<html><head></head><body><div style="color:#000; background-color:#fff; font-family:Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:16px"><div id="yui_3_16_0_ym19_1_1498066764383_35290"><span></span></div>Fernando, muito obrigado pelo pronto retorno.<br id="yui_3_16_0_ym19_1_1498066764383_35633"><br id="yui_3_16_0_ym19_1_1498066764383_35634">De fato, eu costumo obter as SQs parciais (tipo 2) mudando a ordem dos termos do modelo, usando a própria função mais conhecida anova(), mas tinha me entusiasmado com a existência de uma função pronta como a Anova().<br id="yui_3_16_0_ym19_1_1498066764383_35635"><br id="yui_3_16_0_ym19_1_1498066764383_35636">Quanto às tipo 3, mesmo seguindo a sua sugestão, Fernando, continuo obtendo aquela mensagem de erro:<br id="yui_3_16_0_ym19_1_1498066764383_35637"><br id="yui_3_16_0_ym19_1_1498066764383_35638">> library(car) <br id="yui_3_16_0_ym19_1_1498066764383_35639">> Anova(lm(y ~ factorA * factorB, data =dados, contrasts = list(factorA = contr.sum, factorB = contr.sum)), type = 3)<br id="yui_3_16_0_ym19_1_1498066764383_35640">Error in Anova.III.lm(mod, error, singular.ok = singular.ok, ...) : <br id="yui_3_16_0_ym19_1_1498066764383_35641"> there are aliased coefficients in the model<br id="yui_3_16_0_ym19_1_1498066764383_35642">> Anova(lm(y ~ factorB * factorA, data =dados, contrasts = list(factorA = contr.sum, factorB = contr.sum)), type = 3)<br id="yui_3_16_0_ym19_1_1498066764383_35643">Error in Anova.III.lm(mod, error, singular.ok = singular.ok, ...) : <br id="yui_3_16_0_ym19_1_1498066764383_35644"> there are aliased coefficients in the model<br id="yui_3_16_0_ym19_1_1498066764383_35645"><br id="yui_3_16_0_ym19_1_1498066764383_35646"><br id="yui_3_16_0_ym19_1_1498066764383_35647">Será que estou fazendo alguma coisa equivocada?<br id="yui_3_16_0_ym19_1_1498066764383_35648"><br id="yui_3_16_0_ym19_1_1498066764383_35649"><br id="yui_3_16_0_ym19_1_1498066764383_35650">Fernando Souza e Cesar, obrigado também pelos retornos. Quis propositadamente inventar um conjunto de dados fortemente desbalanceado, justamente para verificar os resultados das funções drop1() e Anova(). Minha preocupação é realmente apenas com a mecânica do cálculo.<br id="yui_3_16_0_ym19_1_1498066764383_35651"><br id="yui_3_16_0_ym19_1_1498066764383_35652">O fato de haver um único grau de liberdade para a interação AxB neste conjunto desbalanceado fictício é que aqui só se pode compor um único "grid" regular envolvendo dois níveis do fator A e dois níveis do fator B (o segundo e o quarto níveis de ambos os fatores), ou seja, um único grid 2x2, e assim temos (2-1)(2-1) = 1 único grau de liberdade.<br id="yui_3_16_0_ym19_1_1498066764383_35653"><br id="yui_3_16_0_ym19_1_1498066764383_35654">Abraços,<br id="yui_3_16_0_ym19_1_1498066764383_35657">Eduardo.<br><div class="qtdSeparateBR"><br><br></div><div class="yahoo_quoted" style="display: block;"> <div style="font-family: Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 16px;"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 16px;"> <div dir="ltr"><font size="2" face="Arial"> Em Quarta-feira, 21 de Junho de 2017 16:19, Cesar Rabak <cesar.rabak@gmail.com> escreveu:<br></font></div> <br><br> <div class="y_msg_container"><div id="yiv5730108687"><div><div dir="ltr">Eduardo,<div><br clear="none"></div><div>Além das excelentes respostas que vc já recebeu, note que até a <i>terminologia</i> sobre "Somas de Quadrados Tipos II e III" é na verdade estranha à Estatística e sim um artifício inventado por um dos 'fabricantes' de pacote de SW estatístico cuja terminologia "pegou".</div><div><br clear="none"></div><div>Comecei o post com essa observação para poder comentar que sua afirmação « . . . nem sempre o R as calcula corretamente. » não está certa, na verdade nem errada está (W. Pauli)¹!</div><div><br clear="none"></div><div>Como seu exemplo é "sintético" e visando apenas à mecânica/matemática do cálculo, não há mais que se possa dizer.</div><div><br clear="none"></div><div>Com relação a uma análise mais concreta com objetivos no domínio do problema você deve estudar o quê está em jogo na análise e se os resultados de dados tão desbalanceados fariam sentido 'prático' para o problema físico.</div><div><br clear="none"></div><div>HTH</div><div>--</div><div>Cesar Rabak</div><div><br clear="none"></div><div><br clear="none"></div><div>[1] « Das ist nicht nur nicht richtig, es ist nicht einmal falsch! »</div><div> -- Wolfgang Pauli</div></div><div class="yiv5730108687gmail_extra"><br clear="none"><div class="yiv5730108687gmail_quote">2017-06-21 12:52 GMT-03:00 Fernando Souza via R-br <span dir="ltr"><<a rel="nofollow" shape="rect" ymailto="mailto:r-br@listas.c3sl.ufpr.br" target="_blank" href="mailto:r-br@listas.c3sl.ufpr.br">r-br@listas.c3sl.ufpr.br</a>></span>:<br clear="none"><blockquote class="yiv5730108687gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><div dir="ltr"><div><div>Se você possui 4 GL para o fator A e 4 GL para o fator B, como podem
haver somente 1 GL para a interação? Acredito que por isso o R retorna <span id="yiv5730108687m_6669419026985202093gmail-m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133224">"there are aliased coefficients in the model". Uma vez que você não possui informações em todas as combinações dos fatores A e B. <br clear="none"><br clear="none">with(dados,table(factorA, factorB))<br clear="none"><br clear="none"></span></div><span id="yiv5730108687m_6669419026985202093gmail-m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133224">Veja com um banco de dados completo e nos retorne<br clear="none"><br clear="none"><br clear="none"></span></div><span id="yiv5730108687m_6669419026985202093gmail-m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133224">Att<br clear="none"></span></div><div class="yiv5730108687gmail_extra"><br clear="none"><div class="yiv5730108687gmail_quote"><div><div class="yiv5730108687h5">Em 21 de junho de 2017 11:23, Eduardo Bearzoti via R-br <span dir="ltr"><<a rel="nofollow" shape="rect" ymailto="mailto:r-br@listas.c3sl.ufpr.br" target="_blank" href="mailto:r-br@listas.c3sl.ufpr.br">r-br@listas.c3sl.ufpr.br</a>></span> escreveu:<br clear="none"></div></div><blockquote class="yiv5730108687gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><div><div class="yiv5730108687h5"><div><div style="color:#000;background-color:#fff;font-family:Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:16px;"><div dir="ltr" id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_132816"><span id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133224">Bom dia, pessoal.