William Boone discusses "Rasch Analysis for Instrument Development: Why, When, and How?" in a Journal article: www.ncbi.nlm.nih.gov/pmc/articles/PMC5132390/
In general, Rasch analysis constructs a unidimensional latent variable from the data. It verifies that each person and item can be placed on it, reporting the persons and items locations by means of linear (additive, interval) measures - the type of measures taken for granted in most scientific and day-to-day activities. Rasch identifies departures in the data for persons, items and even data points from the ideal of unidimensionality. These are reported with fit statistics that guide the improvement of the instrument and point out possible flaws in the data. Rasch also has techniques for identifying multi-dimensionality in the data (PCA of residuals).
Raw scores? Rasch confirms that raw scores mean what we think they mean. For instance, that a higher score indicates more of the latent variable than a lower score. Raw scores are non-linear. They have strong ceiling and floor effects, so Rasch also tells us how much more of the latent variable 1 more score-point indicates at different places along the latent variable. This can have important consequences when change-scores influence decision-making. A 10-point gain near the ends of the raw score range can be 4 times more change along the latent variable than a 10-point gain near the center of the raw score range - www.rasch.org/memo62.htm
Factor analysis? Factor analysis is a useful technique, but is not as exact as Rasch for our data. Our intention is to construct a unidimensional latent variable from the data, not to describe the data with all its variety and intricacies. We need to identify specific areas in the data that do not aid in this construction. Then remedy them, eliminate them or decide that flaws in the data are inconsequential. For instance, in an arithmetic test, factor analysis may point out that "addition" and "subtraction" items are different factors, but provides little help in the decision as to whether "arithmetic" can be treated as one construct. Factor analysis also tends to assign items in different difficulty strata (nodes) to different factors. This has produced misleading findings, see www.rasch.org/rmt/rmt81p.htm - When we have a clear picture of the data and the latent variable, factor analytic techniques, such as PCA of residuals, can be helpful to identify subtle departures in the data from the ideal. Factor analysis may assist in identifying clusters of items which threaten the invariance of the measurement system, but this is indirect and inexact compared with Rasch-based identification of anomalies in the data.
Reliability? This applies equally to Rasch or Classical analysis: With 53 dichotomous items and a reasonably range of person abilities, we would hope the reliability is around 0.9. This gives us about 4 statistically-different measurement strata - www.rasch.org/rmt/rmt63i.htm - So, if this set of items is to be used for decision-making, and this person sample is representative, how many levels of performance need to be identified? If 4 levels, then around 53 items. If only high-low, then 25 items are probably enough.
Invariance? Rasch is rigorous in applying the ordinary definition of invariance: "The property of remaining unchanged regardless of changes in the conditions of measurement." (Dictionary.com). Rasch examines every observation to discover the extent to which it is independent of which particular person and which particular item participates, apart from the person's ability and the item's difficulty. In general, Rasch measures are independent of which items and which persons participate in the measurement process. This is the expected situation for invariant measurement in the physical sciences. In principle, it does not matter which thermometer is used to measure heat, or what the source of the heat is. Rasch applies this to social science data, operationalizing L.L. Thurstone's ideals that (1) "A measuring instrument must not be seriously affected in its measuring function by the object of measurement." (Thurstone, 1928, p.547) and "It should be possible to omit several test questions at different levels of the scale without affecting the individual score (measure)." (Thurstone, 1926, p.446) - cited in .rasch.org/memo62.htm
