Polarization Measurement Through Ordered Latent Class Analysis
Polarization Measurement throughOrdered Latent Class AnalysisBoris SokolovLCSR HSE, Junior Research Fellow,SPbU, Postgraduate Studentbssokolov@gmail.comLCSR International Workshop,April 3, 2014Moscow
Why polarization? Polarization refers to level of diversity in society onsome specific dimension. Polarization also reflects a conflict potential caused bydiversity. Attitudinal polarization is an evidence of culturalcleavage (e.g. so called ‘modernization’ cleavageassumed by ‘losers of modernization’ thesis) Attitudinal polarization may be used as a second-levelpredictor for analyses of many social processes,especially related to politics and ethnic relations. Polarization (and related cleavages) may be interestingto model as well.
Measurement of PolarizationPrevious developments Variance (or Standard Deviation)KurtosisFoster-Wolfson IndexDuclos-Esteban-Ray family of indicesEthno-Linguistic Fractionalization IndexReynal-Querol Index of polarizationVarious measures of ordinal variationVisual distribution comparisonsAd hoc methods (like Mouw and Sobel 2001)
Polarization in Survey Data The main objects of interest are latent constructs(measured through multiple manifest variables). Information about distributional parameters oflatent variables provided by relevant statisticalsoftware is limited. Measuring polarization for aggregated factorscores seems to be an inaccurate approach dueto possible non-normality, multidimensionality,and measurement non-equivalence of latentscale.
Why (Ordinal) Latent Classes? LCA may easily handle non-normality of latent variable LCA allows for multidimensionality: when the latentcategorical variable is nominal rather than ordinal, it isimpossible to order all individuals on all items in thesame direction. LCA allows for testing measurement Invariance LCA provides unique observed indicator for latentvariable by classifying respondents according to theirvalue patterns. Several existing ordinal measures ofpolarization are easily applicable to the resultingclassification
Latent Class Model
Ordinal Latent Classes
Approach to the Measurement ofPolarizationStep 1. Selecting a model with an optimal number of latent classes. Best model mustsatisfy three following requirements 1) be parsimonious: model with K classes should not include classes which aresubgroups of classes identified in a model with K - 1 latent categories. 2) be almost ordinal: include very few parameters violating class-ordering 3) show the best fit (aBIC and BLRT) comparing to all other models which satisfy 1)and 2)Step 2. Testing for ordinality (unidimensionality, or strict monotonicity) of latent trait:comparing unconstrained and strictly ordered models. Order-constrained hypothesis istested directly by using Bayes factor approachStep 3. Applying relevant index of nominal or ordinal polarization (depending on theresults from the Step 2) to class proportions for each country obtained at the firststage.Bonus. Exploring measurement invariance and cross-country differences in classproportions
Polarization Indices Reynal-Querol Index (nominal) Standardized Van der Eijk’s Agreement Ameasure Berry/Mielke Index of Ordinal Variation Leik’s Ordinal Variation Index L-Squared
Data Survival/Self-Expression Values. WVS, Fifth Wave Manifest variables 1: Happiness, Tolerance forHomosexuality, Trust, Four-Item Postmaterialism Index(as a single variable), Signing Petition Manifest variables 2: Tolerance for Homosexuality.Four-Item Postmaterialism, Signing Petition 29 European Countries: 27 EU members, Norway, andSwitzerland 42817 respondents Data were not weighted Data were not imputed
Fit Statistics for Competing ModelsaBICLMR Testp-valueBLRT p-valueFreeParametersViolationsof OrderingThree Classes471413.6820.0000.000300Four Classes463097.6720.0000.000401Five Classes448977.3230.0000.000501Five Classes Ord448977.441******500Six Classes446572.6090.0000.000603Six Classes Ord469077.511******550Seven Classes444052.8290.0000.000706*********640Seven Classes Ord
Thresholds and Means Estimates for the FiveClass Unconstrained ModelPetition Petition 6610.394-1.637-0.1347.5574
Thresholds and Means Estimates for the FiveClass Model with Inequality ConstraintsPetition Petition 6610.394-1.637-0.1347.5574
vakiaCzech RepublicItalyUnited ss proportionClass Proportions in Different European ass525%0%
SpainNorwayFranceFinlandLuxembourgAustriaUnited KingdomItalyCzech niaLithuiniaPolarizationBerry/Mielke's Polarization Index0.90.80.70.60.50.40.30.20.10.0
7565Berry Mielke0.80.6550.40.24535-20-100102030
Polarization Patterns forFive-Class Five-Item Model Class proportions vary in a large amount betweencountries There is a clear pattern: Eastern Europeancountries shows larger proportions of survivalclasses (that is, less “modernized” classes) The less polarized countries are at the same timethe less modernized while many developedcountries are highly polarized Modernization and spread of self-expressionvalues lead to the growth of value polarization?
