How to Analyze Interpersonal and Individual Effects in Peer-Tutored Reading Intervention

Abstract

Reading strategy interventions relying upon peer tutoring are a common way to foster poor readers' comprehension skills. Those interventions are based on the assumption that tutees benefit from the (higher) reading skills of their tutors. However, this interpersonal effect has not yet been tested explicitly because the effectiveness of peer tutoring is commonly analyzed separately for tutees and tutors or with aggregated data. The present study illustrates how interpersonal and individual effects of a peer-tutored reading strategy intervention can be estimated using dyads as units of analysis in structural equation modeling. To demonstrate the application of the model, data from an experimental intervention study comparing the effects of a peer-tutored reading strategy training and a control condition in Grade 4 (N = 68 dyads) were analyzed.

Keywords:

• Actor-Partner Interdependence Model
• dyadic data analysis
• peer tutoring
• primary school
• reading strategy intervention

ONE PROMISING METHOD for fostering struggling readers' comprehension skills is to train the readers to apply reading strategies (e.g., Guthrie et al., 2004; National Reading Panel, NICHD, 2000; Palincsar & Brown, 1984). Since Fuchs and colleagues developed and evaluated their manual for peer-assisted learning strategies in reading (Fuchs, Fuchs, Mathes, & Simmons, 1997), types of reading training using peer learning gained popularity in the field. Despite the fact that peer-tutored reading interventions are widely used, little is known about one crucial aspect for their effectiveness: To what extent does the success of peer-tutored reading interventions on the individual level depend on the composition of the tutor-tutee dyad? Common methods to evaluate the effectiveness of peer-tutored reading interventions are the analysis of the training outcomes separately for the two members of the dyad or the analysis of the aggregated effects for tutees and tutors, treating them as completely independent. However, the reading ability scores of the dyad members are likely to be linked because of the interdependence that is created by the peer-tutored learning setting. Thus, the independence of observations that form the endogenous variable, as assumed in commonly used statistical models, is violated, leading to biased estimations of the parameters (Cook & Kenny, 2005). Moreover, the underlying assumptions of peer-tutored reading training are that tutors act as models for their tutees and that tutees benefit from the reading skills of their tutors (Topping, 1987). These assumptions cannot be tested by analyzing the treatment outcomes separately for tutees and tutors or with aggregated data. Thus, the interpersonal effects taking place within the dyads—that is, whether and how the treatment outcome of the tutees is affected by the tutors' reading abilities and how the treatment outcome of the tutors is affected by the tutees' reading abilities—remains obscure. In this paper, we tackle the issue of interpersonal effects directly by using the Actor-Partner Interdependence Model (APIM, Kenny, 1996), a type of structural equation model specifically designed to analyze interdependence in dyadic data. To give an example of how to use the APIM in educational intervention studies, the model was applied to data from an experimental intervention study that assessed the effectiveness of a peer-tutored reading strategy intervention in Grade 4.

In the following sections, we briefly explain how reading strategies and peer-tutoring can help struggling readers in primary school and give an overview of how data from peer-tutored reading studies are commonly analyzed. Finally, we describe the APIM and its application to the dyadic data structure of peer-tutored interventions in more detail. This model represents the framework for the hypotheses tested in the study used as an example.

Peer-Tutored Learning in the Field of Reading Strategy Intervention

Since the 1980s, broad evidence has accumulated that strategy-oriented reading instructions are a powerful approach to foster reading comprehension (e.g., Dole, Duffy, Roehler, & Pearson, 1991; Pressley, Johnson, Symons, McGoldrick, & Kurita, 1989). In the first studies on the issue, a major goal was to identify effective reading strategies (see Pressley, 2000, for an overview). This research indicates that specific cognitive strategies such as summarizing (e.g., Dole et al., 1991), generating questions (e.g., Yuill & Oakhill, 1988), and activating prior knowledge (e.g., Cain & Oakhill, 1999) can enhance reading comprehension skills in primary school. In later studies, the focus switched to how to combine multiple strategies within comprehension instructions (Pressley, 2000). In the context of this research, several reading strategy programs have been developed and broadly evaluated—for instance, the small-group training reciprocal teaching (Palincsar & Brown, 1984; Rosenshine & Meister, 1994) and the concept-oriented reading instruction program (CORI, Guthrie et al., 2004).

