorp, L. J., Schmittmann, V. D., & Borsboom, D. (2012). qgraph: Network visualizations of relationships in psychometric data. Journal of Statistical Software, 48(4), 1–18. doi:10.18637/jss.v048.i04
  • Epskamp, S., Kruis, J., & Marsman, M. (2017). Estimating psychopathological networks: Be careful what you wish for. PloS One, 12(6), e0179891. doi:10.1371/journal.pone.0179891
  • Epskamp, S., Maris, G., Waldorp, L. J., & Borsboom, D. (2018). Network psychometrics. In P. Irwing, T. Booth, & D. J. Hughes (Eds.), The Wiley Handbook of Psychometric Testing, 2 Volume Set: A Multidisciplinary Reference on Survey, Scale and Test Development (pp. 953–986). New York, NY: Wiley. doi:10.1002/9781118489772.ch30.
  • Epskamp, S., Rhemtulla, M., & Borsboom, D. (2017). Generalized network pschometrics: Combining network and latent variable models. Psychometrika, 82(4), 904–927. doi:10.1007/s11336-017-9557-x
  • Epskamp, S., Waldorp, L. J., Mõttus, R., & Borsboom, D. (2018). Discovering psychological dynamics: The Gaussian graphical model in cross-sectional and time-series data. Multivariate Behavioral Research, 0, 1–28. doi:10.1080/00273171.2018.1454823
  • Foygel, R., & Drton, M. (2010). Extended Bayesian information criteria for Gaussian graphical models. Advances in Neural Information Processing Systems, 23, 2020–2028. arXiv:1011.6640v1.
  • Friedman, J., Hastie, T., & Tibshirani, R. (2008). Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9(3), 432–441. doi:10.1093/biostatistics/kxm045
  • Gignac, G. E. (2016). Residual group-level factor associations: Possibly negative implications for the mutualism theory of general intelligence. Intelligence, 55, 69–78. doi:10.1016/j.intell.2016.01.007
  • Guttman, L. (1940). Multiple rectilinear prediction and the resolution into components. Psychometrika, 5(2), 75–99. doi:10.1007/BF02287866
  • Guttman, L. (1953). Image theory for the structure of quantitative variates. Psychometrika, 18(4), 277–296. doi:10.1007/BF02289264
  • Holland, P. W., & Rosenbaum, P. R. (1986). Conditional association and unidimensionality in monotone latent variable models. The Annals of Statistics, 14(4), 1523–1543. doi:10.1214/aos/1176350174
  • Ising, E. (1925). Beitrag zur theorie des ferromagnetismus. Zeitschrift Für Physik, 31(1), 253–258. doi:10.1007/BF02980577
  • Isvoranu, A.-M., Borkulo, C. D., van, Boyette, L.-L., Wigman, J. T., Vinkers, C. H., Borsboom, D., … Nvestigators, G. (2017). A network approach to psychosis: Pathways between childhood trauma and psychotic symptoms. Schizophrenia Bulletin, 43(1), 187–196. doi:10.1093/schbul/sbw055
  • Jöreskog, K. G. (1971). Statistical analysis of sets of congeneric tests. Psychometrika, 36(2), 109–133. doi:10.1007/BF02291393
  • Kac, M. (1968). Mathematical mechanisms of phase transitions. In M. Chrétien, E. P. Gross, and S. Deser (Eds.), Statistical physics: Phase transitions and superfluidity, Brandeis university summer institute in theoretical physics (Vol. 1, pp. 241–305). New York, NY: Gordon and Breach Science Publishers.
  • Kass, R. E., & Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association, 90(430), 773–795. doi:10.2307/2291091
  • Koller, D., & Friedman, N. (2009). Probabilistic graphical models: Principles and techniques. Cambridge, MA: MIT Press.
  • Krueger, R. F. (1999). The structure of common mental disorders. Archives of General Psychiatry, 56(10), 921–926. doi:10.1001/archpsyc.56.10.921
  • Kruis, J., & Maris, G. (2016). Three representations of the ising model. Scientific Reports, 6(34175), 1–11. doi:10.1038/srep34175
  • Lauritzen, S. L. (1996). Graphical models (Vol. 17). Oxford: Oxford University Press.
