The Relationship between Alliance & Outcome in PTSD
1. Journal of Counseling Psychology
Alliance and Outcome in Varying Imagery Procedures for
PTSD: A Study of Within-Person Processes
Asle Hoffart, Tuva Øktedalen, Tomas Formo Langkaas, and Bruce E. Wampold
Online First Publication, August 19, 2013. doi: 10.1037/a0033604
CITATION
Hoffart, A., Øktedalen, T., Formo Langkaas, T., & Wampold, B. E. (2013, August 19). Alliance
and Outcome in Varying Imagery Procedures for PTSD: A Study of Within-Person Processes.
Journal of Counseling Psychology. Advance online publication. doi: 10.1037/a0033604
3. This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
2
HOFFART, ØKTEDALEN, LANGKAAS, AND WAMPOLD
tasks and also lead them to question the therapist’s care for them.
Therefore, there should be much variation in the levels of task
agreement and bond, both between patients and within patients
over time, which in turn might well covary with outcome. An
agreement about goals is necessary in trauma-focused therapy as
well. However, there should be more uniformity of levels of
agreement about the goals because the goals of trauma-focused
therapy—reducing the fear of the trauma memory and of the
trauma reminders (Foa et al., 2007)—should be strongly endorsed
by the patients as well as the therapists. Consequently, restricted
range reduces the possibility of finding covariation between agreements of goals and outcome. In general, task agreement has been
found to be more strongly related to outcome than goal agreement
and bond have (Horvath, 2011). With respect to PTSD patients,
early alliance has been shown to predict their adherence to prolonged exposure (Keller et al., 2010) and their emotion regulation
skills and outcome in a two-phase stabilization/skill development
and exposure therapy for childhood abuse-related PTSD (Cloitre,
Stovall-McClough, Miranda, & Chemtob, 2004). Based on this
literature, we specifically expected that task agreement in particular, and perhaps bond as well, would predict better weekly as well
as overall outcome in trauma-focused therapy of PTSD.
Although the IE component of prolonged exposure is an effective intervention for trauma-related fear through the mechanisms
of habituation and experienced nonoccurrence of feared event (Foa
et al., 2007), it may be less effective for other trauma-related
emotions such as shame, guilt, and anger. Repeated exposure to a
traumatic memory involving shame and guilt may provide little
corrective information and actually run the risk of reinforcing
these emotions (Dalgleish & Power, 2004). To address the range of
emotions in PTSD, some authors have advocated (Arntz et al.,
2007) the addition of an element of imagery rescripting (IR;
Smucker, 2005), in which an imagined change of the course of
events of the trauma memory is induced. In a randomized controlled trial (RCT), Arntz et al. (2007) compared a combination of
IE and IR to IE alone. They found no difference in reduction of
PTSD severity but did find the IE and IR combination to be more
effective for anger control, externalization of anger, hostility, and
guilt, especially at 1-month follow-up. The IR method used in this
study was to provide the patient with an opportunity to discover
and express in imagery any trauma-related inhibited emotional
responses (e.g., anger about what happened). The present study,
the data for which was obtained in an RCT, replicates and extends
the study of Arntz et al. by using a broader form of IR developed
by Smucker (2005). In this method, the patient’s current self
is—after an initial imagery reliving phase—invited to enter the
imagery at the worst moment of the trauma, bring the situation to
a solution (e.g., overpower a perpetrator), and then interact with
the traumatized self back then. The patient’s anger is used as a
resource in overpowering perpetrators and the current self–
traumatized self interaction stimulates the development of selfcompassion instead of shame, guilt, and self-critique. The empowering and relieving features of IR may put less strain on the patient
and the therapist by making them feel less helpless and distressed
compared to IE and thus help them both to engage in imagery
work. In the study by Arntz et al., therapists tended to favor the
combination of IE and IR, as it decreased their feelings of helplessness compared to IE alone. Supporting the effectiveness of the
broader form of IR, Grunert, Weis, Smucker, and Christianson
(2007) found in an open trial that IR was extremely helpful for
PTSD patients who had previously not profited from IE. The
present study does not focus on therapy outcome per se but on how
the influence of the alliance on outcome may relate to the specific
trauma-focused therapy model being applied. We expected that,
due to the empowering and relieving features of IR compared to
IE, the influence of task agreement and bond on subsequent PTSD
symptoms would be weaker in IR than in IE.
Understanding the nature of the alliance depends on the methods
used to examine it. For example, the well-established alliance/
outcome relationship is cross-sectional (i.e., bivariate observations
for each psychotherapy dyad) and is thus focused on betweenperson differences (i.e., interindividual processes). That is, variations between patients in early alliance have been found to correlate with between-patient variations in outcome at the end of
therapy (Horvath et al., 2011). However, it is also important to
consider the development of the alliance for a particular patient.
For example, the rupture-repair model (Safran & Muran, 1996)
assumes that alliance ruptures represent opportunities for patients
to learn about their problems relating to others, and repairs represent such opportunities having been taken in the here-and-now of
the therapeutic relationship. This process is indicated by marked
drops in alliance followed by a quick return to previous or higher
levels, which represents within-person variations in the alliance. In
general, therapy models, and particularly therapists, focus on
within-person relationships, which would be the case, for example,
when a change in the alliance for a particular patient leads to a
subsequent alleviation of PTSD symptoms in that patient.
The typical alliance data, collected once early in therapy, or
occasionally during therapy, are unsuitable for evaluating withinperson processes (Curran & Bauer, 2011). Only repeated measures
data allow for the proper disaggregation of between-person and
within-person effects (Curran & Bauer, 2011; Hoffman & Stawski,
2009). Such a disaggregation not only allows the study of withinperson processes separated from between-person effects, but also
is able to examine cross-level interactions of between- and withinperson effects. For instance, the effect of having a stronger alliance
than expected for a particular patient may matter more for patients
who have lower alliance in general. When the general (betweenperson) level of bond is low, for example when the patient has low
trust that the therapist wants the best for him/her and is therefore
preoccupied with this issue, a certain increase of this trust in a
particular session might be a valued event with an immediate
effect on symptoms. On the other hand, when the patient’s trust is
already high and is not an issue for him/her, the same increase
would probably have fewer consequences. That is, one should
expect within-person variations in alliance to affect PTSD symptoms more when the between-person level of alliance is low.
So far, the ability to separate these effects has not been fully
capitalized upon in alliance research. Two notable exceptions are
the studies of Tasca and Lampard (2012) and Falkenström, Granström, and Holmqvist (2013). Using latent change score modeling,
in which between- and within-person components of both the
predictor and outcome variables are separated, Tasca and Lampard
obtained evidence for a reciprocal influence of alliance to the
patient group and outcome among eating disordered individuals.
