Master Linear Mixed Models

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Questions and Answers

What type of distribution are the random effects assumed to follow in the linear mixed model for autism study?

Normal distribution (correct)

Multinomial distribution

Poisson distribution

Binomial distribution

What is the covariance matrix assumption for the random errors in the linear mixed model for autism study?

Diagonal covariance matrix (correct)

Compound symmetry covariance matrix

Unstructured covariance matrix

Spherical covariance matrix

What type of likelihood ratio tests are used for hypothesis testing of the random effects in the linear mixed model for autism study?

Poisson-based likelihood ratio tests

ANOVA-based likelihood ratio tests

ML-based likelihood ratio tests

REML-based likelihood ratio tests (correct)

What is the final model selected for the analysis of language development in children study?

Model (3) Signup and view all the answers

What is the linear effect of Age on Vsae for children with a Low level of initial language development represented by in the analysis of language development in children study?

β1 Signup and view all the answers

What is the main finding of the analysis of social development trajectories for autistic children study?

Social development for autistic children improves linearly over time Signup and view all the answers

What is the estimate of the variance-covariance matrix, D, in model (3) of the analysis of social development trajectories for autistic children study?

ô Signup and view all the answers

What is the estimate of the correlation matrix of the random effect vector, µi, in model (3) of the analysis of social development trajectories for autistic children study?

ñ Signup and view all the answers

What do the estimates of the fixed effects suggest about the mean Vsae score for children with a High level of initial language development in the analysis of social development trajectories for autistic children study?

It improves linearly over time Signup and view all the answers

What is the assumption made about the distribution of the random effects in the linear mixed model for autism study?

They are child-specific and follow a multivariate normal distribution Signup and view all the answers

What is the purpose of comparing different structures for the covariance matrix of the random errors in the linear mixed model for autism study?

To see which fits the data appropriately Signup and view all the answers

What type of likelihood ratio tests are used for hypothesis testing of the random effects in the linear mixed model for autism study?

REML-based Signup and view all the answers

What type of likelihood ratio tests are used for hypothesis testing of the fixed effects in the linear mixed model for autism study?

ML-based Signup and view all the answers

What is the final model selected in the analysis of language development in children study?

Model (3) Signup and view all the answers

What is the purpose of model diagnostics in the analysis of language development in children study?

To check the agreement between predicted and observed values of Vsae Signup and view all the answers

What is the estimate of the variance-covariance matrix, D, of model (3) in the analysis of social development trajectories for autistic children?

ô Signup and view all the answers

What is the estimate of the correlation matrix of the random effect vector, µi, of model (3) in the analysis of social development trajectories for autistic children?

ñ Signup and view all the answers

What do the estimates of the fixed effects suggest in the analysis of social development trajectories for autistic children?

The mean Vsae score for children with a High level of initial language development accelerates faster over time than those with a Low level Signup and view all the answers

What is the purpose of Cook's distance in the analysis of language development in children study?

To identify influential observations when regressing the observed values of Vsae on the predicted conditional values of Vsae Signup and view all the answers

Which type of effect was found to differ between children and included in the final model in the autism study?

Quadratic effect of Age2 on Vsae Signup and view all the answers

What type of effect was tested and found to be insignificant and removed from the final model in the autism study?

Interaction effect of Age2Sq × Sicdegp Signup and view all the answers

What type of effect was found to be significant and included in the final model in the autism study?

Interaction effect of Age2 × Sicdegp Signup and view all the answers

What type of effect was found to be significant in the language development model and retained in the final model?

Quadratic effect of Age2 Signup and view all the answers

What type of effect significantly influences social development trajectories over time in the analysis of social development trajectories for autistic children study?

Initial language development level Signup and view all the answers

What do the confidence intervals for the fixed effects show in the analysis of social development trajectories for autistic children study?

Significant differences between the mean social development of children with high and low levels of initial language development Signup and view all the answers

What type of effect is greater for children with high levels of initial language development than those with low levels in the analysis of social development trajectories for autistic children study?

Linear effect of age on social development Signup and view all the answers

What type of models are marginal residuals usually analyzed in, rather than models that include random effects?

