Los Tres Niveles de Representación de la Química

Before multilevel analysis can take place it is necessary to screen or prepare the data and code or transform both the general data arrangement and the individual variables into an appropriate format for running the multilevel analysis.

Data Coding

Consideration was given to the coding of each variable included in the analysis for Study 3. For observational interrater data (i.e., the CRS and HAACS) where two scores were generated for each observation, the average score for each pair of ratings was selected to represent the true score. This was done in consideration of high interrater reliability score obtained in Study 2. All remaining data was treated as continuous time series data to maximise variation within the data set and to allow for the possibility of differences in the level of variables over time (i.e., Level 1). The exception to this was the treatment of symptom severity (i.e., CIDI) and personality beliefs (i.e., PBQ) which were intended as controls were made to remain constant over time (i.e., Level 2). Specifically, the CIDI generates four possibilities for indications of symptom severity associated with depression: “no diagnosis” and “mild” (coded as ‘0’), “moderate” (coded as ‘1’) and “severe” (coded as ‘2’). The PBQ generates values associated with lesser or greater degrees of disordered

personality beliefs and patient complexity. Total scale personality beliefs scores were divided evenly between the lower and higher 50th percentile (coded as ‘0’ and ‘1’ respectively) splitting patients into one of two categories (i.e., high or low personality beliefs. This splitting of the total scale PBQ score also coincided with

recommendations for measuring observable differences in personality beliefs in patients with features of personality disordered beliefs (Beck et al., 2001). However, there is no formal cut-off score for diagnosing personality disorders using the PBQ.

Centering

In order to make multilevel output more easily interpretable it is common practice to adopt “centering” or rescaling of variables (Peugh & Enders, 2005). However, a number of considerations must be made when choosing when and how to centre variables (Singer & Willett, 1998). For the present thesis, session data was coded starting from ‘0’ from the initial intake session by default. As a result ‘time’ was centred on ‘0’ and results are interpreted relative to the intake session

representing the initial status in the MLM analysis conducted in Study 3. Data for the dependent variable and predictor variables were measured on reasonably comparable scales from the outset reducing the utility of centering data. For example, both

HAACS and CRS scores representing therapist competence were measured on 7-point scales with average scores of 49.08 and 24.75 a standard deviation of 14.37 and 9.87 respectively. The restriction and similarity in the range of the scales supports the plausibility of analysing the data as a natural metric due to them already being centred to each other in relative terms (Kreft, de Leeuw, & Aiken, 1995). Moreover, the use of non-linear time (Session; see below) in the unconditional growth model changes the parameters for which to base interpretations. This restricts the utility of centering

confounding the interpretation of the magnitude of fixed effects based on raw data (Singer & Willet, 2003).

Missing Data

As introduced in section 9.2, MLM is able to accommodate missing data. In particular, in the analysis for the present study, this was done using Maximum Likelihood (ML) estimation. Simply put, ML estimation is a more computationally intensive alternative to OLS and related methods that utilises all available data to estimate relationships between variables based on probabilities (Aldrich, 1997; Singer & Willet, 2003). Kwok et al., (2008) explain further:

An advantage of MLM is that it can make use of all available data in the estimation of model parameters due to its flexible treatment of the time predictor. A research participant with only baseline data can be included in an analysis and contribute to the estimation of model parameters. The validity of using all available data does depend on whether missing data are missing completely at random (MCAR) (or missing at random (MAR) which is a less restrictive missing data assumption), and methods of assessing this

requirement are available. (p.4).

None-the-less, for observational interrater data where a single rating was missing, the score generated by the remaining rater was used to make maximum use of all available data. This was done in consideration of high interrater reliability obtained in Study 2. In order to further ensure that the remaining missing data was not due to any systematic problems in the data collection process, the data was analysed

using a Missing Completely at Random (MCAR; Rubin, 1976; Little, 1988; Little & Rubin, 1987) analysis in SPSS missing values analysis based on a “trimmed” version of the data set that did not include BDI-II, and session data after session 11 in order to run the analysis in the traditional manner. All variables used in the analysis were included in the analysis. However, the variable CRS_Fit was excluded from the total missing variables analysis due to known systematic difference in the collection of the data, namely that J. Beck CCDs (J. Beck, 1995) needed for ratings to be collected were systematically completed at specific sessions (see Chapter VIII). This limitation in the inclusion of CRS_Fit in MLM analyses was considered and discussed in section 9.7. The MCAR analysis produced non-significant results. The non-significant result of the MCAR analysis (2 = 27.095, df = 28, p = .513) revealed that there was no systematic pattern of missing data in the dataset. In this way, missing data for the purposes of MLM analysis can be considered ignorable and meets the assumptions associated with missing data (Schafer, 1997).