Using the disaggregation methods in multilevel models proposed
by Curran and Bauer (2011), Falkenström et al. also found evidence for a reciprocal causal model of alliance and outcome in
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WITHIN-PERSON EFFECTS OF ALLIANCE ON OUTCOME
primary care psychotherapy. Based on the results of these welldesigned studies, we expected to find that over the course of
trauma-focused therapy, prior growth in task and bond would be
associated with subsequent reduction in PTSD symptoms, and
prior reduction in PTSD symptoms would be associated with
subsequent growth in task and bond.
The main purpose of the present study was to examine the role
of alliance components in the process of therapeutic time-specific
change in patients diagnosed with PTSD. The patients received
either standard prolonged exposure, which includes IE, or modified prolonged exposure, where IR replaced IE as the imagery
component of prolonged exposure, in a 10-week residential program. They were assessed repeatedly (weekly) on alliance and
PTSD symptom measures, allowing us to separate the variance
related to individual differences (between-person component) at
the start of treatment from variance related to the intraindividual
process of change during treatment (within-person component). To
summarize, we wanted to examine the following hypotheses:
Hypothesis 1: Time-specific change in a patient’s task and
bond components of the alliance over the course of therapy are
negatively related to subsequent change in PTSD symptoms
assessed 3 days later (within-person effect). That is, when the
task agreement and bond for a given patient is higher than is
expected for that patient, subsequent symptoms will be lower.
Hypothesis 2: Time-specific change in a patient’s PTSD
symptoms over the course of therapy are negatively related to
subsequent change in task agreement and bond assessed 4
days later (within-person effect). That is, when the PTSD
symptoms for a given patient are less than is expected for that
patient, subsequent task agreement and bond will be higher.
Hypothesis 3: Individual differences in task agreement and
bond at the start of imagery therapy are negatively related to
individual differences in the rate of change of PTSD symptoms over the course of therapy (between-person effect). That
is, patients who have a higher task agreement and bond at the
start of imagery therapy will have a more negative rate of
change of PTSD symptoms.
Hypothesis 4: There is a cross-level interaction of betweenperson and within-person effects. That is, the lower the level
of task agreement and bond is at the start of imagery therapy,
the stronger the relationship between time-specific change in
alliance and subsequent change in PTSD symptoms will be
during therapy, and the higher the level of task agreement and
bond is at the start of imagery therapy, the weaker the relationship between time-specific change in alliance and subsequent change in PTSD symptoms will be during therapy.
Hypothesis 5: The within-person effect of task agreement and
bond on subsequent PTSD symptoms is stronger for IE within
prolonged exposure than for IR within prolonged exposure.
We also wanted to explore the relationships between goal agreement and PTSD symptoms but expected the magnitude of this
relation to be less than the magnitudes for task agreement and
bond.
3
Method
Participants
The participants were selected from referrals to a PTSD treatment program at a national clinic. The clinic was established for
the residential treatment of nonpsychotic patients who lack adequate local treatment opportunities or have not responded adequately to outpatient care and require more extensive and/or specialized treatment. The study eligibility was similar to treatment
eligibility, that is, all patients who were considered to potentially
benefit from the PTSD treatment were included. The inclusion
criteria were (a) satisfying Diagnostic and Statistical Manual of
Mental Disorders (4th ed.; DSM–IV; American Psychiatric Association, 1994) criteria for PTSD, (b) PTSD identified as the primary disorder in need of treatment, (c) age 18 to 67 years (regulated by the hospital), and (d) accepting withdrawal of all
psychotropic medication (regulated by the hospital—patients referred to the hospital have usually received medication without
effect). The exclusion criteria were (a) extensive dissociative
symptoms, (b) current suicidal risk, (c) current psychosis, and (d)
ongoing trauma (e.g., current involvement in an abusive relationship). The study was approved by the Regional Ethics Committee,
and the patients’ gave informed consent after the procedures had
been fully explained.
A flow chart of patients is presented in Figure 1. Seventy-one
patients were found eligible for treatment at the assessment stay
and admitted to treatment from December 2008 to November
2010. At admission, all these 71 patients were found to meet
research criteria, but three of them declined participation. One
patient dropped out from treatment before randomization because
she changed her mind about receiving trauma-focused therapy.
The remaining 67 patients were randomized, 33 to IE within
prolonged exposure and 34 to IR within prolonged exposure. Two
IE patients lost their eligibility after randomization— one was
found to need an eating disorder focus to the exclusion of imagery
work, and another was inadvertently treated by the IR protocol.
Thus, our intent-to-treat (ITT) with imagery sample consisted of
65 patients—31 IE and 34 IR patients—who signed consent, were
randomized to an imagery condition, and were not removed by the
investigators. Of these, three patients— one IE and two IR patients— dropped out within 5 to 6 weeks into the program. The
reasons for dropout were conflict with therapist in two cases and
serious somatic illness in one case. One IR patient received a
restricted dose of rescripting, as she insisted to focus on her
relationship to her parents after three sessions in accordance with
the IR manual. This left a completer sample of 61 patients—30 IE
and 31 IR patients.
The mean age of 65 patients—38 women and 27 men—was 45.2
years (SD ϭ 9.7). The mean length of time since the index trauma
was 17.5 years (SD ϭ 13.3). The most prevalent index trauma,
defined as the one experienced by the patient as currently most
distressing or most frequently reexperienced or both, among the 38
women was nonsexual assault by a familiar person (n ϭ 12;
31.6%), sexual assault by a familiar person (n ϭ 9; 23.7%), and
sexual assault by a stranger (n ϭ 8; 21.1%). Among the 27 men,
war experience was most frequent (n ϭ 7; 25.9%), followed by
assault by a familiar person (n ϭ 6; 22.2%) and accidents (n ϭ 4;
14.8%). Over half the index traumas were prolonged and/or re-
5. HOFFART, ØKTEDALEN, LANGKAAS, AND WAMPOLD
4
Assessed for eligibility (N = 71)
Excluded (n = 4)
♦ Declined to participate (n = 3)
♦ Dropped out before randomization (n = 1)
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Randomized (n = 67)
Allocated to imagery exposure (n = 33)
♦ Received full intervention (n = 30)
♦
♦
Allocated to imagery rescripting (n=34)
♦ Received full intervention (n = 31)
Lost eligibility (n = 2)
Dropped out after 6 weeks (n = 1)
♦
Analyzed (n = 31)
♦ Excluded because lost eligibility (n = 2)
Figure 1.