<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133123" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133124" clear="none">Minha dúvida é particularmente sobre o cálculo de somas de quadrados tipo III (mas também do tipo II) no R com conjuntos de dados desbalanceados.<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133125" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133126" clear="none">Estou ciente da polêmica em torno do uso destas somas de quadrados na comunidade estatística, mas gostaria muito de poder calculá-las no R, e, a não ser que eu esteja enganado, nem sempre o R as calcula corretamente.<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133127" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133128" clear="none">Pesquisando na rede, descobri que em geral são apontadas duas maneiras de se calcular somas de quadrados tipo III no R: a) Utilizando a função drop1() em modelos ajustados com a especificação de contrastes contr.sum (ou contr.helmert), e b) utilizando a função Anova() (com "A" maiúsculo), do pacote car. <br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133129" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133130" clear="none">Abaixo, eu apresento um exemplo simulado de um ensaio fatorial altamente desbalanceado, faltando várias combinações entre os níveis dos dois fatores. A interação entre eles, por exemplo, apresenta um único grau de liberdade, tamanho o desbalanceamento.<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133131" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133132" clear="none">dados <- data.frame(y=c(35.44627,43.433 53,40.20125,38.1061,39.96211, 44.21636,19.78237,23.58636,31. 73537,<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133133" clear="none"> 36.49977,38.71573,41.00456,19. 6787,16.43436,32.05407,33.3784 ,18.58266,17.74051),<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133134" clear="none"> factorA=as.factor(c(2,2,4,4,4, 4,6,6,6,6,6,6,8,8,8,8,10,10)),<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133135" clear="none"> factorB=as.factor(c(2,2,1.5,1. 5,2.5,2.5,1,1,2,2,3,3,1.5,1.5, 2.5,2.5,2,2)))<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133136" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133137" clear="none">Tenho em mente o modelo contendo os fatores A e B, bem como sua interação. <br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133138" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133139" clear="none">No SAS, utilizando o proc glm, obtenho as seguintes somas de quadrados tipo I, tipo II e tipo III:<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133140" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133141" clear="none">Source DF Type I SS<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133142" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133143" clear="none">factorA 4 964.4164933<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133144" clear="none">factorB 3 500.0771638<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133145" clear="none">factorA*factorB 1 68.7277880<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133146" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133147" clear="none">Source DF Type II SS<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133148" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133149" clear="none">factorA 3 <a rel="nofollow" shape="rect" href="">954.6730970</a><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133150" clear="none">factorB 3 500.0771638<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133151" clear="none">factorA*factorB 1 68.7277880<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133152" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133153" clear="none">Source DF Type III SS<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133154" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133155" clear="none">factorA 3 <a rel="nofollow" shape="rect" href="">954.6730970</a><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133156" clear="none">factorB 3 500.0771638<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133157" clear="none">factorA*factorB 1 68.7277880<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133158" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133159" clear="none">Percebam que neste exemplo as somas de quadrados tipo II e III são iguais, pois as "caselas" apresentam o mesmo número de repetições (duas).<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133160" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133161" clear="none">No R, tentei reproduzir este resultado seguindo os dois procedimentos citados acima:<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133162" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133163" clear="none">1) Utilizando a função drop1()<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133164" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133165" clear="none">> mod <- lm(y ~ factorA*factorB, <br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133166" clear="none"> contrasts=list(factorA=contr.s um, factorB=contr.sum),<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133167" clear="none"> data=dados)<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133168" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133169" clear="none">> drop1(mod, ~.,test = "F")<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133170" clear="none">Single