Ridderprint

Expanding the methodological toolbox of HRM researchers 55 lengths, OMA can handle these as long as the length of the shortest included sequence is at least 70% of that of the longest sequence. Nonetheless, specific sequences may contain more than 30%missing values. These sequences can either be deleted or, if missing values gather around the start or end of the sequences, the timeframe of observation can be shortened. However, both these approaches may introduce bias to the results and, as an alternative, researchers can decide to impute the missing values. Despite potential collinearity between sequential and missing elements, gap closure by recursive imputation has been demonstrated to provide accurate estimates of the missing data points (Halpin, 2012). 3.3.2 Penalty Costs OMA determines the similarity between sequences based on the operations needed to align them – to make them similar. There are two types of operations that can be used to align sequences: indel and substitution. Indel is short for the insertion or the deletion of an element somewhere in the sequence whereas substitution refers to the replacement of an element by another element in that same exact place in the sequence. Both operations need to be assigned a penalty cost to reflect the dissimilarity the operation corrected, and especially the ratio between these respective costs is important (Aisenbrey & Fasang, 2010; Biemann & Datta, 2014). By default, OMA uses a standard indel- substitution cost ratio of 1:2, meaning that deleting an element and inserting another comes at the same penalty cost of a substitution. This standard ratio implies that OMA views all underlying states as equally dissimilar. However, as discussed earlier, HRM research often uses ordinal variables, which imply that certain states are more similar to each other based on their place in the underlying order. To reflect this similarity, the penalty cost of substitutions between those states can be decreased. Such a decrease can be based solely on theoretical assumptions but, alternatively, the observed transitions in the actual data function as a basis. Here, the rationale is that the observed transition frequency between states provides information about the similarity between these states (Biemann & Datta, 2014). To illustrate the above, assume three five-week sequences: E-E-E-E-E, representing a consistently engaged employee; N-N-E-E-E, representing an employee who went from neutral to engaged; and D-D-E-E-E, representing an employee who was disengaged for two weeks. Using the standard cost ratio, either sequence can be changed into the other at a penalty cost of 4: either by two element deletions and two element insertions, or by two substitutions. Alternatively, researchers could set theory-based substitution costs, penalizing transitions between states adjacent in the underlying order at a lower rate. For example, 1.75 for the adjacent levels of engagement whereas the standard 2 for more ‘distant’ levels. Subsequently, the penalty costs between the first and the last sequence in the above example would still equal 4 whereas those between the first two sequences and the last two sequences would now amount to 3.5. Data-based substitution costs would have the same effect if transitions between distant ordinal states occur less frequent. Although setting custom substitution costs thus seems sensible, the approach has two downsides. First, substitution costs are not sensitive to the direction of a transition. Hence, Aisenberg and Fasang (2010) argue that custom costs should only be used “ if there