Changed focus after 6 weeks (n = 1)
♦
Dropped out after 5 weeks (n = 2)
Analyzed (n = 34)
♦ Excluded from analysis (n = 0)
Flow of patients through the study.
peated events. Among the 65 patients, 40 (61.5%) had current
major depression or dysthymia, 44 (67.7%) had panic disorder
with or without agoraphobia or agoraphobia without a history of
panic disorder, 39 (60.0%) social phobia, 16 (24.6%) obsessive–
compulsive disorder (Axis I), 11 (16.9%) generalized anxiety
disorder, 18 (27.7%) alcohol abuse/dependence, 11 (16.9%)
avoidant personality disorder, 9 (13.9%) substance abuse/dependence, and 9 (13.9%) obsessive-compulsive personality disorder.
No other diagnosis exceeded a proportion of 10% in the present
sample. According to chi-square tests, there were no diagnostic
differences between the patients in the two treatment conditions.
Measures
PTSD Symptom Scale–Interview (PSS-I). The PSS-I (Foa,
Riggs, Dancu, & Rothbaum, 1993) is a semistructured interview
consisting of 17 items corresponding to the DSM–IV PTSD symptoms. Both PTSD diagnosis and PTSD symptom severity are
assessed. Items are rated on 0 –3 scales for combined frequency
and severity in the past 2 weeks (0 ϭ not at all, 1 ϭ once per week
or less/a little bit, 2 ϭ 2 to 4 times per week/somewhat, and 3 ϭ
5 or more times per week/very much). Symptom severity is determined by the sum of the 17 ratings. The PSS-I has demonstrated
satisfactory internal consistency reliability (Cronbach’s ␣ ϭ .85),
high interrater agreement (interclass correlation [ICC] ϭ .97), high
1-month test–retest reliability (r ϭ .80), good concurrent validity
with other measures of psychopathology, and excellent convergent
validity with the Structured Clinical Interview for DSM–III–R
(SCID; Spitzer, Williams, Gibbon, & First, 1988), correctly identifying the PTSD status of 94% of the studied subjects (Foa et al.,
1993). The PSS-I was translated into Norwegian (see later) and
used as the primary outcome measure in this study. Ten pretreat-
ment and 10 posttreatment PSS-I interviews were randomly selected from the total sample of interviews and scored independently. Interrater agreement for the PSS-I total score was evaluated
by means of ICC (3, 1; Shrout & Fleiss, 1979), with a value of .91
at pretreatment and .95 at posttreatment.
PTSD Symptom Scale–Self-Report (PSS-SR). The PSS-SR
(Foa et al., 1993) is a self-report version of the PSS-I and was used
as a suboutcome measure in the present study. This measure is
usually rated for the last week, but the rating period was shortened
to the last 3 days in this study. The frequency part of the criteria
was changed correspondingly (0 ϭ not at all, 1 ϭ 1 time/sometimes, 2 ϭ 2 times/half of the time, 3 ϭ 3 or more times/almost
always. As for the PSS-I, symptom severity is determined by the
sum of the 17 ratings. PSS-SR symptom severity has demonstrated
satisfactory internal consistency reliability (Cronbach’s ␣ ϭ .91),
high 1-month test–retest reliability (r ϭ .74), good concurrent
validity with other measures of psychopathology, and excellent
convergent validity with the SCID, correctly identifying the PTSD
status of 86% of the studied subjects (Foa et al., 1993). The PSS-I
and the PSS-SR were translated to Norwegian by the first and the
third author and back-translated to English by a native-Englishspeaking professional also competent in Norwegian, until satisfactory formulations were found. Internal consistency reliability of
the first-week PSS-SR rating was .88. One-week test–retest reliability coefficient for the PSS-SR scores from the first to the
second week (before the more active therapy components were
introduced) was .70. Concurrent validity was supported by a
correlation of .68 between the first-week PSS-SR scores and
pretreatment PSS-I scores.
Working Alliance Inventory–Short Revised (WAI-SR).
The WAI-SR (Hatcher & Gillaspy, 2006) is a shortened 12-item
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WITHIN-PERSON EFFECTS OF ALLIANCE ON OUTCOME
version of the original 36-item WAI (Horvath & Greenberg, 1989).
Items are rated on a 1–7 Likert-type scale, and subscale scores for
the task (four items), goal (four items) and bond (four items)
components of alliance are computed by averaging across items.
The WAI-SR has been found to differentiate well between these
three components and has shown high internal consistency reliability (subscale score alphas ranging from .85 to .90) and high
correlations with other alliance scales (Hatcher & Gillaspy, 2006).
The WAI-SR has been translated to Norwegian and backtranslated to English until satisfactory formulations have been
found (Horvath, 1981, 1984, 1991/2006). The internal consistency
reliabilities of the four-item Task, Goal, and Bond subscales at the
first assessment for the second week were .90, .91, and .85,
respectively, and their 1-week test–retest reliabilities from the
second to the third week were .72, .80, and .80, respectively.
Procedure
During a 3-day assessment stay, one of two research psychologists (the second and the third authors) evaluated the applicants by
conducting the PSS-I to ascertain the diagnosis of PTSD, whereas
the two individual therapists associated with the program evaluated the overall eligibility for the program. At the patients’ admission to the program (pretreatment), one of the two research psychologists conducted a comprehensive interview consisting of the
PSS-I, the Mini International Neuropsychiatric Interview (MINI;
Sheehan et al., 1994), and the Structural Clinical Interview for
Axis II Personality Disorders (SCID-II; First, Spitzer, Gibbon,
Williams, & Benjamin, 1994). The PSS-I was also conducted at
discharge (posttreatment), but this time by a psychologist not
involved in the study and blind to the patients’ treatment condition.
The alliance measure (together with other process measures not
analyzed here) was completed every Friday morning. The patients
were asked to base their ratings on their experiences during the last
4 days, that is, during the most treatment-intensive part of the
week. The PSS-SR was completed every Monday morning. The
patients were asked to base their ratings on their experiences
during the last 3 days, that is, during a less treatment-intensive
period. To control for potential expectancy bias with respect to the
alliance measure, patients were informed that the therapists were
blind to the process ratings.