Marginal models Signup and view all the answers

What is the purpose of using maximum likelihood or restricted maximum likelihood in the linear mixed model for autism study?

To estimate the variance-covariance parameter vector of the random effects and error terms Signup and view all the answers

What is the difference between marginal and conditional values of Vsaeti in the analysis of language development in children study?

Marginal values are estimated using fixed effects, while conditional values include random effects Signup and view all the answers

What is the purpose of Cook's distance in the analysis of language development in children study?

To identify influential observations when regressing the observed values of Vsae on the predicted conditional values of Vsae Signup and view all the answers

What is the main finding of the analysis of social development trajectories in autistic children study?

The quadratic effect of age decreases as the linear effect increases Signup and view all the answers

What is the estimate of the correlation between the random effects in model (3) of the analysis of social development trajectories in autistic children study?

Cannot be determined from the text Signup and view all the answers

What is the purpose of using linear mixed models in the analysis of social development trajectories in autistic children study?

To estimate the variance-covariance parameter vector of the random effects and error terms Signup and view all the answers

What is the difference between marginal and conditional residuals in the analysis of language development in children study?

Marginal residuals are estimated using fixed effects, while conditional residuals include random effects Signup and view all the answers

What is the estimate of the variance-covariance matrix of the model used in the analysis of social development trajectories in autistic children study?

The estimate of the variance-covariance matrix of the model shows that the variability of Vsae scores for a child increases with age Signup and view all the answers

What is the purpose of hypothesis testing for fixed effects in the linear mixed model for autism study?

To test the significance of predictors Signup and view all the answers

What is the difference between marginal and conditional models in the analysis of language development data?

Marginal models estimate the expected value of the response variable while conditional models estimate the expected value of the response variable given the random effects Signup and view all the answers

What is the purpose of Cook's distance in the analysis of language development data?

To identify influential observations when regressing the observed values of Vsae on the predicted conditional values of Vsae Signup and view all the answers

What is the significance of the interaction effect of Age2 × Sicdegp in the linear mixed model for autism study?

It was found to be significant and included in the final model Signup and view all the answers

What is the difference between maximum likelihood and restricted maximum likelihood in the estimation of variance-covariance parameter vector in the linear mixed model for autism study?

Maximum likelihood estimates the variance-covariance parameter vector using all the data while restricted maximum likelihood uses a subset of the data Signup and view all the answers

What is the main finding of the analysis of social development trajectories in autistic children study?

Children with high levels of initial language development have greater mean social development and improve faster over time than those with low levels Signup and view all the answers

What is the purpose of examining histograms and scatter plots in the analysis of social development trajectories in autistic children study?

To examine the assumptions associated with the random effects and errors Signup and view all the answers

What is the difference between fixed and random effects in the linear mixed model for autism study?

Fixed effects are predictors while random effects are individual-specific Signup and view all the answers

What is the purpose of hypothesis testing for the random effects in the linear mixed model for autism study?

To determine which random effects are significant predictors of the response variable Signup and view all the answers

What is the difference between marginal and conditional residuals in the analysis of social development trajectories in autistic children study?

Marginal residuals are the difference between the observed and predicted values of the response variable while conditional residuals are the difference between the observed and predicted values of the response variable given the random effects Signup and view all the answers

