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Measurement invariance (MI) entails that measurements in different groups are comparable, and is a logical prerequisite when studying difference or change across groups. MI is commonly evaluated using multi-group structural equation modeling through a sequence of chi-square and chi-square-difference tests. However, under the conventional null hypothesis testing (NHT) one can never be confident enough to claim MI even when all test statistics are not significant. Equivalence testing (ET) has been recently proposed to replace NHT for studying MI. ET informs researchers a size of possible misspecification and allows them to claim that measurements are practically equivalent across groups if the size of misspecification is smaller than a tolerable value. Another recent advancement in studying MI is a projection-based method under which testing the cross-group equality of means of latent traits does not require the intercepts equal across groups. The purpose of this article is to introduce the key ideas of the two advancements in MI and present a newly developed R package for researchers to easily apply the two methods. A real data example is provided to illustrate the use of the package. It is advocated that researchers should always consider using the two methods whenever MI needs to be examined.

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The trans-ocular barrier is a key factor limiting the therapeutic efficacy of triamcinolone acetonide. We developed a poly(lactic-co-glycolic acid) nanoparticles (PLGA NPs) surface modified respectively with 2-hydroxypropyl-β-cyclodextrin (2-HP-β-CD), chitosan oligosaccharide and trehalose. Determination of the drug/nanoparticles interactions, characterization of the nanoparticles, in vivo ocular compatibility tests, comparisons of their corneal permeability and their pharmacokinetics in aqueous humor were carried out. Methods: All PLGA NPs were prepared by the single emulsion and evaporation method and the drug-nanoparticle interaction was studied. The physiochemical features and in vitro corneal permeability of NPs were characterized while the aqueous humor pharmacokinetics was performed to evaluate in vivo corneal permeability of NPs. Ocular compatibility of NPs was investigated through Draize and histopathological test. Results: The PLGA NPs with lactide/glycolide ratio of 50:50 and small particle size (molecular weight 10 kDa) achieved optimal drug release and corneal permeability. Surface modification with different oligosaccharides resulted in uniform particle sizes and similar drug-nanoparticle interactions, although 2-HP-β-CD/PLGA NPs showed the highest entrapment efficiency. In vitro evaluation and aqueous humor pharmacokinetics further revealed that 2-HP-β-CD/PLGA NPs had greater trans-ocular permeation and retention compared to chitosan oligosaccharide/PLGA and trehalose/PLGA NPs. No ocular irritation in vivo was detected after applying modified/unmodified PLGA NPs to rabbit's eyes. Conclusion: 2-HP-β-CD/PLGA NPs are a promising nanoplatform for localized ocular drug delivery through topical administration.