The effectiveness of reading strategy treatments teaching strategies, isolated or in combination, is empirically well established by meta-analytic results (e.g., effect size d =.58, synthesis of nine meta-analyses summarizing evaluations of reading comprehension programs [Hattie, 2009, p. 136]). Providing the theoretical foundation for reading strategy instruction are cognitive models of reading comprehension positing that reading comprehension is based on the construction of a coherent situation model from the text content (Van Dijk & Kintsch, 1983) by identifying and linking the main text ideas and making inferences using prior knowledge (Graesser, Singer, & Trabasso, 1994). Skilled readers possess a broad repertoire of cognitive reading strategies that they use flexibly to organize and to enrich the information given in a text to construct a local and global coherent representation of the text content. Poor comprehenders, however, have difficulties in the spontaneous production of text-connecting and gap-filling inferences that require inferring information beyond the text (Cain & Oakhill, 1999). In addition, children with poor comprehension skills experience difficulties in using metacognitive strategies to monitor comprehension breakdowns, especially inconsistencies within a text and with their prior knowledge (Baker & Zimlin, 1989). The abilities to draw inferences and to self-monitor their comprehension contribute unique variance of reading comprehension skills in 7- to 11-year-old children, even after controlling for effects of decoding skills, verbal intelligence, vocabulary knowledge, and working memory capacity (Cain, Oakhill, & Bryant, 2004). Thus, conveying knowledge about reading strategies and giving children ample opportunity to practice the application of these strategies seems promising to foster text comprehension in self-regulated reading activities (Pressley et al., 1989).

Multiple reading strategies are often taught in peer-assisted learning arrangements, which have proven to be generally effective as a method of instruction (d =.55, synthesis of 14 meta-analyses of peer-tutoring learning [Hattie, 2009, p. 186]). In primary school, the effectiveness of peer tutoring has been demonstrated for the acquisition of knowledge in various academic domains (d =.26, meta-analysis of 26 studies that used classwide peer-assisted learning, Rohrbeck, Ginsburg-Block, Fantuzzo, & Miller, 2003). Peer tutoring is a structured learning process taking place in dyads of peers with well-defined interaction rules and a focus on curriculum content. Each dyad member assumes a specific role: Most often, the higher-skilled student is the tutor and the lower-skilled student is the tutee (Topping, 1987, 2005). A general theoretical perspective on peer-tutored interaction in heterogeneous dyads is Vygotsky's (1978) theory of social-mediated learning. According to Vygotsky, learning occurs in interaction with a more knowledgeable person who offers support in the zone of proximal development. Dyadic interaction in peer-tutored reading strategy trainings leads to the joint construction of text meaning by application of the reading strategies. The tutors for their part support the tutees in using the strategies and provide a cognitive model for their dyad members. Their tasks include detecting, correcting, or otherwise managing their tutees' errors (Topping, 2005). As a consequence, tutors need to restructure their own comprehension and to validate and clarify their explanations (Van Keer & Verhaeghe, 2005). The tutees become more and more familiar in using the strategies, internalize them, and practice to use them flexibly. Moreover, working in a dyad provides opportunities for individualized practice and mentoring (Greenwood, 1991) and it fosters the students' autonomy and elicits their motivation (Rohrbeck et al., 2003).

The most popular reading treatment using peer tutoring to increase strategic reading comprehension is PALS (peer-assisted learning strategies, Fuchs et al., 1997), a classwide program with students working in dyads with reciprocal roles as tutors and tutees. The effectiveness of PALS for improving reading comprehension has repeatedly been demonstrated for students from Grades 2 to 6, for children with learning disabilities, and children with below-average and average reading skills (Fuchs et al., 1997; for an overview see Fuchs & Fuchs, 2007). In addition to the work of Fuchs and colleagues, several studies investigated peer-assisted learning as an instructional technique to teach reading strategies to primary school students (e.g., Greenwood, 1991; Greenwood, Delquadri, & Hall, 1989; Spörer, Brunstein, & Kieschke, 2009; Van Keer & Verhaeghe, 2005; Van Keer & Vanderlinde, 2010). Overall, these studies showed that students learning reading strategies by peer-assisted learning outperformed the control students who received traditional teacher-centered reading instruction.