Study Notes

Linear Mixed Model for Autism Study

The linear mixed model assumes that there are random effects and random errors.
The random effects are child-specific and assumed to follow a multivariate normal distribution.
The random errors are associated with social development scores and assumed to follow a multivariate normal distribution.
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.
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.
Different structures for the covariance matrix of the random errors can be compared to see which fits the data appropriately.
Hypothesis tests for the random effects are done using REML-based likelihood ratio tests.
Hypothesis tests for the fixed effects are done using ML-based likelihood ratio tests.
The quadratic effect of age on social development was found to differ between children and was included in the model.
The interaction effect of age squared and initial language development was not found to be significant and was dropped from the model.
The interaction effect of age and initial language development was found to be significant and was retained in the model.
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
The study examines the relationship between language development in children and various demographic factors.
Model (3) is selected as the final model, which includes quadratic effects of Age and interaction terms with initial language development level.
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.
The linear effect of Age on Vsae for children with a Low level of initial language development is represented by β1.
The model also allows for conditional values of Vsaeti, which are specific to each child and include random linear and quadratic effects of Age.
Predicted marginal and conditional values of Vsae are calculated using GLS estimates of fixed and random effects.
Residuals are the difference between observed and predicted values of Vsae.
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.
There are outliers associated with child 49, 180, and 124 in the data.
The constant variance and normality assumption for εij as a function of Age are not severely violated.
The model is refit without the outliers and produces similar results.
The study highlights the importance of model selection and diagnostics in LMMs for accurately analyzing data.Analysis of Social Development Trajectories for Autistic Children
The social development for autistic children improves linearly over time on average.
The level of language development at age 2 (initial language development) influences the social development trajectory over time for autistic children.
Children with a High level of initial language development have greater mean social development at age 2 than those with a Low level.
The mean social development for children with a High level of initial language development improves faster over time than those with a Low level.
There are varying social development trajectories over time for children at all levels of initial language development.
Some children show no improvement over time, while others improve linearly or accelerate over time.
The observations of all 158 children were used to fit model (3).
The estimate of the variance-covariance matrix, D, of model (3) is ô.
The estimate of the correlation matrix of the random effect vector, µi, of model (3) is ñ.
The estimate of the variance-covariance matrix, R, of model (3) is 38.790.
Estimates of the fixed effects in model (3) are presented in Table 6.
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.

Linear Mixed Model for Autism Study

The linear mixed model assumes that the response variable follows a normal distribution.
The model includes both fixed effects (predictors) and random effects (individual-specific effects).
The random effect vectors are assumed to be independent between children.
The model assumes that the random effects and error terms are normally distributed with zero means and specific covariance matrices.
The variance-covariance parameter vector of the random effects and error terms can be estimated using maximum likelihood or restricted maximum likelihood.
The covariance matrix for the error terms is assumed to be diagonal, but different structures can be tested to see which fits the data better.
The hypothesis tests for random effects are based on the likelihood ratio test using restricted maximum likelihood.
The hypothesis tests for fixed effects are based on the likelihood ratio test using maximum likelihood.
The quadratic effect of Age2 on Vsae was found to differ between children, and was included in the final model.
The interaction effect of Age2Sq × Sicdegp was tested, and found to be insignificant and removed from the final model.
The interaction effect of Age2 × Sicdegp was found to be significant and included in the final model.
There was some doubt over whether the quadratic effect of Age2 should be included in the final model, but it was found to be significant and included.Analysis of Language Development Data using Linear Mixed Effects Models
The quadratic effect of Age2 is found to be significant in the language development model, indicating its retention in the final model.
The marginal value of Vsaeti is the same for children who belong to the same initial language development level.
The linear effect of Age2 on Vsae for children who have a Low level of initial language development is represented by β1.
The model used for examining research questions is model (3), which includes various fixed and random effects.
The predicted marginal value of Vsaeti is given by the GLS estimates of the fixed effects.
Marginal residuals are usually analyzed in marginal models rather than in models that include random effects.
Each child has their own conditional value of Vsaeti, which is the expected value of Vsaeti in model (3) at a given age, conditional on the child-specific random linear and quadratic effects of Age2.
Cook’s distance is used to identify influential observations when regressing the observed values of Vsae on the predicted conditional values of Vsae.
Histograms and scatter plots are used to examine the assumptions associated with the random effects and errors.
Outliers are identified in the data, associated with child 49, 180, and 124.
The data fits the marginal and conditional parts of the model quite well, with no severe violation of constant variance and normality assumption for εij as a function of Age.
Refitting the model without the outliers did not significantly change the results.Analysis of Social Development Trajectories in Autistic Children
The study analyzed social development trajectories in autistic children over time.
The model used included fixed effects for initial language development level and age, and random effects for individual variability.
The estimate of the variance-covariance matrix for the random effects suggests that the quadratic effect of age decreases as the linear effect increases.
The confidence interval for the correlation between the random effects does not contain 0, indicating that the effects are not similar.
The estimate of the variance-covariance matrix of the model shows that the variability of Vsae scores for a child increases with age.
Estimates of the fixed effects show that initial language development level significantly influences social development trajectories over time.
Children with high levels of initial language development have greater mean social development and improve faster over time than those with low levels.
The mean social development of some children does not improve over time, while others improve linearly or accelerate.
Confidence intervals for the fixed effects show significant differences between the mean social development of children with high and low levels of initial language development.
The linear effect of age on social development is greater for children with high levels of initial language development than those with low levels.
The study used linear mixed models and likelihood ratio testing to analyze the data.
References include resources on linear mixed models and longitudinal data analysis.

