The composite quantile regression for longitudinal data using the mixture of asymmetric laplace distributions
We propose a linear mixture quantile regression approach, with composite quantile regression (CQR) as a special case, to analyze continuous longitudinal data via a finite mixture of asymmetric Laplace distributions (ALD). Compared with the conventional mean regression approach, the proposed quantile...
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| Format: | Final Year Project (FYP) |
| Language: | English |
| Published: |
2019
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| Online Access: | http://hdl.handle.net/10356/77163 |
| _version_ | 1811679064172265472 |
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| author | Jin, Ye |
| author2 | Xiang Liming |
| author_facet | Xiang Liming Jin, Ye |
| author_sort | Jin, Ye |
| collection | NTU |
| description | We propose a linear mixture quantile regression approach, with composite quantile regression (CQR) as a special case, to analyze continuous longitudinal data via a finite mixture of asymmetric Laplace distributions (ALD). Compared with the conventional mean regression approach, the proposed quantile regression model can characterize the entire conditional distribution of the response variable and is more robust to heavy tails and misspecification in the error distribution. To implement the model, we develop a two-layer MCEM-EM algorithm to approximate random effects through a Monte Carlo simulation and derive the exact maximum likelihood estimates of the parameters in each step with the nice hierarchical representation of the ALD. The proposed algorithm performs similarly to the traditional linear mixed model when the error term follows a Gaussian distribution, but provides more efficient estimates for heavy-tailed data or with few low leverage outliers. We evaluate the finite sample performance of the algorithm and asymptotic properties of the maximum likelihood estimates through simulation studies and illustrate its usefulness through an application to a real life data set. |
| first_indexed | 2024-10-01T03:03:13Z |
| format | Final Year Project (FYP) |
| id | ntu-10356/77163 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:03:13Z |
| publishDate | 2019 |
| record_format | dspace |
| spelling | ntu-10356/771632023-02-28T23:12:01Z The composite quantile regression for longitudinal data using the mixture of asymmetric laplace distributions Jin, Ye Xiang Liming School of Physical and Mathematical Sciences DRNTU::Science::Mathematics We propose a linear mixture quantile regression approach, with composite quantile regression (CQR) as a special case, to analyze continuous longitudinal data via a finite mixture of asymmetric Laplace distributions (ALD). Compared with the conventional mean regression approach, the proposed quantile regression model can characterize the entire conditional distribution of the response variable and is more robust to heavy tails and misspecification in the error distribution. To implement the model, we develop a two-layer MCEM-EM algorithm to approximate random effects through a Monte Carlo simulation and derive the exact maximum likelihood estimates of the parameters in each step with the nice hierarchical representation of the ALD. The proposed algorithm performs similarly to the traditional linear mixed model when the error term follows a Gaussian distribution, but provides more efficient estimates for heavy-tailed data or with few low leverage outliers. We evaluate the finite sample performance of the algorithm and asymptotic properties of the maximum likelihood estimates through simulation studies and illustrate its usefulness through an application to a real life data set. Bachelor of Science in Mathematics and Economics 2019-05-14T12:54:27Z 2019-05-14T12:54:27Z 2019 Final Year Project (FYP) http://hdl.handle.net/10356/77163 en 57 p. application/pdf |
| spellingShingle | DRNTU::Science::Mathematics Jin, Ye The composite quantile regression for longitudinal data using the mixture of asymmetric laplace distributions |
| title | The composite quantile regression for longitudinal data using the mixture of asymmetric laplace distributions |
| title_full | The composite quantile regression for longitudinal data using the mixture of asymmetric laplace distributions |
| title_fullStr | The composite quantile regression for longitudinal data using the mixture of asymmetric laplace distributions |
| title_full_unstemmed | The composite quantile regression for longitudinal data using the mixture of asymmetric laplace distributions |
| title_short | The composite quantile regression for longitudinal data using the mixture of asymmetric laplace distributions |
| title_sort | composite quantile regression for longitudinal data using the mixture of asymmetric laplace distributions |
| topic | DRNTU::Science::Mathematics |
| url | http://hdl.handle.net/10356/77163 |
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