Measurement invariance,the lack thereof,and modeling change

Purpose

Measurement invariance issues should be considered during test construction. In this paper, we provide a conceptual overview of measurement invariance and describe how the concept is implemented in several different statistical approaches. Typical applications look for invariance over things such as mode of administration (paper and pencil vs. computer based), language/translation, age, time, and gender, to cite just a few examples. To the extent that the relationships between items and constructs are stable/invariant, we can be more confident in score interpretations.

Methods

A series of simulated examples are reported which highlight different kinds of non-invariance, the impact it can have, and the effect of appropriately modeling a lack of invariance. One example focuses on the longitudinal context, where measurement invariance is critical to understanding trends over time. Software syntax is provided to help researchers apply these models with their own data.

Results

The simulation studies demonstrate the negative impact an erroneous assumption of invariance may have on scores and substantive conclusions drawn from naively analyzing those scores.

Conclusions

Measurement invariance implies that the links between the items and the construct of interest are invariant over some domain, grouping, or classification. Examining a new or existing test for measurement invariance should be part of any test construction/implementation plan. In addition to reviewing implications of the simulation study results, we also provide a discussion of the limitations of current approaches and areas in need of additional research.

     

Detection and Sizing of Ti-Containing Particles in Recreational Waters Using Single Particle ICP-MS

Single particle inductively coupled plasma mass spectrometry (spICP-MS) was used to detect Ti-containing particles in heavily-used bathing areas of a river (Salt River) and five swimming pools. Ti-containing particle concentrations in swimming pools ranged from 2.8?×?10³ to 4.4?×?10³ particles/mL and were an order of magnitude lower than those detected in the Salt River. Measurements from the Salt River showed an 80% increase in Ti-containing particle concentration over baseline concentration during peak recreational activity (at 16:00 h) in the river. Cloud point extraction followed by transmission electron microscopy with energy dispersive X-ray analysis confirmed presence of aggregated TiO₂ particles in river samples, showing morphological similarity to particles present in an over-the-counter sunscreen product. The maximum particle mass concentration detected in a sample from the Salt River (659 ng/L) is only slightly lower than the predicted no effect concentration for TiO₂ to aquatic organisms (<?1 μg/L).