Design and Randomization
The patients received 10 individual sessions lasting 90 min over
a period of 10 weeks. After 1 week of treatment (two first sessions
according to the prolonged exposure protocol), the patients were
randomized to either IE or IR as the imagery component of the
treatment. A person who was not affiliated with the research team
organized the randomization procedure. Random sequences generated from http://www.random.org were used for assignment to
conditions. A blocked randomization procedure was used in which
each therapist was assigned an equal number of cases in each
condition. The probability of every patient ending up in any of the
two conditions was kept constant at 0.5, and no measures were
taken to correct for any imbalance in numbers between the conditions due to discontinued treatments.
5
Treatment
The outpatient manuals for prolonged exposure, including IE
(Foa et al., 2007) and IR (Smucker, 2005), were used but adapted
for the inpatient setting. Essentially, it meant that milieu therapists
were available to assist in between-session assignments (in vivo
exposure, listening to tapes of the imagery work) and to provide
safety and support after intensive individual sessions. The first two
individual sessions were the same for all patients and consisted of
giving a general treatment rationale and providing trauma education (first session) and introducing and planning in vivo exposure
by constructing an exposure hierarchy (second session). Then,
before the third session, patients were stratified by therapist and
randomly allocated to either the IE or the IR condition, after which
they followed the relevant protocols for the third (occurring toward
the end of the second week of treatment) to ninth session. In the
tenth and final session, the content was again identical and consisted of imagery exposure to the total memory, a review of
progress, and suggestions of continued practice. In the sixth week,
the patients returned home to test their newly acquired skill in their
natural environment. All the time, there was one other treatment
group of anxiety patients at the ward, and the PTSD patients
participated in the ward’s general program, consisting of one
physical exercise session and one ward meeting per week.
The IE approach consisted of having participants relive the
traumatic event in their imagination and recount the memory in the
present tense. To increase vividness, patients were asked to report
as much detail as possible, including sights, sounds, smells, behaviors, bodily sensations, feelings, and thoughts. The memory
was repeated if necessary to allow total reliving for a period of 40
to 60 min. The entire memory was relived during the first two or
three sessions. In the subsequent sessions, the hot spots procedure
was usually applied, where reliving was focused on the currently
most distressing parts of the memory.
The IR approach consisted of three continuous phases. The first
phase consisted of imagery reliving of traumatic event in order to
activate the trauma memory and to identify the hot spot(s). In
Phase 2, without pause in imagery, the memory was relived from
the beginning, but this time—at the identified hot spot—the patient
was asked to imagine the current self entering the scene at the hot
spot and bringing the situation to a solution (overpowering the
perpetrators or updating the traumatized self back then with future
information). Finally, in Phase 3, patients were stimulated to
imagine an interaction between the current self and the traumatized
self back then. As in IE, the imagery was supposed to last 40 to 60
min.
Therapists
One of the individual therapists was a 57-year-old male clinical
psychologist with a PhD. The other was a 55-year-old female
psychiatric nurse with a master’s degree. The milieu therapists
were four psychiatric nurses ranging from 45 to 60 years old. All
the individual and milieu therapists had at least 10 years of
experience in the cognitive therapy programs for anxiety disorders
at the unit and had completed the cognitive therapy specialization
program provided by the Norwegian Association of Cognitive
Therapy. Of the 65 ITT patients, the psychologist treated 16 IR
patients and 15 IE patients, whereas the nurse individual therapist
treated 18 IR patients and 16 IE patients.
7. 6
HOFFART, ØKTEDALEN, LANGKAAS, AND WAMPOLD
Training and Supervision
All the staff received prestudy workshops and supervision by
experts Elizabeth Hembree (in prolonged exposure including IE)
and Mervin R. Smucker (in IR) during several pilot treatment
groups. Throughout the study period, all of the individual sessions
were videotaped, and each of the experts provided 90-min supervision sessions of taped imagery biweekly. In addition, the first
author provided two 60-min supervision sessions per week to the
milieu staff and individual therapists in a group format.
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Treatment Integrity
The Treatment Integrity Checklist (Foa, Hearst-Ikeda, Dancu,
Hembree, & Jaycox, 1997) contains items describing essential and
desirable ingredients of prolonged exposure therapy across the 10
sessions described in the manual (Foa et al., 2007). As we were
particularly interested in assessing the imagery component, which
was the only intended difference between the two treatment conditions, we rated the eight items of the Prolonged Exposure Sessions 4 –9, Section C: Imaginal Exposure. Three of the eight items
refer to ingredients that are obligatory (e.g., “reviews instructions
for imaginal exposure”), whereas five refer to ingredients that
should be present if needed (e.g., “titrates the experience as
needed”). Based on discussions with the originator of IR, Mervin
R. Smucker, a corresponding checklist for this method was constructed. It consisted of the same three obligatory items as for the
IE checklist, one unique obligatory item, and six unique per-asneeded items (e.g., “identifies relevant action impulses coming
from the client and helps the client to implement them within
imagery”). A score for percentage adherence during an imagery
episode is computed by dividing the number of obligatory and
per-as-needed ingredients present by the total number of items
rated. An overall adequacy (competence) rating for the episode
was given using a 1–5 scale with the anchor points poor, mediocre,
satisfactory, good, and excellent. Finally, the presence or absence
of IR elements was rated. The expert on the therapy form (Elizabeth Hembree or Mervin R. Smucker) rated the episode together
with the first and the second author, whereas the third author did
simultaneous translation of the videotape. A pilot case in each
therapy form was first rated and discussed to calibrate the ratings.
Then, 10 random cases, stratified for order of treatment group in
the trial and individual therapist, from each therapy form were
selected. From these 20 cases, the imagery part of the fifth individual session was rated. One of the cases turned out to be the one
who was inadvertently treated by IR instead of IE (see Participants), and this case was omitted from all analyses. Thus, 19
(4.3%) of the total of 440 sessions including the specific imagery
component were analyzed. The intraclass correlation (ICC [3, 2];
Shrout & Fleiss, 1979) was .69 in IE and .92 in IR for adherence
and .93 in IE and .87 in IR for adequacy.
The results are based on the expert ratings. Mean adherence
rating was 75% (SD ϭ 15%) in IE and 80% (SD ϭ 21%) in IR.
Mean adequacy rating was 2.78 (SD ϭ 1.30) in IE, corresponding
to a level a little below satisfactory, and 3.20 (SD ϭ 1.32) in IR,
corresponding to a level a little above satisfactory. One minor
protocol violation was detected in one of the IE sessions, where the
therapist asked questions typical of IR for a couple of minutes.
After the trial, we asked the individual therapists to fill in a
questionnaire about their preference for IE or IR. The psychologist
indicated no preference, whereas the psychiatric nurse reported
preference for IR because she felt patients’ experience of taking
the power from the perpetrator was particularly helpful.