Interdependence in Peer-Assisted Learning Settings

Despite broad evidence for the usefulness of peer-tutored reading interventions, research has more or less ignored one crucial aspect of the method: the extent to which the effectiveness of peer-tutored reading interventions depends on the composition of the dyad. The effectiveness of peer tutoring is commonly analyzed separately for tutees and tutors (e.g., Cohen, Kulik, & Kulik, 1982; Mathes, Torgesen, & Allor, 2001; Topping, 1987; Van Keer & Verhaeghe, 2005) or with aggregated data (Fuchs et al., 1997; Van Keer & Vanderlinde, 2010). However, this procedure is problematic for two reasons: Matching peers in dyads usually occurs based on their reading abilities before the intervention by combining the best reader above the class average with the best reader below the average, the second best above-average reader with the second best below-average reader and so forth (cf. Fuchs et al., 1997). Furthermore, the tutees' learning outcome might be affected by the abilities of his or her tutor because the tutor is acting as a model in the zone of proximal development. Hence, peer tutoring yields nonindependent data of tutors and tutees working together in dyads as distinguishable members (Kenny, Kashy, & Cook, 2006, chap. 1). As a consequence, the assumption of independence of observations, which is crucial for typical linear models, is violated (Cook & Kenny, 2005). Another critical aspect concerns the underlying assumptions of peer tutoring. By analyzing the treatment outcomes separately for tutees and tutors or with aggregated data it cannot be tested explicitly whether and to what extent the tutors' reading skills influenced the tutees' reading comprehension after the peer-tutored treatment and whether and if so to what extent reciprocal effects occurred.

Accounting for Dyadic Interdependence with the Actor-Partner Interdependence Model

The purpose of the present study was to demonstrate how the Actor-Partner Interdependence Model (APIM, Kenny, 1996), a type of structural equation model that controls for dyadic interdependence, can be applied fruitfully to analyzing the effects of peer-tutored reading interventions. Most previous applications of the APIM focused on investigating interdependence in interpersonal relationships (e.g., close partnerships; for an overview see Cook & Kenny, 2005). We would like to argue that the model can also be used to analyze the interdependence of tutors and tutees that arises in peer-tutored learning settings provided that a pre-/posttest design is used to assess the effectiveness of an intervention. To this end, data from a peer-tutored reading strategy intervention in same-age groups in Grade 4 were used to examine interpersonal and individual effects on reading comprehension. The effects within this reading strategy training were compared to those within a control treatment of the visuospatial working memory. Both treatments were implemented in a peer-tutored learning setting with dyads comprising a poor reader (tutee) and a good reader (tutor).

In the APIM, effects of both dyad members are assessed simultaneously by estimating interpersonal effects (partner effects) and individual effects (actor effects) within one single structural equation model (see Figure 1). The model is based on dyads as units of analysis; that is, tutees and tutors are treated as nested within dyads. Hence, two outcome variables are generated: the posttest reading comprehension scores of tutees and tutors. The pretest reading comprehension scores of tutees and tutors measured with the same instrument serve as two correlated exogenous variables. The residual variables of the outcomes are also correlated, indicating that the nonindependence of the outcomes may be (in part) due to other variables not captured by the exogenous variables (Cook & Kenny, 2005). These features of the APIM provide a powerful method to investigate different facets of peer-tutored reading intervention effectiveness.

Figure 1 The Actor-Partner Interdependence Model (APIM) Note. pre = reading comprehension at pretest; post = reading comprehension at posttest; the triangle indicates the intercept; e = residual variables; single-headed arrows indicate the direction of the effects; double-headed arrows indicate correlations.

