Non-linear regression and seemingly unrelated regression A \ Prof. - - PowerPoint PPT Presentation

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Non-linear regression and seemingly unrelated regression A \ Prof. - - PowerPoint PPT Presentation

Feb 04, 2024 508 likes •879 views

Non-linear regression and seemingly unrelated regression A \ Prof. Steve Quinn Department of Statistics, Data Science and Epidemiology, Swinburne University of Technology, Melbourne, Australia sjquinn@swin.edu.au Two part analysis The

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Non-linear regression and seemingly unrelated regression

A \ Prof. Steve Quinn

Department of Statistics, Data Science and Epidemiology, Swinburne University of Technology, Melbourne, Australia sjquinn@swin.edu.au

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Two part analysis

  • The problem
  • Trying to identify autism
  • believe that ocular response to a flash at different

frequencies is different in autistic vs normal children

  • Want to identify the best flash frequency

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  • They know what the data will look like (roughly)

Mixed model and Non-linear regression

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  • They also know what the wave is made up of a normal density

curve and a logistic curve (a cumulative distribution function)

Non-linear regression

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  • There is a theoretical framework for this decomposition
  • “On-response amplitude” (b-waves) follows the logistic growth

function

  • “Off-response amplitude” (d-waves) follows Gaussian density

function

Non-linear regression

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Mixed model analysis

  • The data – two groups – each person contributes 9 observations

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Mixed model analysis

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Mixed model analysis

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Mixed model analysis

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Mixed model analysis

The authors ended up wanting this picture:

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Non-linear regression

  • The authors wanted to estimate:

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  • The data – one group

Non-linear regression first attempt

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Non-linear regression – first attempt

Wrong starting values:

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Non-linear regression – SigmaPlot - $1250

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Non-linear regression – Stata

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Both groups, one analysis - nlsur

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Zellner, A. An efficient method of estimating seemingly… American Statistician Journal, 1962

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This example

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Both groups, one analysis - nlsur

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Both groups, one analysis - nlsur

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Robust standard errors

nlsur ….., vce(robust)

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Both groups, one analysis - nlsur

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Provides joint estimates from several regression models Estimates are more efficient

  • accounts for correlated errors
  • Greater correlation increases errors
  • Multicollinearity between independent variables

increases efficiency

  • SE’s are smaller

Seemingly unrelated regression

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Seemingly unrelated regression – rarely used

  • Chen. C, et.al. Altered metabolite levels and

correlations… (Metabolomics) 2017. n = 158, 113 response variables, 15 covariates SUR doesn’t account for multiple comparisons. (Benjamini-Hochberg false discovery algorithm)

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Outcomes don’t need to be the same in kind

Xuecai, Xu, et.al. Accident severity and traffic signs… (Accident analysis and prevention) 2018.

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This example

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Joint model – nlsur Separate model – nl

This example

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Questions or comment?

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clustered standard errors

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Seemingly unrelated non-linear regression

The code:

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Seemingly unrelated regression

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Mixed model analysis

How do you model this curve?

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Mixed model analysis

Every function can be modelled as accurately as required by a polynomial curve. Why did I know to stop at freq4? – can run the model with freq up to the 5th power and do a LR test – can run the model with freq up to the 5th power and check the highest terms – they will be non-significant .

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The output:

Seemingly unrelated non-linear regression

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Seemingly unrelated non-linear regression

The code:

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Comparing the estimates:

Seemingly unrelated non-linear regression

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