Statistical Analysis
A main purpose of this study was to examine how within-person
changes in components of alliance affected subsequent withinperson changes in outcome. Such a focus on within-person processes necessitates a proper disaggregation of the within-person
and between-person components of change in the time-varying
predictor. The choice of method of disaggregating within-person
and between-person effects in a time-varying predictor depends on
how it is related to time (Curran & Bauer, 2011). Specifically, it is
important to know if this relationship is characterized by a fixed
effect of time or if it is characterized by both a fixed and random
effect of time. To estimate these parameters, we conducted several
series of mixed models using the three alliance scales (WAI-Task,
WAI-Goal, WAI-Bond) and the PTSD symptom measure (PSSSR) as dependent variables. The intent-to-treat sample was analyzed, and due to our research purposes, scores were included from
the start of the imagery part of therapy (from the second week of
treatment). Moreover, as only active treatment time was of interest,
ratings from the week at home were not included, and the home
week was not counted in the time term. The fit of these nested
models for the covariance was compared by using the likelihood
ratio test, in which the difference in model –2 log likelihood values
is divided by the difference in degrees of freedom of the models
(Fitzmaurice, Laird, & Ware, 2004). Restricted maximum likelihood estimation was used to estimate nested models with only
varying random effects (Fitzmaurice et al., 2004). Models with
different fixed effects were compared using maximum likelihood
estimation. We used an unstructured covariance structure for the
random effects, thus allowing the estimation of covariance between the random intercepts and slopes. By contrast, we used a
diagonal covariance structure for the residuals, thus allowing the
variances of the residuals to differ over time points but setting the
covariance between the residuals across time points to zero. Thus,
the correlation between the scores across assessments had to be
modeled exclusively by the random effects. We started with a
model with only a fixed intercept and no random effects, added a
random intercept, and, finally, added a random effect of week in
therapy. After the best random effects structure had been found in
this way, we tested whether another residual covariance structure
besides the diagonal—for example, a first-order autoregressive
(e.g., AR(1), Toeplitz)— could improve model fit.
We then tested whether the inclusion of a fixed linear time term
(week in therapy) and—in a second step—a fixed quadratic time
term (week2) as independent variables improved model fit. Again,
the fit of these nested models was compared by using the likelihood ratio test.
For all the alliance scales, a fixed and random intercept and a
fixed and random linear effect of time gave the best model fit.
Moreover, no alternative residual covariance structure to the diagonal turned out to improve the fit. For the PSS-SR scores as well,
a fixed and random intercept and a fixed and random effect of time
turned out to be the most appropriate model. In addition, an AR(1)
residual covariance structure improved model fit compared to the
diagonal structure.
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WITHIN-PERSON EFFECTS OF ALLIANCE ON OUTCOME
In order to disaggregate the within-person and between-person
variability in the time-varying alliance and symptom measures, we
utilized the statistical centering method of detrending presented by
Curran and Bauer (2011). This method was chosen because these
time-varying predictors were characterized by a fixed and random
effect of time. We created two new variables representing the
within-person change and between-person differences for bond,
task, goal, and PSS-SR scores, respectively (see the applied equations in the Appendix). First, we created the within-person predictor by regressing the variables on time separately for each individual using ordinary least squares. The resulting within-person
deviations over weeks in therapy represent the within-person component of the time-varying alliance and symptom measures. In this
way, the within-person deviations are conceptualized as the difference between a time-specific observation and the trend line for
the variable (i.e., the expected value given a linear growth in the
variable).
Due to our present research purpose to examine the effect of
between-person differences in alliance at the start of the differing
imagery therapies, we used the estimated differences on the timevarying predictors at this time point (second week of treatment) to
represent their between-person component. By setting time to zero
at this point, the between-person component of the time-varying
measures are represented by the estimated intercept at the second
week for each individual.
To correct for the possibility of Type I error, the chosen alpha
significance level of .05 was divided by the number of tests (two)
for each hypothesis, yielding a level of .025 for the individual test.
Because all of the hypotheses were directional in nature, one-tailed
tests were used. The effect size (ES) of the overall outcome was
computed as Hedges’s g for dependent samples (Borenstein,
Hedges, Higgins, & Rothstein, 2009). ESs of the between-person
and within-person effects were calculated as the proportion of
explained outcome variance for each predictor (Snijder & Bosker,
1999; see the applied equations in the Appendix). We used the
program SPSS 19.0.
Results
Overall Outcome
In the following ITT analyses, pretreatment PSS-I ratings substituted missing posttreatment ratings. Due to a failure in administrative routines, one IE patient missed the pretreatment PSS-I
interview, and his ratings were substituted by the first and the last
PSS-SR score. On the PSS-I, the 34 IR patients changed from
33.32 (SD ϭ 6.88) at pretreatment to 22.71 (SD ϭ 14.27) at
posttreatment, yielding an ES of Ϫ0.83, 95% CI [Ϫ0.46, Ϫ1.20].
The corresponding change among the 31 IE patients was from
35.19 (SD ϭ 8.24) to 19.90 (SD ϭ 13.76), with an ES of Ϫ1.27,
95% CI [Ϫ0.76, Ϫ1.78]. In the total sample of 65 patients, the ES
was Ϫ1.06, 95% CI [Ϫ0.74, Ϫ1.38]. A time by treatment
repeated-measures analysis of variance yielded a time effect, F(1,
63) ϭ 69.87, p Ͻ .0001, but no treatment effect, F(1, 63) ϭ 0.04,
ns., or time by treatment effect, F(1, 63) ϭ 2.27, p ϭ .137
(two-tailed).
7
Summary Statistics for the Weekly Outcome and
Alliance Measures
Missing data in the intent-to-treat sample during active imagery
treatment was 6.4% for PSS-SR scores, 9.8% for Task scores,
10.0% for Goal scores, and 10.5% for Bond scores. The mean
between-person PSS-SR score at the second week (estimated intercept) was 31.31 (SD ϭ 9.06). At the second week of treatment,
mean between-person Task score (estimated intercept) was 5.33
(SD ϭ 1.17), Goal score was 5.65 (SD ϭ 1.12), and Bond score
was 5.14 (SD ϭ 1.34). An F test for comparing variances in
correlated variables showed that the standard deviations of the
between-person Task, Goal, and Bond scores were not significantly different. The standard deviations of the within-person
Task, Goal, and Bond scores were 0.4752, 0.4367, and 0.4127,
respectively. An F test showed that Task scores had larger variances than did Goal and Bond scores (both ps Ͻ .025). The
intercorrelations for the estimated between-person alliance scores
at the second week (intercept) were high: .87 for Task and Goal,
.62 for Task and Bond, and .73 for Goal and Bond. The intercorrelations for the within-person alliance scores over the course of
imagery treatment were more moderate: .64 for Task and Goal, .46
for Task and Bond, and .51 for Goal and Bond.