  • MacCallum, R. C., Wegener, D. T., Uchino, B. N., & Fabrigar, L. R. (1993). The problem of equivalent models in applications of covariance structure analysis. Psychological Bulletin, 114(1), 185–199. doi:10.1037/0033-2909.114.1.185
  • Markus, K. A. (2002). Statistical equivalence, semantic equivalence, eliminative induction, and the Raykov-Marcoulides proof of infinite equivalence. Structural Equation Modeling: A Multidisciplinary Journal, 9(4), 503–522. doi:10.1207/S15328007SEM0904_3
  • Marsman, M., Borsboom, D., Kruis, J., Epskamp, S., van Bork, R., Waldorp, L. J., … Maris, G. (2018). A psychometric introduction to the relation between Ising network models and item response theory models. Multivariate Behavioral Research, 53(1), 15–35. doi:10.1080/00273171.2017.1379379
  • Marsman, M., Maris, G., Bechger, T., & Glas, C. (2015). Bayesian inference for low-rank Ising networks. Scientific Reports, 5(9050), 1–7. doi:10.1038/srep09050
  • McCrae, R. R., & Costa, P. T. (1987). Validation of the five-factor model of personality across instruments and observers. Journal of Personality and Social Psychology, 52(1), 81–90. doi:10.1037//0022-3514.52.1.81
  • McNally, R. J., Robinaugh, D. J., Wu, G. W. Y., Wang, L., Deserno, M. K., & Borsboom, D. (2014). Mental disorders as causal systems: A network approach to posttraumatic stress disorder. Clinical Psychological Science, 3, 1–14. doi:10.1177/2167702614553230
  • Mellenbergh, G. J. (1994). Generalized linear item response theory. Psychological Bulletin, 115(2), 300–300. doi:10.1037/0033-2909.115.2.300
  • Mokken, R. J. (1971). A theory and procedure of scale analysis. The Hague, The Netherlands: De Gruyter.
  • Pe, M. L., Kircanski, K., Thompson, R. J., Bringmann, L. F., Tuerlinckx, F., Mestdagh, M., … Gotlib, I. H. (2015). Emotion-network density in major depressive disorder. Clinical Psychological Science, 3(2), 292–300. doi:10.1177/2167702614540645
  • Pearl, J. (2000). Causality: Models, reasoning and inference. New York, NY: Cambridge University Press.
  • R Core Team. (2018). R: A language and environment for statistical computing [Computer software manual]. Vienna, Austria. Retrieved from https://www.R-project.org/
  • Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: The Danish Institute of Educational Research.
  • Raykov, T., & Marcoulides, G. A. (2001). Can there be infinitely many models equivalent to a given covariance structure model? Structural Equation Modeling: A Multidisciplinary Journal, 8(1), 142–149. doi:10.1207/S15328007SEM0801_8
  • Rosseel, Y. (2012). Lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1–36. doi:10.18637/jss.v048.i02
  • Royall, R. M. (1997). Statistical evidence: A likelihood paradigm. London, England: Chapman & Hall.
  • Rozental, A., Forsell, E., Svensson, A., Forsström, D., Andersson, G., & Carlbring, P. (2014). Psychometric evaluation of the Swedish version of the pure procrastination scale, the irrational procrastination scale, and the susceptibility to temptation scale in a clinical population. BMC Psychology, 2(1), 54. doi:10.1186/s40359-014-0054-z
  • Siegler, R. S., & Alibali, M. W. (2005). Children’s thinking (4th ed.). Upper Saddle River, NJ: Prentice Hall.
  • Spearman, C. (1904). General intelligence,” objectively determined and measured. The American Journal of Psychology, 15(2), 201–292. doi:10.2307/1412107
  • Steel, P. (2010). Arousal, avoidant and decisional procrastinators: Do they exist? Personality and Individual Differences, 48(8), 926–934. doi:10.1016/j.paid.2010.02.025
  • Svartdal, F. (2017). Measuring procrastination: Psychometric properties of the Norwegian versions of the Irrational Procrastination Scale (IPS) and the Pure Procrastination Scale (PPS). Scandinavian Journal of Educational Research, 61(1), 18–30. doi:10.1080/00313831.2015.1066439
  • van Bork, R., Grasman, R. P. P. P., & Waldorp, L. J. (2018). Unidimensional factor models imply weaker partial correlations than zero-order correlations. Psychometrika, 83(2), 443–452. doi:10.1007/s11336-018-9607-z
  • van Borkulo, C., Boschloo, L., Borsboom, D., Penninx, B. W. J. H., Waldorp, L. J., & Schoevers, R. A. (2015). Association of symptom network structure with the course of longitudinal depression. JAMA Psychiatry, 72(12), 1219–1226. doi:10.1001/jamapsychiatry.2015.2079
  • Van der Maas, H. L. J., Dolan, C. V., Grasman, R. P. P. P., Wicherts, J. M., Huizenga, H. M., & Raijmakers, M. E. J. (2006). A dynamical model of general intelligence: The positive manifold of intelligence by mutualism. Psychological Review, 113, 842–861. doi:10.1037/0033-295X.113.4.842
  • Van der Maas, H. L. J., & Kan, K. J. (2016). Comment on “Residual group-level factor associations: Possibly negative implications for the mutualism theory of general intelligence” by Gilles E. Gignac (2016). Intelligence, 57, 81–83. doi:10.1016/j.intell.2016.03.008
  • Venables, W. N., & Ripley, B. D. (2002). Modern Applied Statistics with S (4th ed.). New York: Springer. Retrieved from http://www.stats.ox.ac.uk/pub/MASS4 (ISBN 0-387-95457-0)
  • Wagenmakers, E. J., & Farrell, S. (2004). AIC model selection using Akaike weights. Psychonomic Bulletin & Review, 11, 192–196. doi:10.3758/BF03206482