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中文摘要：
指数族非线性模型或广义非线性模型是广义线性模型和正态回归模型的自然推广.本文针对可分的连续型指数族回归模型（如正态模型,Γ模型,逆高斯模型）,讨论广义非线性纵向数据模型中偏离名义离差的检验问题,得到了检验的score统计量,并推导了它们的渐近分布和局部近似功效.然后利用Monte Carlo方法研究了检验统计量的性质.最后利用百慕大草地数据说明了检验方法的应用.
英文摘要：
Exponential family nonlinear models, or generalized nonlinear models are generalized from generalized linear models and nonlinear regression. For separable and continous exponential family models （such as normal, gamma, and inverse Gaussian models）, this paper discusses the tests for departures from nominal dispersion in the framework of longitudinal nonlinear models with varying dispersion and/or random effects. The score test statistics are constructed and their asymptotic distributions and local powers are derived. The properties of test statistics are investigated through Monte Carlo simulations. We illustrate our test methods by data concerning the yield of coastal Bermuda grass.
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Heteroscedasticity and/or autocorrelation diagnostics in nonlinear models with AR(1) and symmetrical
Testing for departures from nominal dispersion in generalized nonlinear models with varying dispersi
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