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Likelihood Ratio Tests for Fixed Model Terms using Residual Maximum Likelihood

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  • S. J. Welham
  • R. Thompson

Abstract

Likelihood ratio tests for fixed model terms are proposed for the analysis of linear mixed models when using residual maximum likelihood estimation. Bartlett‐type adjustments, using an approximate decomposition of the data, are developed for the test statistics. A simulation study is used to compare properties of the test statistics proposed, with or without adjustment, with a Wald test. A proposed test statistic constructed by dropping fixed terms from the full fixed model is shown to give a better approximation to the asymptotic χ2‐distribution than the Wald test for small data sets. Bartlett adjustment is shown to improve the χ2‐approximation for the proposed tests substantially.

Suggested Citation

  • S. J. Welham & R. Thompson, 1997. "Likelihood Ratio Tests for Fixed Model Terms using Residual Maximum Likelihood," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(3), pages 701-714.
    • Handle: RePEc:bla:jorssb:v:59:y:1997:i:3:p:701-714
    DOI: 10.1111/1467-9868.00092
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    Cited by:

    1. Orelien, Jean G. & Edwards, Lloyd J., 2008. "Fixed-effect variable selection in linear mixed models using R2 statistics," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1896-1907, January.
    2. Pringle, M.J. & Marchant, B.P. & Lark, R.M., 2008. "Analysis of two variants of a spatially distributed crop model, using wavelet transforms and geostatistics," Agricultural Systems, Elsevier, vol. 98(2), pages 135-146, September.
    3. Stein, Markus Chagas & da Silva, Michel Ferreira & Duczmal, Luiz Henrique, 2014. "Alternatives to the usual likelihood ratio test in mixed linear models," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 184-197.
    4. Pringle, M.J. & Baxter, S.J. & Marchant, B.P. & Lark, R.M., 2008. "Spatial analysis of the error in a model of soil nitrogen," Ecological Modelling, Elsevier, vol. 211(3), pages 453-467.
    5. Jing, Qi & Bouman, Bas & van Keulen, Herman & Hengsdijk, Huib & Cao, Weixing & Dai, Tingbo, 2008. "Disentangling the effect of environmental factors on yield and nitrogen uptake of irrigated rice in Asia," Agricultural Systems, Elsevier, vol. 98(3), pages 177-188, October.
    6. Josafhat Salinas-Ruíz & Sandra Luz Hernández-Valladolid & Juan Valente Hidalgo-Contreras & Juan Manuel Romero-Padilla, 2022. "Selection and Fitting of Mixed Models in Sugarcane Yield Trials," Agriculture, MDPI, vol. 12(3), pages 1-12, March.
    7. Manor, Orly & Zucker, D.M.David M., 2004. "Small sample inference for the fixed effects in the mixed linear model," Computational Statistics & Data Analysis, Elsevier, vol. 46(4), pages 801-817, July.
    8. Walter Dempsey & Peter McCullagh, 2018. "Survival models and health sequences," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(4), pages 550-584, October.

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