Detecting and explaining BLIM's unidentifiability: Forward and backward parameter transformation groups

The basic local independence model (BLIM) is a probabilistic model, widely applied in knowledge space theory. It has recently received attention concerning its identifiability. In particular it was shown that the BLIM is not identifiable for forward-graded (FG) and backward-graded (BG) knowledge structures, such as quasi-ordinal and learning spaces. These structures are widely and fruitfully applied in practice, providing one of the reasons for the investigations carried out in this article. Following up recent contributions on the BLIM identifiability, this article seeks to study the issue by examining groups of parameter transformations that, for FG and BG structures, keep constant the model's prediction function, thus making it unidentifiable. This transformational approach is compared to the standard way of testing the local identifiability of a model, and its benefits are discussed.