<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332016000100199</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[An alternative to classical latent class models selection methods for sparse binary data: an illustration with simulated data]]></article-title>
<article-title xml:lang="es"><![CDATA[Un método alternativo para la selección de modelos de clases latentes en datos binarios escasos: una ilustración con datos simulados]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Araya Alpízar]]></surname>
<given-names><![CDATA[Carlomagno]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Costa Rica  ]]></institution>
<addr-line><![CDATA[San Ramón ]]></addr-line>
<country>CR</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2016</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2016</year>
</pub-date>
<volume>23</volume>
<numero>1</numero>
<fpage>199</fpage>
<lpage>220</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332016000100199&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332016000100199&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332016000100199&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[AbstractWithin the context of a latent class model with manifest binary variables, we propose an alternative method that solves the problem of estimating empirical distribution with sparse contingency tables and the chisquare approximation for goodness-of-fit will not be valid. We analyze sparse binary data, where there are many response patterns with very small expected frequencies in several data sets varying in degree of sparseness from 1 to 5 defined d = n/2p = n/R is a factor that is mentioned in almost all prior literature as being an important determinant of how well the distribution is represented by the chi-squared.The proposed approach produced results that were valid and reliable under the mentioned problematic data conditions. Results from the proposal presented compare the rates of Type I for traditional goodness-of-fit tests. We also show that with data density d &#8804; 5, Pearson's statistic  should not be used to select latent class models using the Patterns Method, given that this has the probability of Type I error being greater than 5%. By comparing the Patterns Method and the Parametric Bootstrap for data density d = 2, we show that the Patterns Method has more accurate Type I error probabilities since the likelihood ratio, Read-Cressie and Freeman-Tukey statistics afford values of &#945;&lt;0.05. In contrast, the Parametric Bootstrap provides values in these statistics that surpass 5%.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[ResumenEn el contexto de modelos de clases latentes con variables manifiestas binarias, se propone un método alternativo para resolver el problema de la estimación de la distribución empírica con tablas de contingencias escasas, donde la aproximación de los estadísticos de bondad de ajuste por la distribución Chi-Cuadrada no es válida. Se analiza datos binarios escasos, donde muchos patrones de respuesta que tienen frecuencias esperadas pequeñas, en conjuntos de datos con grados de datos escasos de 1 a 5, donde d = n/2p = n/R es un factor es mencionado en la literatura como determinante de la bondad de ajuste a la distribución Chi-Cuadrada. La propuesta presenta resultados válidos y confiables en las condiciones de los datos mencionadas. Para los resultados se presenta tasas de error tipo I para las pruebas tradiciones de bondad de ajuste. También se muestra que para niveles de densidad de datos d &#8804; 5, el estadístico Pearson no es el apropiado para seleccionar modelos de clases latentes utilizando el Método de Patrones, dado que presenta probabilidad de error de tipo I más grandes que 5%. Al comparar el Método de Patrones y el Bootstrap Paramétrico para la densidad d = 2, se muestra que el Método de Patrones tiene probabilidades de error de tipo I menores de 5% en los estadísticos de razón de verosimilitud, Read-Cressie y Freeman-Tukey. En contraste, el Bootstrap Paramétrico produce valores en estos estadísticos que superan un 5%.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[sparse data]]></kwd>
<kwd lng="en"><![CDATA[latent class]]></kwd>
<kwd lng="en"><![CDATA[goodness-of-fit]]></kwd>
<kwd lng="en"><![CDATA[binary data]]></kwd>
<kwd lng="es"><![CDATA[datos escasos]]></kwd>
<kwd lng="es"><![CDATA[clases latentes]]></kwd>
<kwd lng="es"><![CDATA[bondad de ajuste]]></kwd>
<kwd lng="es"><![CDATA[datos binarios]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Agresti]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[An Introduction to Categorical Data Analysis]]></source>
<year>2007</year>
<edition>2nd</edition>
<publisher-loc><![CDATA[Hoboken NJ ]]></publisher-loc>
<publisher-name><![CDATA[Wiley Interscience]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[An empirical investigation of some effects of sparseness in contingency tables]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Agresti]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Yang]]></surname>
<given-names><![CDATA[M.C.]]></given-names>
</name>
</person-group>
<source><![CDATA[Computational Statistics &amp; Data Analysis]]></source>
