Measurement Error Models Enable Accurate Correlation of Nanoscale Properties and Structures

Measurement errors can catastrophically bias parameter estimates in models to correlate nanoscale properties and structures, undercutting a foundation of nanoscience and nanotechnology. In a general solution to this latent problem, we derive a method-of-moments correction for least-squares estimates of correlative model parameters. Our correction applies to many relations of dependent and independent variables, subject to many types of measurement errors of the independent variable. Focusing on the prevalent power-law model to correlate optical intensity and nanoparticle size, we test the limits of accuracy of our correction and study the use of either reference size distributions or sizing uncertainty estimates to inform a measurement error model. We critically evaluate representative measurements of various nanoparticles, impacting the conclusions of several studies and changing expectations of intensity scaling exponents for nanoscale optical inferences. Our correction is immediately available, highly interpretable, and broadly applicable to gain reliable insights and prevent future mistakes.