Generalized Least Squares Regression

In OLS regression, assumptions such as independent and identically distributed errors are important for accurate estimation and inference. Heteroskedasticity, or unequal variances of residuals, can lead to biased estimates and incorrect standard errors. Alternatives to OLS, such as GLS and WLS regression, can be considered when OLS assumptions are violated. GLS is used for dependent errors, while WLS is used for independent but non-identically distributed errors.

Weighted Least Squares Regression

Heteroscedasticity in regression analysis refers to varying levels of scatter in the residuals. Its presence affects OLS estimators and standard errors, leading to biased estimates and misleading results. When errors are independent, but not identically distributed, weighted least squares regression can be used to address heteroscedasticity by placing more weight on observations with smaller error variance. This results in smaller standard errors and more precise estimators.

Trend Detection Using Survival Analysis

Non-detects in environmental data can complicate analysis if not handled properly, leading to incorrect conclusions. The mathematical structure of survival analysis is general enough that it can be used in diverse fields examining various types of data not typically associated with survival/death events or failure analysis. In this post, survival analysis methods will be applied to fit a censored linear regression model to weekly ammonium deposition data to assess temporal trends.

Arctic Sea Ice Time Series Analysis

The modeltime R library offers a wide range of features for model evaluation, selection, and forecasting using the tidymodels ecosystem. Time-series analysis of sea ice in the Arctic polar regions performed using the modeltime library suggests that the Arctic sea will be nearly ice-free in the very near future.

Temporal Behavior of Arctic Sea Ice

Passive-microwave instrumentation on satellites has allowed for the monitoring of Arctic sea ice coverage since the late 1970s, showing a long-term downward trend due to both natural variability and climate change. The rate of decline in Arctic sea ice has varied over the past 43 years, with some periods showing faster rates of loss than others. This blog post explores the temporal changes in Arctic sea ice extent using the R language for statistical computing and visualization.