<year>1987</year>
<volume>5</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>9-21</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bartholomew]]></surname>
<given-names><![CDATA[D.J.]]></given-names>
</name>
<name>
<surname><![CDATA[Knott]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Moustaki]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
</person-group>
<source><![CDATA[Latent Variable Models and Factor Analysis: A Unified Approach]]></source>
<year>2011</year>
<publisher-loc><![CDATA[Chichester UK ]]></publisher-loc>
<publisher-name><![CDATA[John Wiley & Sons]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[A goodness of fit test for sparse 2p contingency tables]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bartholomew]]></surname>
<given-names><![CDATA[D.J.]]></given-names>
</name>
<name>
<surname><![CDATA[Leung]]></surname>
<given-names><![CDATA[S.O.]]></given-names>
</name>
</person-group>
<source><![CDATA[British Journal of Mathematical and Statistical Psychology]]></source>
<year>2002</year>
<volume>55</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>1-15</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[The goodness of fit of latent trait models in attitude measurement]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bartholomew]]></surname>
<given-names><![CDATA[D.J.]]></given-names>
</name>
<name>
<surname><![CDATA[Tzamourani]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Sociological Methods &amp; Research]]></source>
<year>1999</year>
<volume>27</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>525-46</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[The &#967;2 test of goodness of fit]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cochran]]></surname>
<given-names><![CDATA[W.G.]]></given-names>
</name>
</person-group>
<source><![CDATA[The Annals of Mathematical Statistics]]></source>
<year>1952</year>
<volume>23</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>315-45</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Some methods for strengthening the common &#967;2 tests]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cochran]]></surname>
<given-names><![CDATA[W.G.]]></given-names>
</name>
</person-group>
<source><![CDATA[Biometrics]]></source>
<year>1954</year>
<volume>10</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>417-51</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Goodnessof-fit testing for latent class models]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Collins]]></surname>
<given-names><![CDATA[L.M.]]></given-names>
</name>
<name>
<surname><![CDATA[Fidler]]></surname>
<given-names><![CDATA[P.L.]]></given-names>
</name>
<name>
<surname><![CDATA[Wugalter]]></surname>
<given-names><![CDATA[S.E.]]></given-names>
</name>
<name>
<surname><![CDATA[Long]]></surname>
<given-names><![CDATA[J.D.]]></given-names>
</name>
</person-group>
<source><![CDATA[Multivariate Behavioral Research]]></source>
<year>1993</year>
<volume>28</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>375-89</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cramér]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematical Methods of Statistics]]></source>
<year>1946</year>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Princeton University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Accurate directional inference for vector parameters in linear exponential families]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Davison]]></surname>
<given-names><![CDATA[A.C.]]></given-names>
</name>
<name>
<surname><![CDATA[Fraser]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Reid]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Sartori]]></surname>
<given-names><![CDATA[N]]></given-names>
</name>
</person-group>
<source><![CDATA[Journal of the American Statistical Association]]></source>
<year>2013</year>
<volume>109</volume>
<page-range>302-14</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dayton]]></surname>
<given-names><![CDATA[C.M]]></given-names>
</name>
</person-group>
<source><![CDATA[Latent Class Scaling Analysis]]></source>
<year>1998</year>
<publisher-loc><![CDATA[Thousand Oaks CA ]]></publisher-loc>
<publisher-name><![CDATA[Sage Publications]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dias]]></surname>
<given-names><![CDATA[J.G.]]></given-names>
</name>
<name>
<surname><![CDATA[Vermunt]]></surname>
<given-names><![CDATA[J.K]]></given-names>
</name>
</person-group>
<source><![CDATA[Bootstrap methods for measuring classification uncertainty in latent class analysis]]></source>
<year>2006</year>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fisher]]></surname>
<given-names><![CDATA[R.A]]></given-names>
</name>
</person-group>
<source><![CDATA[Statistical Methods for Research Workers]]></source>
<year>1941</year>
<publisher-loc><![CDATA[Edinburgh ]]></publisher-loc>
<publisher-name><![CDATA[Oliver and Boyd]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gong]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<source><![CDATA[Modeling and Measuring Association for Ordinal Data]]></source>
<year>2012</year>
<publisher-loc><![CDATA[Canada ]]></publisher-loc>