Testing Hypotheses
Our weekly outcome measure—the PSS-SR—was used as dependent variable in mixed models with random intercept and slope
and an AR(1) covariance structure for the residuals (see the Statistical Analysis section). Time (week), treatment (IR vs. IE), and
the within-person and between-person components of the three
WAI scales were used as predictors. Separate analyses were conducted for each scale. To establish a temporal sequence between
predictor and outcome, within-person alliance scores were lagged
and thus related to the PSS-SR scores the following week (3 days
later).
A summary of the fixed main effects for the three alliance
components (viz., task, goal, and bond) on PTSD symptoms, as
well as the random effects, are shown in Table 1. Our first
hypothesis, about a negative within-person effect of task agreement and bond on subsequent symptoms, was supported for the
Task scale. That is, if a patient had stronger agreement on tasks in
a given week than would be predicted for that patient given his/her
general trend, then this patient’s subsequent (3 days later) symptoms were lower than would be expected. The Goal and Bond
scales showed no such within-person effect.
Unrelated to our hypotheses, Table 1 also shows that there was
a negative relationship between interindividual differences in initial Task scores and mean level of PTSD symptoms over the
course of therapy but no such relationship for the other two WAI
scales. In addition, there was a negative effect of time, which
indicates that the PSS-SR scores were reduced over the course of
therapy. There was no effect of treatment (viz., IR vs. IE) on the
mean level of PSS-SR scores over the course of therapy.
To examine our hypothesis about reciprocal causation, that is, that
the PTSD symptoms would be negatively related to subsequent task
agreement and bond, the three WAI scales were used as dependent
variables in mixed models with random intercept and slope and a
diagonal covariance structure for the residuals (see the Statistical
9. HOFFART, ØKTEDALEN, LANGKAAS, AND WAMPOLD
8
Table 1
Fixed Effects Estimates and Random Effects (Variance–Covariance) Estimates for the Three
Models of the Predictors of PTSD Symptoms
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This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
Parameter
Intercept
Week
Treatment: IR
Treatment: IE
Within-person task
Between-person task
Within-person goal
Between-person goal
Within-person bond
Between-person bond
Residual
AR(1) rho
Intercept
Week
Intercept ϫ Week
–2 log likelihood
Task
Goal
Bond
Fixed effects
40.885)602.6( ء
43.138)453.5( ء
Ϫ1.312)071.0( ء
Ϫ1.272)361.0( ء
Ϫ2.446 (2.265)
Ϫ3.470 (2.374)
0 (0)
0 (0)
Ϫ0.820)193.0( ء
Ϫ2.139)779.0( ء
Ϫ0.527 (0.426)
Ϫ1.667 (1.065)
37.054)179.4( ء
Ϫ1.316)771.0( ء
Ϫ1.110 (2.411)
0 (0)
Ϫ0.724 (0.464)
Ϫ1.174 (0.910)
Random effects
17.136)249.1( ء
16.638)997.1( ء
0.210)980.0( ء
0.193)680.0( ء
68.460)872.41( ء
79.295)442.61( ء
1.118)003.0( ء
1.235)433.0( ء
2.947 (1.617)
3.897)856.1( ء
2737.418
2727.652
16.096)348.1( ء
0.191)390.0( ء
74.918)367.51( ء
1.296)343.0( ء
2.712 (1.752)
2549.456
Note. Standard errors are in parentheses. PTSD ϭ posttraumatic stress disorder; IR ϭ imagery rescripting; IE ϭ
imaginal exposure; task ϭ agreement about tasks; goal ϭ agreement about goals; bond ϭ patient–therapist emotional
bond; AR(1) ϭ first order autoregressive.
ء
p Ͻ .05.
Analysis section). Within-person and between-person PSS-SR scores
were used as predictors. In addition, we included time and treatment
as predictors of the alliance scores. Our hypothesis that within-person
variations in PTSD symptoms would predict subsequent withinperson variations in PTSD symptoms was not supported for any of the
WAI scales. That is, there was no within-person effect of PSS-SR
scores on Task, Goal, or Bond scores (all absolute t values Ͻ 1).
To examine our third to fifth hypotheses, all the six interactions
between our four predictors were added in the three models. Our third
hypothesis, stating that higher initial task agreement and bond predicted a steeper negative slope of PTSD symptoms, was supported.
That is, there was a significant time by between-person task effect,
 ϭ Ϫ0.272, SE ϭ 0.136, t(55.5) ϭ Ϫ2.00, p ϭ .025, and a
significant time by between-person bond effect,  ϭ Ϫ0.337, SE ϭ
0.125, t(55.6) ϭ Ϫ2.71 p Ͻ .01. As these interaction effects were
negative, they indicate that with longer time into therapy, higher initial
alliance was associated with lower PTSD symptoms. There was no
time by between-person goal effect on symptoms.
Our fourth hypothesis, that the within-person effect of alliance on
outcome is stronger with lower initial levels of alliance, was contradicted by the results for the Task scale. That is, there was a cross-level
interaction of between-person and within-person effects of task,  ϭ
Ϫ0.814, SE ϭ 0.403, t(320.7) ϭ Ϫ2.02, p Ͻ .025. The negative
direction of this interaction effect shows that— opposite to what we
expected—the higher the initial task alliance, the stronger the negative
relationship between within-person variations in task alliance and
subsequent within-person variations in PTSD symptoms. No crosslevel interactions of the within- and between-person effects were
evident for the Goal and Bond scales.
Our fifth hypothesis, stating that the within-person relationship
between alliance and outcome is stronger in IE than in IR, was
supported for the Task scale. That is, treatment interacted with the
within-person effect of Task scores on PSS-SR scores. When using
IE as a baseline, there was a positive effect of IR on PSS-SR
scores,  ϭ 2.031, SE ϭ 0.775, t(325.4) ϭ 2.62, p Ͻ .01.
Considering the overall negative within-person effect of Task
scores on PSS-SR scores (see Table 1), the positive direction of
this relationship in IR compared to IE shows that the relationship
is weaker in IR than in IE.
It should also be noted that there was a time by treatment effect.