In particular, three types of effects can be estimated and tested. First, the partner effects indicate the average influence of the tutors on the tutees as well as the average influence of the tutees on the tutors. These effects are of special interest in the field of peer tutoring as working together in heterogeneous dyads is based on the assumption that the poor readers benefit from the (higher) reading skills of their tutors. The APIM offers the opportunity to test this assumption explicitly. Second, the actor effects can be used to assess the average stability of reading skills from the pre- to the posttest for each dyad member. Actor effects can give a first indication to the effectiveness of an intervention since reading skills are assumed to be altered by a treatment instead of remaining stable. Third, a comparison of the intercepts of the models in the treatment and the control group (or in several treatment groups) can be used to assess average treatment effects on the posttest reading comprehension. Provided that the pretest scores are centered around the mean of tutors and tutees, the intercepts represent group means of the outcome variable—that is, estimates of the mean outcome of the reading intervention for tutees and tutors while controlling for actor and partner effects (for a thorough discussion of centering options on the interpretation of intercepts in clustered data, see Kreft & DeLeuw, 1998). To analyze the effectiveness of a reading intervention compared to a control group, the expected mean posttest reading comprehension in the training group (i.e., the intercept in this group) can be compared to the expected mean outcome of the control training (i.e., the intercept in that group).

In the present study, we tested three research questions and associated hypotheses (Table 1) to illustrate the most important analytical possibilities that the APIM offers for research on peer-tutored reading interventions:

1. Does the tutor's reading comprehension score at the pretest predict the tutee's reading comprehension after the treatment? While learning in dyads, communication about the text content occurs according to the reading strategies used. Tutors monitor tutees' remarks, and they modify and support tutees' strategy use (Palincsar & Brown, 1984). For this reason, we expected a positive partner effect within the reading strategy group from the tutors' reading comprehension skill at pretest to the tutees' score according to the posttest. In contrast, no partner effects should be observed within the control group that involved no reading activities and, thus, no opportunity for the tutors' reading comprehension ability to influence the tutees' reading comprehension.

   Table 1 Explanation of the Effects of the APIM and the Tested Hypotheses

   Type of effects		Coefficient	Explanation	Hypotheses
   Interpersonal effects	partner effecttutee-tutor	p12	influence of the tutees' pretest reading skill on the tutors' posttest reading skill	no effect expected
   	partner effecttutor-tutee	p21	influence of the tutors' pretest reading skill on the tutees' posttest reading skill	positive effect in strategy group, no effect in control group
   Individual effects	actor effecttutee	a1	stability of the tutees' reading skill from pre- to posttest	strategy group < control group
   	actor effecttutor	a2	stability of the tutors' reading skill from pre- to posttest	strategy group < control group
   	treatment effecttutee	c1 − c1	difference between the tutees' mean posttest reading skill of the reading strategy group and of the control group	strategy group > control group
   	treatment effecttutor	c2 − c2	difference between the tutors' mean posttest reading skill of the reading strategy group and of the control group	strategy group > control group

2. To what extent does the reading comprehension skill at the pretest predict the reading comprehension after the intervention? The reading strategy training may be expected to foster reading comprehension for poor as well as good readers (Van Keer & Verhaeghe, 2005) but probably more strongly for poor than for good readers. In other words, it is supposed to exert a compensatory effect. Therefore, the stability of individual differences in reading comprehension skills (i.e., the actor effects for tutees and tutors) should be lower in the group that received the reading strategy training than in the control group.

3. Are there any differences between the reading strategy group and the control group in the reading comprehension scores after the interventions? Against the background of positive evidence for reading strategy treatments for tutees but also for tutors (e.g., Cohen, Kulik, & Kulik, 1982; Fuchs & Fuchs, 2007; Rohrbeck et al., 2003; Topping, Peter, Stephen, & Whale, 2004), we expected the tutees in the reading strategy group to reach higher comprehension scores (i.e., a higher intercept) than the tutees in the control group after the treatment. Tutors should reveal the same effect.

