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What is the assumption made about the random effects in the linear mixed model for the autism study?
What is the assumption made about the random effects in the linear mixed model for the autism study?
What is the assumption made about the random errors in the linear mixed model for the autism study?
What is the assumption made about the random errors in the linear mixed model for the autism study?
What is the covariance matrix assumed for the random effects in the linear mixed model for the autism study?
What is the covariance matrix assumed for the random effects in the linear mixed model for the autism study?
What is the covariance matrix assumed for the random errors in the linear mixed model for the autism study?
What is the covariance matrix assumed for the random errors in the linear mixed model for the autism study?
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What type of likelihood ratio tests are used for hypothesis testing of the random effects in the linear mixed model for the autism study?
What type of likelihood ratio tests are used for hypothesis testing of the random effects in the linear mixed model for the autism study?
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What type of likelihood ratio tests are used for hypothesis testing of the fixed effects in the linear mixed model for the autism study?
What type of likelihood ratio tests are used for hypothesis testing of the fixed effects in the linear mixed model for the autism study?
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What was found about the quadratic effect of age on social development in the autism study?
What was found about the quadratic effect of age on social development in the autism study?
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What was found about the interaction effect of age squared and initial language development in the autism study?
What was found about the interaction effect of age squared and initial language development in the autism study?
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What was found about the interaction effect of age and initial language development in the autism study?
What was found about the interaction effect of age and initial language development in the autism study?
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What was the final model selected for the analysis of language development in children study?
What was the final model selected for the analysis of language development in children study?
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What is the expected value of Vsaeti at a given age called in the analysis of language development in children study?
What is the expected value of Vsaeti at a given age called in the analysis of language development in children study?
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What is the estimate of the variance-covariance matrix of model (3) in the analysis of social development trajectories for autistic children study?
What is the estimate of the variance-covariance matrix of model (3) in the analysis of social development trajectories for autistic children study?
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Study Notes
Linear Mixed Model for Autism Study
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The linear mixed model assumes that there are random effects and random errors.
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The random effects are child-specific and assumed to follow a multivariate normal distribution.
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The random errors are associated with social development scores and assumed to follow a multivariate normal distribution.
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The model assumes that the random effect vectors are independent between children and that the random error vectors between children are independent of each other.
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The model is specified with a mean vector of 0 and an unstructured covariance matrix for the random effects and a diagonal covariance matrix for the random errors.
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Different structures for the covariance matrix of the random errors can be compared to see which fits the data appropriately.
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Hypothesis tests for the random effects are done using REML-based likelihood ratio tests.
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Hypothesis tests for the fixed effects are done using ML-based likelihood ratio tests.
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The quadratic effect of age on social development was found to differ between children and was included in the model.
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The interaction effect of age squared and initial language development was not found to be significant and was dropped from the model.
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The interaction effect of age and initial language development was found to be significant and was retained in the model.
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The quadratic effect of age was found to be in doubt and was tested, but the results were inconclusive.Analysis of Language Development in Children: Model Selection and Diagnostics
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The study examines the relationship between language development in children and various demographic factors.
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Model (3) is selected as the final model, which includes quadratic effects of Age and interaction terms with initial language development level.
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The marginal value of Vsaeti is the expected value of Vsaeti at a given age, and is the same for children with the same initial language development level.
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The linear effect of Age on Vsae for children with a Low level of initial language development is represented by β1.
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The model also allows for conditional values of Vsaeti, which are specific to each child and include random linear and quadratic effects of Age.
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Predicted marginal and conditional values of Vsae are calculated using GLS estimates of fixed and random effects.
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Residuals are the difference between observed and predicted values of Vsae.
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Model diagnostics include checking the agreement between predicted and observed values of Vsae, assumptions of the LMM, and examining the distribution of random effects and errors.
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There are outliers associated with child 49, 180, and 124 in the data.
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The constant variance and normality assumption for εij as a function of Age are not severely violated.
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The model is refit without the outliers and produces similar results.
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The study highlights the importance of model selection and diagnostics in LMMs for accurately analyzing data.Analysis of Social Development Trajectories for Autistic Children
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The social development for autistic children improves linearly over time on average.
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The level of language development at age 2 (initial language development) influences the social development trajectory over time for autistic children.
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Children with a High level of initial language development have greater mean social development at age 2 than those with a Low level.
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The mean social development for children with a High level of initial language development improves faster over time than those with a Low level.
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There are varying social development trajectories over time for children at all levels of initial language development.
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Some children show no improvement over time, while others improve linearly or accelerate over time.
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The observations of all 158 children were used to fit model (3).
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The estimate of the variance-covariance matrix, D, of model (3) is ô.
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The estimate of the correlation matrix of the random effect vector, µi, of model (3) is ñ.
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The estimate of the variance-covariance matrix, R, of model (3) is 38.790.
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Estimates of the fixed effects in model (3) are presented in Table 6.
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The estimates of the fixed effects suggest that the mean Vsae score for children with a High level of initial language development accelerates faster over time than those with a Low level.
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Description
Test your knowledge of Linear Mixed Models with these quizzes on autism and language development. Learn about the assumptions and specifications of the models, model selection and diagnostics, and the analysis of social development trajectories for autistic children. With keywords like linear mixed model, autism, language development, social development trajectories, and model selection, these quizzes will help you improve your understanding of LMMs and their applications in research.