Linear Mixed Model for Autism Study

The linear mixed model assumes that the response variable follows a normal distribution.
The model includes both fixed effects (predictors) and random effects (individual-specific effects).
The random effect vectors are assumed to be independent between children.
The model assumes that the random effects and error terms are normally distributed with zero means and specific covariance matrices.
The variance-covariance parameter vector of the random effects and error terms can be estimated using maximum likelihood or restricted maximum likelihood.
The covariance matrix for the error terms is assumed to be diagonal, but different structures can be tested to see which fits the data better.
The hypothesis tests for random effects are based on the likelihood ratio test using restricted maximum likelihood.
The hypothesis tests for fixed effects are based on the likelihood ratio test using maximum likelihood.
The quadratic effect of Age2 on Vsae was found to differ between children, and was included in the final model.
The interaction effect of Age2Sq × Sicdegp was tested, and found to be insignificant and removed from the final model.
The interaction effect of Age2 × Sicdegp was found to be significant and included in the final model.
There was some doubt over whether the quadratic effect of Age2 should be included in the final model, but it was found to be significant and included.Analysis of Language Development Data using Linear Mixed Effects Models
The quadratic effect of Age2 is found to be significant in the language development model, indicating its retention in the final model.
The marginal value of Vsaeti is the same for children who belong to the same initial language development level.
The linear effect of Age2 on Vsae for children who have a Low level of initial language development is represented by β1.
The model used for examining research questions is model (3), which includes various fixed and random effects.
The predicted marginal value of Vsaeti is given by the GLS estimates of the fixed effects.
Marginal residuals are usually analyzed in marginal models rather than in models that include random effects.
Each child has their own conditional value of Vsaeti, which is the expected value of Vsaeti in model (3) at a given age, conditional on the child-specific random linear and quadratic effects of Age2.
Cook’s distance is used to identify influential observations when regressing the observed values of Vsae on the predicted conditional values of Vsae.
Histograms and scatter plots are used to examine the assumptions associated with the random effects and errors.
Outliers are identified in the data, associated with child 49, 180, and 124.
The data fits the marginal and conditional parts of the model quite well, with no severe violation of constant variance and normality assumption for εij as a function of Age.
Refitting the model without the outliers did not significantly change the results.Analysis of Social Development Trajectories in Autistic Children
The study analyzed social development trajectories in autistic children over time.
The model used included fixed effects for initial language development level and age, and random effects for individual variability.
The estimate of the variance-covariance matrix for the random effects suggests that the quadratic effect of age decreases as the linear effect increases.
The confidence interval for the correlation between the random effects does not contain 0, indicating that the effects are not similar.
The estimate of the variance-covariance matrix of the model shows that the variability of Vsae scores for a child increases with age.
Estimates of the fixed effects show that initial language development level significantly influences social development trajectories over time.
Children with high levels of initial language development have greater mean social development and improve faster over time than those with low levels.
The mean social development of some children does not improve over time, while others improve linearly or accelerate.
Confidence intervals for the fixed effects show significant differences between the mean social development of children with high and low levels of initial language development.
The linear effect of age on social development is greater for children with high levels of initial language development than those with low levels.
The study used linear mixed models and likelihood ratio testing to analyze the data.
References include resources on linear mixed models and longitudinal data analysis.