Investigating the latent trait underlyingthe survival/self-expression values For five-item models, strict unidimensionality (class ordering) holdsonly for models with no more than five classes. For three-itemmodels even nine-class solution is plausible. When the number of classes is relatively large (to approximatecontinuous distribution), the distribution of latent trait is trimodal,which indicates non-normality of the self-expression index. Country-by-country analysis shows that the class ordering identifiedin five-class five-tem solution is not robust across countries.Therefore, it is likely that configural measurement invariance doesnot hold for categorical representation of self-expression valuesindex. Surprisingly, class ordering is more frequently violated in WesternEuropean countries, rather than in less developed post-communistor southern European societies.
Shortcomings and limitations Trade-off between efficiency andcomputational time might lead to biasedparameter estimates Measurement invariance was not tested in aformal way LCA model selection may seem quite arbitrary
Further development Bayesian LCA Testing for local homogeneity in IRTframework instead of LCA measurementinvariance Adding covariates Any advice is highly welcomed!!
Thank you very muchfor your attention!
Thresholds and Means Estimates for the SixClass Unconstrained der
Thresholds and Means Estimates for the SevenClass Unconstrained .2674
CountryAustriaSpainGermanyUnited KingdomFranceCzech oniaCyprusRomaniaLithuiniaPolarizationVan der Eijk's Polarization Index0.50.40.30.20.10.0
SpainNorwayFranceFinlandLuxembourgAustriaUnited KingdomItalyCzech niaLithuiniaPolarizationBerry/Mielke's Polarization Index0.90.80.70.60.50.40.30.20.10.0
CountryCzech akiaAustriaSloveniaUnited nLeik's Polarization Index0.70.60.50.40.30.20.10.0
CountryCzech RepublicLuxembourgItalyFinlandAustriaSpainUnited RomaniaLithuiniaPolarizationL-Squared Polarization Index0.90.80.70.60.50.40.30.20.10.0
Pairwise Correlations betweenPolarization MeasuresRQ IndexRQ IndexBerryMielkeLsquared PolarizationLeik10.350.520.280.55Berry larization0.280.830.9410.91Leik0.550.790.990.911
Further development Bayesian LCA Testing for local homogeneity in IRTframeworks instead of LCA measurementinvariance Adding covariates Any good advice is highly welcomed!!
Polarization in Survey Data The main objects of interest are latent constructs (measured through multiple manifest variables). Information about distributional parameters of latent variables provided by relevant statistical software is limited. Measuring polarization for aggregated factor scores seems to be an inaccurate approach due
What polarization means? Polarization describes the alignment of a particle's spin with its momentum. Quantified using the helicity: Transversal polarization (T): the spin and momenta are (anti)-aligned (h 1, -1) Longitudinal polarization (L): spin parallel with the momenta (h 0) A caveat Polarization measurements are frame dependent
PMD (Polarization Mode Dispersion) is the differential arrival time of the different polarization components of an input light pulse, transmitted by an optical fiber. This light pulse can always be decomposed into pairs of orthogonal polarization modes. These polarization modes propagate at different speeds according to a slow and
whose signature measurements are sensitive to the polarization ofthe targets and their backgrounds. Fusion is achieved by constructing the joint statistical measures for the target's polarization states. Target polarization states are in terms ofthe intensity, percent of linear polarization, and the angle ofpolarization plane. Applications .
applicable to any linear polarization data set for which the noise covariance matrices are known. Key words. polarization - methods: statistical - methods: data analysis - techniques: polarimetric 1. Introduction The linear polarization of the incoming radiation can be de-scribed by the Stokes parameters Q and U along with the to-tal .
A Ka band dual-polarization direct detection total power MMW radiometer is designed in the literature [ ]; this system receives targets and background radiation signal s horizontal polarization component and vertical polarization component through dual-channel receiver; a er comparing the di erences, the system detects and identi es some false
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