Estimating Slope and Level Change in N = 1 Designs

Abstract

The current study proposes a new procedure for separately estimating slope change and level change between two adjacent phases in single-case designs. The procedure eliminates baseline trend from the whole data series before assessing treatment effectiveness. The steps necessary to obtain the estimates are presented in detail, explained, and illustrated. A simulation study is carried out to explore the bias and precision of the estimators and compare them to an analytical procedure matching the data simulation model. The experimental conditions include 2 data generation models, several degrees of serial dependence, trend, and level and/or slope change. The results suggest that the level and slope change estimates provided by the procedure are unbiased for all levels of serial dependence tested and trend is effectively controlled for. The efficiency of the slope change estimator is acceptable, whereas the variance of the level change estimator may be problematic for highly negatively autocorrelated data series.

A comparison of mean phase difference and generalized least squares for analyzing single-case data

“…Given this similarity, we expect that the current proposal will control linear trend and will also be only slightly, if at all, distorted by the presence of autocorrelation, as was the case for the SLC (Solanas, Manolov, & Onghena, 2010). The proposal estimates the mean difference between treatment measurements and treatment data as projected using the baseline trend.…”

“…This procedure compares each baseline datum to each treatment datum to quantify the percentage of nonoverlap (i.e., the degree to which the treatment measurements are improved as compared to the baseline measurements). Finally, a procedure was proposed for quantifying separately slope and level change (SLC; Solanas, Manolov, & Onghena, 2010). This procedure first estimates baseline trend as the average of the differenced data, that is, a new series is created subtracting each measurement from the following one and the mean of this series is computed.…”

“…There is evidence that this procedure estimates precisely slope and level changes and is practically unaffected by serial dependence (Solanas, Manolov, & Onghena, 2010;Manolov et al, 2011). In the present study we propose a procedure based on the SLC, with the purpose to explore the gains and losses in the bias and efficiency of the estimation when using a technique simpler than the GLS.…”

Further developments in summarising and meta-analysing single-case data: An illustration with neurobehavioural interventions in acquired brain injury

“…All of these analytical options, in contrast to non-overlap indices (e.g., percentage of non-overlapping data: Scruggs & Mastropieri, 2013; Tau-U: Parker, Vannest, Davis, & Sauber, 2011), directly incorporate the option of summarising the results of an MBD by considering all comparisons between a baseline and a subsequent intervention phase. Nevertheless, we consider it necessary to propose a way to provide summary indices for other existing SCED analytical procedures that are applicable to MBD; specifically, we focus on the slope and level change (SLC; Solanas, Manolov, & Onghena, 2010) and the mean phase difference (MPD; Manolov & Solanas, 2013) procedures. The reason for this choice can be found in the desirable features of these indicators, as well as in the limitations of the above-mentioned procedures.…”

“…The joint use of these procedures answers (a) Beretvas and Chung's (2008) call for separate estimation of different effects, as the SLC quantifies change in slope and then the net change in level, something that is also possible with multilevel models (Van den Noortgate & Onghena, 2008) and (b) Swaminathan, Rogers, and Horner's (2014) emphasis on the need for quantification of the overall effect, as the MPD offers single quantification. Moreover, these procedures have shown acceptable performance (Manolov & Solanas, 2013;Manolov, Solanas, Sierra, & Evans, 2011;Solanas et al, 2010) and are accompanied by easy-to-use code in the open-source software R, which makes their use straightforward.…”