<publisher-name><![CDATA[Faculty of Graduate Studies and Research, University of Regina]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kendall]]></surname>
<given-names><![CDATA[M.G.]]></given-names>
</name>
</person-group>
<source><![CDATA[The Advanced Theory of Statistics. Vol. 1: Distribution Theory]]></source>
<year>1952</year>
<edition>5th</edition>
<publisher-loc><![CDATA[London ]]></publisher-loc>
<publisher-name><![CDATA[Griffin]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Goodness-of-fit testing based on a weighted bootstrap: A fast large-sample alternative to the parametric bootstrap]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kojadinovic]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Yan]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Canadian Journal of Statistics]]></source>
<year>2012</year>
<volume>40</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>480-500</page-range></nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kraus]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<source><![CDATA[On the Measurement of Model Fit for Sparse Categorical Data]]></source>
<year>2012</year>
<publisher-name><![CDATA[Faculty of Social Sciences, Uppsala University]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Bayesian modeling of temporal dependence in large sparse contingency tables]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kunihama]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Dunson]]></surname>
<given-names><![CDATA[D.B.]]></given-names>
</name>
</person-group>
<source><![CDATA[Journal of the American Statistical Association]]></source>
<year>2013</year>
<volume>108</volume>
<numero>504</numero>
<issue>504</issue>
<page-range>1324-38</page-range></nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="book">
<article-title xml:lang=""><![CDATA[Chi-square distribution]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lancaster]]></surname>
<given-names><![CDATA[H.O.]]></given-names>
</name>
<name>
<surname><![CDATA[Seneta]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Encyclopedia of Biostatistics]]></source>
<year>1969</year>
<publisher-loc><![CDATA[Florida ]]></publisher-loc>
<publisher-name><![CDATA[John Wiley & SonsLtd.]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Bootstrapping goodness-of-fit measures in categorical data analysis]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Langeheine]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Pannekoek]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Van de Pol]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<source><![CDATA[Sociological Methods &amp; Research]]></source>
<year>1996</year>
<volume>24</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>492-516</page-range></nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Small-sample comparisons of exact levels for chisquared goodness-of-fit statistics]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Larntz]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Journal of the American Statistical Association]]></source>
<year>1978</year>
<volume>73</volume>
<numero>362</numero>
<issue>362</issue>
<page-range>253-63</page-range></nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lazarsfeld]]></surname>
<given-names><![CDATA[P.F.]]></given-names>
</name>
<name>
<surname><![CDATA[Henry]]></surname>
<given-names><![CDATA[N.W.]]></given-names>
</name>
</person-group>
<source><![CDATA[Latent Structure Analysis]]></source>
<year>1968</year>
<publisher-loc><![CDATA[Boston ]]></publisher-loc>
<publisher-name><![CDATA[Houghton Mifflin]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Categorical independence tests for large sparse r-way contingency tables]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mielke]]></surname>
<given-names><![CDATA[P.W.]]></given-names>
</name>
<name>
<surname><![CDATA[Berry]]></surname>
<given-names><![CDATA[K.J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Perceptual and Motor Skills]]></source>
<year>2002</year>
<volume>95</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>606- 610</page-range></nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Milovanovic]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Chi-Square Orthogonal Components for Assessing Goodness-of-fit of Multidimensional Multinomial Data]]></source>
<year>2011</year>
<publisher-name><![CDATA[Arizona State University]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B25">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Deciding on the number of classes in latent class analysis and growth mixture modeling: a Monte Carlo simulation study]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Nylund]]></surname>
<given-names><![CDATA[K.L.]]></given-names>
</name>
<name>
<surname><![CDATA[Asparouhov]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Muthén]]></surname>
<given-names><![CDATA[B.O.]]></given-names>
</name>
</person-group>
<source><![CDATA[Structural Equation Modeling]]></source>
<year>2007</year>
<volume>14</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>535- 569</page-range></nlm-citation>
</ref>