METHOD

Participants, Procedure, and Design

The data were collected as part of a longitudinal study investigating the effects of several kinds of reading interventions in primary school. The 172 fourth-graders originally taking part in this experimental pre-/posttest study were from 15 schools located in the urban areas of Giessen and Kassel (Germany). Socioeconomic status was measured as the highest level of professional qualification of the participant's parents and compared with the International Classification of Standard Education (ISCED, UNESCO, 2012). In total, 133 parents provided information on their professional qualifications. One participant's parents reported no school-leaving qualification (ISCED-level 0, 0.75% of all parents who provided information), 38 parents reported having finished basic education after Grade 9 or 10 (ISCED-level 1 and 2, 28.57%), 55 parents reported having finished upper secondary education or having received a degree from a vocational school (ISCED-level 3 and 4, 41.35%), and 39 parents reported having received an academic degree (ISCED-level 5 to 8, 29.32%). The distribution of the parents' qualification levels in our sample roughly corresponds to the distribution of parental education in Germany as documented in the International Reading Literacy Study (PIRLS, Mullis, Martin, Kennedy, & Foy, 2007) with a slight overrepresentation of higher levels of education (ISCED-level 3 and above).

The participants were selected according to their results in a standardized reading comprehension test (ELFE 1–6, Lenhard & Schneider, 2006). From each class, the five children with the lowest reading comprehension scores (all of them below the class average) were chosen as tutees and the five children with the highest reading comprehension scores (all of them above the class average) were chosen as tutors. The average z-standardized reading comprehension scores of the classes varied between −0.73 and 0.50 (M = −0.09, SD = 0.36). In order to achieve equal differences between tutees and tutors within the dyads, we combined the best reader of the five students above the average with the best reader of the five below the average, the second best reader of the five above the average with the second best reader of the five below the average, and we repeated this pattern for the remaining three dyads. The five dyads per class were randomly allocated at the class level to either the reading strategy group (35 dyads) or the control group (51 dyads). Due to the overhang of the control group we were able to match the dyads assigned to intervention group versus control group for the analysis according to gender, first language, reading comprehension score of the tutees at the pretest, and difference between tutors and tutees’ pretest scores. One dyad of the reading strategy group was evaluated as an outlier and thus excluded, because the pretest reading comprehension score of the tutee was three standard deviations above the mean of the tutees.

As a result, the data of 68 dyads (34 reading strategy, 34 controls) from 14 schools were included in the analysis (68 tutees, 33 female, and 68 tutors, 34 female). According to their parents, 18 of the 68 tutees had learned another language than German as their first language and 32 were native speakers of German (for the remaining 18 tutees, first language information was missing). Among the 68 tutors, there were 16 non-native speakers and 35 native speakers of German (for 17 tutors, first language information was missing).

Interventions

All materials and manuals for both treatments were designed by the authors and tested in a preliminary study. The training consisted of 25 sessions each, occurring in addition to regular school lessons twice a week and lasting 45 minutes. The training sessions were conducted by university students who provided standardized instructions. Special feedback rules were also given to the tutors to standardize the communication within the dyad.

Reading Strategy Training

The reading strategy treatment conveyed knowledge about three cognitive strategies, which were implemented through the reading of two books.

1. Questioning the headline to activate prior knowledge about vocabulary and the previous events occurring in the book. Thus, before starting to read the chapter the tutees read the headline solely and think aloud afterwards what they already know about the words in the heading. Furthermore they should anticipate what might happen in the chapter. This should increase the likelihood of a deep comprehension, because the incoming information of the text can be connected with the activated prior knowledge in the situation model (Cain & Oakhill, 1999; Kendeou, Van den Broek, White, & Lynch, 2007).

2. Repeated reading and rehearsing of the content of each sentence to foster local coherence processes and to keep the information communicated by a sentence available for further processing. The working memory capacity of poor readers is often bound by visual word recognition processes (Perfetti, 1985). Repeated reading and rehearsing of sentences should increase the likelihood of extracting the semantic structure of the sentence (propositional text base), which may be regarded as the basis for deep comprehension (the construction of a situation model, Kintsch, 1988). Therefore, repeated reading (Samuels, 1979) was adapted to reading phrase by phrase repeatedly. A phrase structure was inserted using spaces between subsequent phrases (cf. O'Shea & Sindelar, 1983).

