Browsing by Subject "Quantile regression"

Now showing 1 - 3 of 3

Predict house prices using quantile regression
(2018-06-19) Xu, Jing, M.S. in Statistics; Zhou, Mingyuan (Assistant professor)
Quantile Regression Model (QRM), introduced by Koenker and Bassett in 1978, is a well-established and widely used technique in theoretical and applied statistics. QRM is a natural extension of the traditional OLS regression model and it is advantageous over the traditional techniques in several aspects: (1) QRM is robust to outliers, non-normal errors and heteroscedasticity; (2) It allows researchers to study the impact of predictors on different quantiles of response variable, not merely its conditional mean. Due to these advantages, QRM is applied in various fields such as risk measurement in finance, and fat-tailed distributions such as if cheaper food cause obesity. The current research paper aims at applying QRM in an open source housing data with 79 house-related features and 1460 cases, and comparing its predictive performance with the OLS model. The article also extends the QRM to Bayesian Quantile Regression and Quantile Random Forest to further explore the application performance of quantile models. The results indicate that all the quantile models outperformed the OLS regression in prediction at the 0.5th quantile and the 0.75th quantile based on RMSE. In general, most estimates derived by QRM and BQR show consistency across quantiles. Quantile Random Forest show similar variable selection results comparing with LASSO, but slightly higher RMSE than the other quantile models.
Research on Texas savannas : fractional woody cover mapping, potential woody cover modelling, and woody plant encroachment analysis
(2017-12) Yang, Xuebin, Ph. D.; Crews, Kelley A.; Young, Kenneth R; Miller, Jennifer A; Arima, Eugenio Y; Huebner, Donald J
Tested in Texas savannas of a wide rainfall gradient, this dissertation endeavors to (1) map fractional woody cover at Landsat scale, for close and continuous woody plant encroachment monitoring, (2) model the pattern of potential woody cover over the present rainfall gradient, for implication of the end-point of woody plant encroachment, (3) analyze the rate and effect factors of woody plant encroachment under the regional context, for pertinent savanna management strategy. Web-Enabled Landsat Data (WELD) was used to calibrate the Salford Systems’ Classification and Regression Trees (CART) against training data of fractional woody cover derived from 1m resolution digital orthophotos. The CART model output was verified against an independent test data. This study provides a way to accurately monitor woody plant encroachment across savanna ecosystems at a fine spatial scale, and sets up a protocol for landscape components mapping at sub-pixel level in other ecosystems. The pattern of potential woody cover was modelled over the wide rainfall gradient at Landsat scale (30m) and MODIS scale (500m) respectively. While a positive linear relationship between potential woody cover and mean annual precipitation (MAP) was revealed at Landsat scale, a prominent three-segment relationship was observed at MODIS scale. This discrepancy corroborates the scale dependency of the primary determinants of savanna woody plant density. According to the three-segment pattern at MODIS scale, Texas savannas are divided into arid savanna (MAP < 600mm), semi-arid savanna (600mm < MAP < 735mm), and mesic savanna (MAP > 735mm). Analysis of the encroachment of Ashe juniper at its early life stage (initial ~20 years) at local (hectare) scale suggests that water availability has a significant positive effect on the encroachment rate in semi-arid savanna, but not in mesic savanna. In addition, a quadratic relationship was revealed between the encroachment rate and woody plant density in mesic savanna. That is, the encroachment rate increases with woody plant density by a threshold density, then starts decreasing with woody plant density. These results demonstrate that regional context such as rainfall and biological traits of woody species is critical to understand the trend of woody plant encroachment.
Winds of change : assessing direct and indirect effects of variable renewable energy growth on the ERCOT market
(2021-12-09) Ramthun, Eli Bjorn; Adelman, David E.; Leibowicz, Benjamin D.
Wind generation in Texas has been growing rapidly, and it is poised to create major disruptive shifts in the generation only market of the Electricity Reliability Council of Texas. The average real time price of electricity has been declining in this market in part due to the merit-order effect, where low marginal cost variable renewable generation undercuts thermal baseload generators with higher operating costs. In a generation only market, depressed energy prices can reduce the economic viability of baseload generators, threatening grid reliability with narrow reserve capacity margins. This work performs empirical analysis on a large market dataset using quantile regression to quantify how the seasonal, diurnal, and regional variation of merit-order effect varies in intensity throughout the distributions of price and as wind generation has increased over time. We demonstrate that while the merit-order effect has increased in intensity alongside increased wind penetration for high percentiles of market prices, the effect is overall reducing in magnitude relative to the amount of wind generation in the system, from a price reduction on top quantiles of price of $11 per GWh of wind generated in 2011 to a respective $5 decrease in prices for the same quantity of wind generation in 2019. This finding alleviates some concerns of baseload generator profitability in the long-term as the price depression from the merit-order effect trends towards zero. We follow with a discussion of the implications for the market as large amounts of solar are poised to come online in the coming years, which will accordingly exert a large but temporary merit-order effect as penetration begins to reach significant amounts. We conclude with policy recommendations to mitigate any potential adverse consequences on grid reliability due to the upcoming short-term price disruptions that will be associated with the ramp up of solar PV capacity in the grid