In the model using task as a predictor, there was a positive effect of
IR on PSS-SR scores with time,  ϭ 0.964, SE ϭ 0.317, t(54.9) ϭ
3.04, p Ͻ .01. Considering the overall negative effect of time on
PSS-SR scores (see Table 1), the positive effect of IR compared to IE
used as baseline shows that the PSS-SR scores were less reduced in IR
than in IE. There was no individual therapist effect on the rate of
change of PSS-SR, Task, Goal, or Bond scores.
The Magnitude of Effects
Compared to a baseline model including only the random effects
(intercept, time) and the fixed effect of time, residual variance was
reduced, with 4.3%, while random intercept variance was reduced,
with 5.8%, when within-person and between-person Task scores
were added in the model.
Discussion
The Role of Alliance in Varying Imagery Procedures
for PTSD
The main purpose of this study was to examine the role of
alliance components in the process of therapeutic change in PTSD
patients. Most importantly, the hypothesis of a negative within-
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WITHIN-PERSON EFFECTS OF ALLIANCE ON OUTCOME
person effect of the components agreement about the tasks of
therapy and bond on subsequent PTSD symptoms was supported
for the task component. That is, when the task score for a given
patient was higher than was expected for that patient, the subsequent symptom score was lower than was expected for him/her,
explaining about 4% of the outcome variance. In any event, this
finding goes beyond previous research in the PTSD treatment field
by indicating that time-specific change in a person’s task agreement during therapy is related to this person’s subsequent change
in PTSD symptoms. On a more general level, this finding supports
and extends those of Tasca and Lampard (2012) and Falkenström
et al. (2013), who found a within-person relationship between
overall alliance and subsequent symptoms but in different treatments and patient populations.
Furthermore, the results indicate that the within-person relationship between task agreement and outcome is dependent on the
specific therapy form. As we hypothesized, this relationship was
stronger in IE than in IR.
On the other hand, within-person changes in PTSD symptoms
did not predict subsequent task agreement and bond. That is,
time-specific change in a person’s symptoms during therapy was
not related to this person’s subsequent change in task and bond.
This finding is at odds with those of Tasca and Lampard (2012)
and Falkenström et al. (2013), who found a bidirectional relationship between alliance and symptoms. A conspicuous difference
between these studies and ours is that we used standardized, highly
structured, and manual-based procedures. One may speculate that
patients’ belief in and agreement to such procedures are less
influenced by symptom variations than is their agreement to less
standardized and less clearly defined procedures.
Our hypotheses about a between-person effect of initial task
agreement and bond was supported. Initial Task and Bond scores
predicted a steeper negative slope of PTSD symptoms. These
findings are consistent with most findings in alliance research
(Horvath et al., 2011) that early alliance predicts the further course
of symptoms. The centrality of the task component in predicting
overall (between-person) outcome is consistent with the results of
Webb et al. (2011), who found therapist–patient agreement on the
tasks and goals of therapy to account for most of the outcome
variance in cognitive therapy for depression. However, our results
indicate that a good initial bond is also important for a successful
overall outcome in exposure-based therapy for PTSD. Thus, alliance components may have different roles in cognitive behavioral
therapy (CBT) for different patient populations. What results
would be obtained for forms of therapy other than CBT is unknown, as it appears that the bond works differently in dynamic
therapy than it does in CBT. For instance, the bond and therapist’s
focus on affect seem to be differently related to each other and to
outcome in these two therapies (Ulvenes et al., 2012).
We expected that task agreement and bond would be of greater
concern for those who had a lower individual level and would thus
be more influential in these persons’ process of change, but in fact
the within-person effect of task scores on subsequent PTSD symptoms was stronger in those with a higher initial task agreement.
Future research must show whether this was a chance finding or
not. However, if this effect is replicated, it would suggest a double
drawback for a patient having a low initial agreement about the
tasks of therapy. First, the patient would experience less overall
improvement over the course of therapy, and, second, greater than
9
expected levels of agreement during the process of therapy for that
patient would not be as effective.
We also explored the role of the alliance component goal
agreement. As expected, this component was unrelated to symptom change. The within-person component of goal agreement also
had less variance than the within-person component of task agreement, and this difference may have contributed to the differential
findings. Our results are consistent with Horvath (2011), who
found— on the between-person level—that the agreement on tasks
as a predictor of outcome was superior to both bond and agreement
on goals.
Strengths and Limitations of the Study
Alliance and PTSD symptoms were assessed weekly, and adequate methods were utilized to separate the within-person and
between-person effects of the time-varying predictors in the applied multilevel models. Thus, we could study within-person relationships over the course of therapy, which are of particular
relevance for psychotherapy theories. This is because therapy
theories concern such relationships, that is, how change in a
process variable relates to subsequent change in an outcome variable. Such knowledge directly informs therapists concerning what
process variables need to be affected to achieve patient improvement. By contrast, knowledge of between-person relationships—
one patient having a low initial alliance and poor outcome and
another having a high initial alliance and good outcome— does not
imply that an increase in the first patient’s alliance would lead to
a better outcome for that patient. Thus, relationships established on
a between-person level do not imply that the same relationships
hold on a within-person level. For instance, the relationship between bond and outcome obtained in the present study on the
between-person level was not replicated on the within-person
level. A further advantage of properly separating the between- and
within-person components of a time-varying predictor is the possibility of examining cross-level interactions of within- and
between-person effects. For therapists, how between-person differences in, for example, alliance or self-concept moderate withinperson relationships over the course of therapy is more directly
relevant than are the correlations of these differences with overall
outcome. Such moderating knowledge informs therapists concerning under what conditions (e.g., high task agreement relative to
other patients) certain within-person change processes are working
(e.g., higher than usual task agreement at a given time point
predicts lower than usual PTSD symptoms). A further advantage
of studying within-person relationships between process and outcome is the possibility of identifying reciprocal or even reversed
causality between process and outcome. The RCT design, where
patients were randomized to two empirically based imagery methods, allowed us to study the moderating influence of therapy form
on the within-person relationships. The studied sample had high
clinical representativeness, as research eligibility was similar to
treatment eligibility and only three (4.2%) of 71 treatment eligible
patients declined research participation. Moreover, the dropout
rate from imagery treatment was low: three (4.6%) of 65 patients.
