2.3. Statistical Analysis

GRM is designed for the analysis of ordered polytomous variables [71]. This particularity makes it suitable for the analysis of the CIUS scale with its 14 survey questions measuring Internet addiction. The items are ranked on a 5-point Likert scale from 1 (never) to 5 (very often). Discrimination and threshold parameters are the two main estimates in GRM. As the latter is basically an ordered logistic model, the threshold parameters of each item are naturally estimated in increasing order and the number of threshold estimates is equal to the number of item categories minus 1. As each CIUS item has 5 categories, four thresholds were estimated for each item. Hence, the probability that a person’s response falls at or above a particular category given the latent trait is expressed as follows:

where:

The discrimination parameter (or slope) refers to the differential capability of an item. It also reflects the strength of association between an item and the construct being measured. A high discrimination parameter value means that the probability of endorsing an item response increases more rapidly as the latent trait or severity increases [78]. The value of the slope parameter also quantifies the amount of information of an item. When this value is high, most of the information is concentrated along a small part of the latent trait range. In reverse, the information contained in items with low discrimination is scattered along a greater part of this range.

Some descriptive rules of thumb allow for a better interpretation of the discrimination parameter value as follows: 0 = non-discriminative power; 0.01–0.34 = very low; 0.35–0.64 = low; 0.65–1.34 = moderate; 1.35–1.69 = high; >1.70 = very high; + infinity = perfect [72].

As for the threshold parameters, they reflect the point along the latent continuum where an individual has a 50% chance of endorsing a particular question [79].

Both latent trait scores and thresholds are on the same z-score metric with mean 0 and unit standard deviation [70].

GRM is derived in terms of cumulative probabilities, and the resulting plots are called Item Characteristic Curves (ICC). The latter are graphical functions that represent the respondent’s latent trait as a function of the probability of endorsing an item [80]. We present these ICCs along with Item Information Curves (IICs), which tell us how much information each ICC provides. The shape of an IIC is determined both by its discrimination and by its threshold parameters, but the steepness of the curves is determined by the magnitude of the discrimination index. Each item contribution can be summed in turn to obtain the total scale information function (TIF), which tells us how accurately the tool can appraise person location estimates. The plot show the amount of psychometric information at each point along a latent severity dimension [81].