Análise conjunta de fatores: distribuição amostral da importância relativa por simulação de dados

• Ano de defesa: 2008
• Autor(a) principal: Temoteo, Alex da Silva
• Orientador(a): Silva, Carlos Henrique Osório
• Banca de defesa: Ribeiro Junior, José Ivo , Minim, Valéria Paula Rodrigues , Martins Filho, Sebastião
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Viçosa
• Programa de Pós-Graduação: Mestrado em Estatística Aplicada e Biometria
• Departamento: Estatística Aplicada e Biometria
• País: BR
• Palavras-chave em Português: Conjoint analysis; Nota de aceitação; Transformação de locação e escala; Distribuição beta
• Palavras-chave em Inglês: Conjoint analysis; Note acceptance; Beta distribution
• Área do conhecimento CNPq: CNPQ::CIENCIAS AGRARIAS
• Link de acesso: http://locus.ufv.br/handle/123456789/4024

Conjoint analysis is a regression analvsis that uses a model with dummy or indicator explanatory variables to study consumer preference for treatments that can be products or services, and are defined by combining levels of each attribute or factor. lt allows the estimation of the Relative Importance (RI ) of each factor that makes up the treatments. Such studies are important to help decide, based on RI estimates obtained from the CA, to which factors should be given more attention when developing the products and/or services. In this research work we conducted a simulation study in order to investigate the robustness of the RI sampling distribution to departures from normality for the distribution of the random error term (&#1108;) of the CA model. We simulated four alternative distributions for &#1108; and generated data (acceptance notes) that allowed estimation of RI for hypothetical factors A, B, C and D considered in our study. In addition to the normal distribution, we used a location and scale transformation of the beta density to generate three alternative distributions: right skewed, left skewed, and also an U-shape distribution. Each one of these four distributions was tested with two standard error values (&#963; = 2.8 and 0.5) which resulted in eight alternative scenarios. Our simulation study considered factors A and B with 3 levels and factors C and D with two levels, hence 36 treatments in a full factorial design. We set reference RI values of 44.25%, 25.66%, 26.55% and 3.54%, respectively for factor A, B, C and D, and simulated data such that each treatment was evaluated by 108 consumers. This data set with 3888 observations was simulated 100 times for each scenario and analyzed by CA which resulted in 100 RI estimates for each factor at every scenario. Results were investigated by 95% confidence intervals (Cl) using the usual normal approximation and also percentile intervals, histograms of RI values sampling distribution to check normality, and also we calculated relative mean errors of estimation (RME) with respect to the reference RI values It was observed that the confidence intervals included the values of RI´s taken as reference in all scenarios, with the exception of: (i) factors A and B, with the normal Cl using normal distribution and &#963; = 2.8; ( i i ) wi th normal Cl and &#963; = 0.5, (iia) for factors A and C with normal distribution, U shaped and left skewed; (iib) for factor B with U shaped model and (iic) for factor D with normal distribution and U shaped. In al l these cases were the Cl missed the RI reference value, we observed close miss left and miss right results. We observed RME < 5% in all scenarios except for normal distribution and factor D only, for which RME = 7.91%. We concluded that sampling distribution of the estimator of the RI of a factor is relatively robust to departures from the normal distribution. In fact, results showed that i t s sampl ing dist r ibut ion must be close to the normal, regardless of the distribution of the random error term of the CA model.