The present study has several limitations. Although the uncontrolled effect size of Ϫ1.27 (Hedges’s g, intent-to-treat analysis)
for standard prolonged exposure (including IE as the imagery
component) is comparable to that in one of the studies conducted
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10
HOFFART, ØKTEDALEN, LANGKAAS, AND WAMPOLD
by the originators of prolonged exposure (e.g., Hedges’s g ϭ
Ϫ1.37 in Foa et al., 2005), the adequacy ratings were only around
a level of satisfactory for both imagery treatments. The adherence
ratings of 75% (IE) and 80% (IR) are lower than those typically
found in the original studies of prolonged exposure (e.g., 97% in
Foa et al., 2005). Thus, the varied component of treatment may
have been delivered in a less than optimal way. Moreover, less
extensive examinations of integrity (4.3% of tapes) than usual
(about 10% of tapes; Foa et al., 1997) were performed. No integrity ratings were performed for the other components of treatment
(e.g., in vivo exposure). Although well-validated measures were
used, their Norwegian translations have not undergone psychometric evaluation in previous investigations. In the present study, their
internal consistency and test–retest reliability appeared satisfactory, though. Alliance and symptom ratings were collected from
the same individual, that is, the patient, and this may have
inflated their correlation. However, halo effects were prevented
by having the ratings done 3 and 4 days apart. Furthermore,
response biases like acquiescence are supposed to cut across
ratings and may affect within-person variations—which were
the main focus of this study—to a lesser degree. We used a
passive observational design, and unmeasured third variable
confounds could have influenced the results. The power of the
study, based on about eight repeated measurements of 65 patients
(minus some missing data), may be too low to detect some withinperson relationships. We studied process on a weekly time scale,
and larger or lesser scales could be associated with different
results. The strategy of using the same therapists across therapies
has both strengths and weaknesses. The therapists may not be
equally competent and have the same preferences for both therapies. Actually, one of the therapists reported a preference for IR.
However, this bias could not explain the present results, as PTSD
symptoms measured weekly were less reduced over the course of
therapy in IR than in IE. In the context of the present study, an
advantage of crossing therapists was that the general ability to
form alliances was balanced between conditions.
Research Implications
As elaborated above, our study invites an increased focus on
within-person relationships in psychotherapy research. In highly
structured therapies like those of the present study and cognitive
therapy of depression (Webb et al., 2011), symptomatic improvement is supposed to result from the relatively specific tasks of
these therapies. Agreement about tasks may therefore be particularly important in such therapies. Moreover, the studied PTSD
sample was a severe one with a high degree of comorbidity and a
long duration of PTSD, and over half of the patients had experienced repeated and/or prolonged traumas. Future studies should
investigate the within-person relationships between alliance components and outcome across therapies and type and severity of
disorders. Furthermore, studies of within-person relationships between therapy events/therapist actions and alliance components are
needed.
Clinical Implications
The present within-person results make a firm basis for the
recommendation to monitor, increase, and restore decreases of
agreement about therapy tasks over the course of IE or IR within
prolonged exposure for PTSD patients. They also suggest that
addressing agreement about the tasks of therapy is particularly
important in IE compared to IR. Given that these exposure methods consist of confronting the feared trauma memory and feared
external situations, agreeing to their use based on an understanding
of the rationale for these methods and a belief in their efficacy
seems paramount. On the other hand, the results do not imply an
increased focus on the agreement about goals of therapy and bond
components of alliance over the course of these treatments. Our
between-person results may inform therapists using prolonged
exposure for PTSD that low initial task agreement and bond signal
a poorer outcome of therapy. Unfortunately, because the crosslevel interaction between interindividual and within-individual
task agreement was contrary to our hypothesis, clinical implications cannot be drawn from this finding.
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(Appendix follows)
13. HOFFART, ØKTEDALEN, LANGKAAS, AND WAMPOLD
12
Appendix
Equations Used in the Statistical Analyses
1i ϭ ␥10 ϩ u1i
Equations for the Multilevel Models
We begin with the Level 1 model:
yti ϭ 0i ϩ 1i x ti ϩ eti
u0i ϭ (zi Ϫ ␥00) Ϫ (␥10 ϩ u1i)xi
(A1)
Composite:
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eti ϭ zti Ϫ 0i Ϫ 1i x ti .
Ei(zti) ϭ (␥00 ϩ u0i) ϩ ␥10Ei(x ti) ϩ Ei(u1i x 0i)
Here the individual-specific value of posttraumatic stress disorder (PTSD) symptoms (yti) is a function of an individual intercept
(0i), the slope coefficient of the time score for time t for individual i (1i xti), and the residual symptoms of PTDS (eti) on time t for
individual i. The equation term eti is computed by deviating the
time-specific predictor (zti) from the regression line (1i xti) estimated separately (case by case) for each individual in the sample.
The deviated measure, eti, is then the residual (i.e., the observed
score minus expected value) from the regression of the timevarying predictor on time computed separately for each individual
case, which then represents the variable for the within-person level
of each predictor (i.e., Task, Goal, or Bond).
The Level 2 between-person predictor represents variance due
to interindividual differences in the time-varying predictor at the
start of treatment, as shown in Equation A2:
ϭ(␥00 ϩ u0i) ϩ (␥10 ϩ u1i)Ei(x ti).
zbi ϭ 1i x 0i .
In the Level 2 model, zbi is the between-person component
of the time-varying predictor and is a function of individual
differences in the time-varying predictor at the start of treatment (1i x0i).
The equations for the model with main effects of the betweenperson and within-person predictors are presented in Equation A3:
Level 1:
eti ϭ (zti Ϫ zi) Ϫ (␥10 ϩ u1i)(x ti Ϫ x i)
Level 2:
0i ϭ ␥00 ϩ u0i
Equations for Proportion Reduction of
Error at Each Level
The proportion reduction of error for predicting the Level 1
outcome is
(A2)
R
zti ϭ 0i ϩ 1i x ti ϩ eti
In the Level 1 model, the individual-specific value of symptoms
of PTSD (yti) is a function of an individual intercept (0i), the
within-person effects of the time-varying predictor (1i xti), and
the residual PTSD symptoms (eti) on time t for individual i. In the
Level 2 model, the individual intercept (0i) is a function of a fixed
intercept (␥00) and an individual-specific random intercept (u0i).
The individual effects of slope (1i) is a function of the fixed
effects in rate of change (␥10) and person-specific slope (u1i).
(A3)
R2 ϭ 1 –
L1
ͩ
residual variance more ϩ intercept variance more
residual variance fewer ϩ intercept variance fewer
ͪ
.
The proportion reduction of error for predicting the Level 2
outcome is
R2 ϭ 1 –
L2
residual variance more
#Level 1 units
residual variance fewer
#Level 1 units
ϩ intercept variance more
ϩ intercept variance fewer
.
Received January 9, 2013
Revision received May 13, 2013
Accepted May 13, 2013 Ⅲ