Treatment of Time

Time was represented by therapy session in the current study. However, there were a number of different ways that therapy sessions could possibly be coded to most accurately model change in depressive symptomology. Table 28 (see Appendix L) provides an analysis of the random effects produced for different methods of coding time as well as an indication of which model of time provides the best fit to the dependent variable (i.e., change in depressive symptomology). The most simple form for modelling time is to use the raw “wave” of data increasing in equal

increments ranging from ‘0’ representing the initial intake session to ‘10’ representing the last session included in the analysis (i.e., session ten). In this case the wave was equivalent to coding time as a linear metric (T1) in subsequent analyses including predictor variables. However, during the first four weeks of beginning active therapy, sessions or dose were administered twice per week then continued at once a week from week five. In order account for this, it was considered that time could be

modelled at shorter intervals during the first 8 waves of data (i.e., the first four weeks of therapy; T2). In this ‘0’ represented intake, ‘0.5’ session one, ‘1’ session two, ‘1.5’ session three, ‘2’ session four, etc, and from session five began to increase increments of one. A third possibility for modelling time would be to use a non-linear function. From visual analysis the dependent variable data (i.e., BDI-II change scores) it was posited that the change in depressive symptom change could be curvilinear (see Figure 26). Subsequently, a curvilinear function was also considered as a potentially accurate means for coding time in subsequent analyses (T3). As in T2, an adjusted model for curvilinear time taking into account the increased frequency of sessions in the first four weeks of therapy was also considered (T4).

A fifth possibility (T5) arose for modelling time by coding the precise time (days) since intake. Although, treatment was intended to be delivered at systematic increments (i.e. twice per week for the first four weeks, then once per week until completion, then follow up sessions at two and six months) treatment often did not occur as intended. For example, patients would at times miss a week of therapy or come in for therapy more or less frequently than intended. To account for these individual patient differences in the timing of therapy, the precise days between one therapy session to the next were coded. For example intake session was coded as ‘0’. If a patient came in seven days later the second session would be coded as ‘7’.

Having coded time in several distinct ways, the results of a random effects analysis revealed that Model T1 explained 47% and T5 explained 46% of the variance in depressive change scores accounting for the most within patient variance on in BDI-II change scores (see Table 28; Appendix L). Model T4 explained the least within in patient variance (38%). Between patient variance explained ranged from 50% (T4) to 72% (T2 and T3). However, while Model T4 explained modest amounts of variance in comparison to the other models, Model T4 obtained superior rates of significance relative to the amount of variance explained. Moreover, the lack of significance obtained for models in non-curvilinear conditions at Level 2 might restrict the ability to introduce and interpret variables at Level 2 using linear metrics of time. Similarly, Model T4 had smaller standard errors relative to the amount of variance explained which would support the use Model T4 for modelling time. Furthermore, Model T5, although explaining a substantial amount of variance was considered from a theoretical point of view to introduce too many unknown sources of error regarding why patients did and did not attend sessions at particular times and thus was excluded for consideration as a coding of time. While the results are

comparable the magnitude of the result provides some evidence to suggest that T1 and T2 provide a better overall fit to the model than T4 (Raferty, 1995). Never-the-less, having been satisfied that the data can be observed to fit a fairly curvilinear structure (see Figure 31; Appendix L), and in consideration of relatively smaller standard errors and higher levels of significance associated with the introduction of non-linear

functions, a conservative choice was made in the modelling of time (Singer & Willet, 2003). Thus, a curvilinear function (T4) was selected for use in subsequent analyses to represent Session as the most accurate coding of time to model the dependent variable (BDI change) in subsequent analyses.