term deletions<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133171" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133172" clear="none">Model:<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133173" clear="none">y ~ factorA * factorB<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133174" clear="none"> Df Sum of Sq RSS AIC F value Pr(>F) <br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133175" clear="none"><none> 70.841 42.661 <br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133176" clear="none">factorA 0 0.000 70.841 42.661 <br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133177" clear="none">factorB 0 0.000 70.841 42.661 <br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133178" clear="none">factorA:factorB 1 68.728 139.569 52.867 8.7315 0.01609 *<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133179" clear="none">---<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133180" clear="none">Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133181" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133182" clear="none">(apenas a soma de quadrados da interação foi calculada)<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133183" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133184" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133185" clear="none">2) Utilizando car::Anova()<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133186" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133187" clear="none">> mod <- lm(y ~ factorA*factorB, data=dados)<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133188" clear="none">> library(car)<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133189" clear="none">> Anova(mod,type = "II")<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133190" clear="none">Anova Table (Type II tests)<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133191" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133192" clear="none">Response: y<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133193" clear="none"> Sum Sq Df F value Pr(>F) <br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133194" clear="none">factorA 1284.10 4 40.7845 8.995e-06 ***<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133195" clear="none">factorB 500.08 3 21.1774 0.0002047 ***<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133196" clear="none">factorA:factorB 68.73 1 8.7315 0.0160919 * <br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133197" clear="none">Residuals 70.84 9 <br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133198" clear="none">---<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133199" clear="none">Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133200" clear="none">> Anova(mod,type = "III")<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133201" clear="none">Error in Anova.III.lm(mod, error, singular.ok = singular.ok, ...) : <br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133202" clear="none"> there are aliased coefficients in the model</span></div><div dir="ltr" id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133297"><br clear="none"><span id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133224"></span></div><div dir="ltr" id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133351"><span id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133224">(soma de quadrados tipo II calculada errada para o fator A, e tipo III não calculadas)<br clear="none"></span></div><div dir="ltr"><span id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133224"><br clear="none"></span></div><div dir="ltr" id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133353"><span id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133224">Ou seja, não consegui reproduzir nem as somas de quadrados tipo III nem as do tipo II, por nenhum dos dois procedimentos sugeridos na rede.<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133205" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133206" clear="none">Estou utilizando:<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133207" clear="none">> sessionInfo()<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133208" clear="none">R version 3.4.0 (2017-04-21)<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133209" clear="none">Platform: x86_64-pc-linux-gnu (64-bit)<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133210" clear="none">Running under: Ubuntu 14.04.5 LTS<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133211" clear="none">(...)<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133212" clear="none">other attached packages:<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133213" clear="none">[1] car_2.1-4<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133214" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133215" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133216" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133217" clear="none">Eu estaria fazendo alguma coisa equivocada? Qualquer observação, sugestão, ou indicação de alguma maneira alternativa para cálculo das somas de quadrados tipo III no R será muito bem vinda.<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133218" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133219" clear="none">Abs,<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133220" clear="none"><br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133221" clear="none">Eduardo Bearzoti<br id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_133222" clear="none">(UFOP)</span></div><div id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_132877"> </div><div class="yiv5730108687m_6669419026985202093m_-6328446204165365820signature" id="yiv5730108687m_6669419026985202093m_-6328446204165365820yui_3_16_0_ym19_1_1498049847166_132878"><br clear="none"></div></div></div><br clear="none"></div></div><span class="yiv5730108687">______________________________ _________________<br clear="none">
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