<ref id="B26">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Papoulis]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Pillai]]></surname>
<given-names><![CDATA[S.U.]]></given-names>
</name>
</person-group>
<source><![CDATA[Probability, Random Variables, and Stochastic Processes]]></source>
<year>2002</year>
<publisher-name><![CDATA[McGraw-Hill Education]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B27">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Profile statistics for sparse contin-&#711; gency tables under Poisson sampling]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Radavicius]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Samusenko]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Austrian Journal of Statistics]]></source>
<year>2011</year>
<volume>40</volume>
<numero>12</numero>
<issue>12</issue>
<page-range>115-23</page-range></nlm-citation>
</ref>
<ref id="B28">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Goodness-of-fit tests for sparse&#711; nominal data based on grouping]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Radavicius]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Samusenko]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Nonlinear Analysis: Modeling and Control]]></source>
<year>2012</year>
<volume>17</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>489-501</page-range></nlm-citation>
</ref>
<ref id="B29">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[A goodness-of-fit test for the latent class model when expected frequencies are small]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Reiser]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Lin]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
</person-group>
<source><![CDATA[Sociological methodology]]></source>
<year>1999</year>
<volume>29</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>81-111</page-range></nlm-citation>
</ref>
<ref id="B30">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Samusenko]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Nonparametric Criteria for Sparse Contingency Tables]]></source>
<year>2012</year>
<publisher-loc><![CDATA[Lithuania ]]></publisher-loc>
<publisher-name><![CDATA[Vilnius Gediminas Technical Univerty]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B31">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Inaccuracy of the &#967;2 test of goodness of fit when expected frequencies are small]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tate]]></surname>
<given-names><![CDATA[M.W.]]></given-names>
</name>
<name>
<surname><![CDATA[Hyer]]></surname>
<given-names><![CDATA[L.A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Journal of the American Statistical Association]]></source>
<year>1973</year>
<volume>68</volume>
<numero>344</numero>
<issue>344</issue>
<page-range>836-41</page-range></nlm-citation>
</ref>
<ref id="B32">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Type I errors and power of the parametric bootstrap goodness-of-fit test: full and limited information]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tollenaar]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Mooijaart]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[British Journal of Mathematical and Statistical Psychology]]></source>
<year>2003</year>
<volume>56</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>271-88</page-range></nlm-citation>
</ref>
<ref id="B33">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Van Der Heijden]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Hart]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Dessens]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A parametric bootstrap procedure to perform statistical tests in a LCA of anti-social behaviour]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Rost]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Applications of Latent Trait and Latent Class Models in the Social Sciences]]></source>
<year>1997</year>
<page-range>196-208</page-range><publisher-loc><![CDATA[Ann Arbor ]]></publisher-loc>
<publisher-name><![CDATA[University of Michigan Library]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B34">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Bootstrapping goodness-of-fit statistics for sparse categorical data-results of a Monte Carlo study]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Von Davier]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Methods of Psychological Research]]></source>
<year>1997</year>
<volume>2</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>29-48</page-range></nlm-citation>
</ref>
<ref id="B35">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Assessing model fit in latent class analysis when asymptotics do not hold methodology]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Van Kollenburg]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Mulder]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Vermunt]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Methodology: European Journal of Research Methods for the Behavioral and Social Sciences]]></source>
<year>2015</year>
<volume>11</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>65-79</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
