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.

Comparison of Random and Geographically Stratified Sampling

The post compares differences between simple random sampling and geographically stratified sampling. Stratified random sampling improves the spatial distribution of sample point locations by stratifying the field geographically and sampling randomly within each stratum. Different sampling patterns are compared using Monte Carlo simulations on a simulated population.

Analyses of Pesticide Concentrations in California Surface Waters

Environmental data are frequently left-censored, indicating that some values are less than the limit of quantification for the analytical methods employed. These data are problematic because censored (non-detect) values are known only to range between zero and the censoring limit. This complicates analysis of the data, including estimating statistical parameters, characterizing data distributions, and conducting inferential statistics. This post demonstrates various procedures and methods that are available in R for analyzing data containing a mixture of detects and non-detects. These methods make few or no assumptions about the data, or substitute arbitrary values (e.g., one-half the detection or reporting limit) for the non-detects.

Clustering on Principal Component Analysis

Combining principal component analysis (PCA) and clustering methods are useful for reducing the dimension of a data set into a few continuous variables containing the most important information in the data. This post illustrates how to combine PCA and clustering methods to identify patterns in a data set using the R language for statistical computing and visualization.

Exploratory Spatial Data Analysis and Kriging in R

This post presents and demonstrates several methods for exploratory spatial data analysis using the R language for statistical computing and visualization. These methods can be used for identifying spatial dependence patterns and spatial heterogeneity, which are critical components of variogram development and the kriging procedure.

Natural Neighbor Interpolation With R

This post presents and demonstrates several methods for natural neighbor interpolation using the R language for statistical computing and visualization. The results are compared to those obtain using ordinary kriging.

Calculation of 95% Upper Confidence Limit for Left-Censored Data

This post presents methods that can be used to calculate a 95% upper confidence limit on the mean of an unknown population for left-censored data sets (i.e., containing a mixture of detects and non-detects). The preferred approach depends on many factors, including the number of samples and the distributional shape of the data.