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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.

Master Linear Mixed Models

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Questions and Answers

What type of distribution are the random effects assumed to follow in the linear mixed model for autism study?

What is the covariance matrix assumption for the random errors in the linear mixed model for autism study?

What type of likelihood ratio tests are used for hypothesis testing of the random effects in the linear mixed model for autism study?

What is the final model selected for the analysis of language development in children study?

What is the linear effect of Age on Vsae for children with a Low level of initial language development represented by in the analysis of language development in children study?

What is the main finding of the analysis of social development trajectories for autistic children study?

What is the estimate of the variance-covariance matrix, D, in model (3) of the analysis of social development trajectories for autistic children study?

What is the estimate of the correlation matrix of the random effect vector, µi, in model (3) of the analysis of social development trajectories for autistic children study?

What do the estimates of the fixed effects suggest about the mean Vsae score for children with a High level of initial language development in the analysis of social development trajectories for autistic children study?

What is the assumption made about the distribution of the random effects in the linear mixed model for autism study?

What is the purpose of comparing different structures for the covariance matrix of the random errors in the linear mixed model for autism study?

What type of likelihood ratio tests are used for hypothesis testing of the random effects in the linear mixed model for autism study?

What type of likelihood ratio tests are used for hypothesis testing of the fixed effects in the linear mixed model for autism study?

What is the final model selected in the analysis of language development in children study?

What is the purpose of model diagnostics in the analysis of language development in children study?

What is the estimate of the variance-covariance matrix, D, of model (3) in the analysis of social development trajectories for autistic children?

What is the estimate of the correlation matrix of the random effect vector, µi, of model (3) in the analysis of social development trajectories for autistic children?

What do the estimates of the fixed effects suggest in the analysis of social development trajectories for autistic children?

What is the purpose of Cook's distance in the analysis of language development in children study?

Which type of effect was found to differ between children and included in the final model in the autism study?

What type of effect was tested and found to be insignificant and removed from the final model in the autism study?

What type of effect was found to be significant and included in the final model in the autism study?

What type of effect was found to be significant in the language development model and retained in the final model?

What type of effect significantly influences social development trajectories over time in the analysis of social development trajectories for autistic children study?

What do the confidence intervals for the fixed effects show in the analysis of social development trajectories for autistic children study?

What type of effect is greater for children with high levels of initial language development than those with low levels in the analysis of social development trajectories for autistic children study?

What type of models are marginal residuals usually analyzed in, rather than models that include random effects?

What is the purpose of using maximum likelihood or restricted maximum likelihood in the linear mixed model for autism study?

What is the difference between marginal and conditional values of Vsaeti in the analysis of language development in children study?

What is the purpose of Cook's distance in the analysis of language development in children study?

What is the main finding of the analysis of social development trajectories in autistic children study?

What is the estimate of the correlation between the random effects in model (3) of the analysis of social development trajectories in autistic children study?

What is the purpose of using linear mixed models in the analysis of social development trajectories in autistic children study?

What is the difference between marginal and conditional residuals in the analysis of language development in children study?

What is the estimate of the variance-covariance matrix of the model used in the analysis of social development trajectories in autistic children study?

What is the purpose of hypothesis testing for fixed effects in the linear mixed model for autism study?

What is the difference between marginal and conditional models in the analysis of language development data?

What is the purpose of Cook's distance in the analysis of language development data?

What is the significance of the interaction effect of Age2 × Sicdegp in the linear mixed model for autism study?

What is the difference between maximum likelihood and restricted maximum likelihood in the estimation of variance-covariance parameter vector in the linear mixed model for autism study?

What is the main finding of the analysis of social development trajectories in autistic children study?

What is the purpose of examining histograms and scatter plots in the analysis of social development trajectories in autistic children study?

What is the difference between fixed and random effects in the linear mixed model for autism study?

What is the purpose of hypothesis testing for the random effects in the linear mixed model for autism study?

What is the difference between marginal and conditional residuals in the analysis of social development trajectories in autistic children study?

Study Notes

Studying That Suits You

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