3. Summarizing the chapter. After reading a chapter, the tutee summarizes whom and what the chapter concerned. Such a strategy should encourage the construction of a globally coherent representation of the text (cf. the constructionist model, Graesser et al., 1994). This representation can then be used for making predictions about the contents of the upcoming chapter and facilitates application of the first strategy.

The three strategies were introduced one by one during the first three sessions of the intervention by the student assistant. Students were encouraged to use and practice all three strategies starting with the fourth session. It was the tutors' task to keep these strategies in mind and support their tutees in using them by asking questions. Difficult words were explained at the beginning to eliminate vocabulary problems as a source of comprehension problems. Similar to previous implementations of different kinds of strategy training (e.g., Gold, Mokhlesgerami, Rühl, Schreblowski, & Souvignier, 2004; Paris, Cross, & Lipson, 1984), the training was embedded in a detective story.

Control Group

The control group received a training of visuospatial working memory. According to Baddeley (1986), the visual-spatial working memory is not of central importance for reading comprehension. Thus, we did not expect any beneficial effect of this training on the reading skills of the participants. Labyrinths and abstract forms were used to teach four strategies to memorize and recall spatial arrangements. All instructions were given verbally by the student assistants. As in the reading strategy training, all exercises were realized in dyads of peers with the less-skilled reader as tutee, who applied the strategies while working on the material, and the higher-skilled reader as tutor, who supervised the tutees' strategy use.

Measurement of Reading Comprehension Skill

Reading comprehension skill on the text level was assessed with the subtest text comprehension of ELFE 1–6 (computer version, Lenhard & Schneider, 2006), a standardized reading comprehension test widely used in Germany. The test consists of 20 short, mostly narrative texts with four multiple choice items each that require identifying information in the text, generating anaphoric references across sentences, and creating local and global inferences. The test score is the sum of correct responses. The same test was used for pre- and posttesting, with the test texts presented in randomized order. The test-retest reliability was 0.81 (considered within the control group).

Data Analysis

Multiple-group structural equation modeling (SEM) was used to estimate and test an APIM with two groups (training group vs. control group). All analyses were conducted with the R system for statistical computing (R Core Team, 2013) and the R package lavaan (Rosseel, 2012). As was expected, given the way the dyads were composed, the reading comprehension skills of tutors and tutees in the same dyads were nonindependent (Pearson product-moment correlation between reading comprehension of tutors and tutees at pretest: r =.42, p <.001; cf. Cook & Kenny, 2005), indicating the need to control for the nonindependence with an appropriate statistical model. The SEMs for the two groups were estimated as saturated models with four manifest variables per treatment condition: the ELFE-scores at pretest as two exogenous variables and the ELFE-scores at posttest as two endogenous variables (see the Appendix for the full statistical model and the R code).

To address research question 1, the average partner effects from tutors to tutees and from tutees to tutors were estimated within each treatment condition (cf. Kenny et al., 2006, chap. 13). The same effects were tested against each other by fixing the partner effects in the two groups to equal values and comparing the chi-square goodness-of-fit values of the constrained versus the unconstrained model. Similarly, with regard to research question 2, the average actor effects for tutees and tutors were estimated for the reading strategy training group and the control group and were tested against each other. To analyze the effectiveness of the reading strategy training compared to the control group (research question 3), we compared the expected mean posttest reading comprehension (controlling for actor and partner effects) of the reading strategy training versus the control training. Those treatment effects were analyzed separately for tutees and tutors. Consequently, differences between the two intercepts of the treatment conditions were tested for the tutees and for the tutors. To facilitate the interpretation of the intercepts, the raw ELFE-scores of the pretest were group-mean centered for tutees and tutors, respectively. As a consequence, the intercepts represent estimates of the training effects for tutees with average reading comprehension abilities and average skilled tutors.

RESULTS

Correlations within the total sample and separated by treatment condition, means, and standard deviations are summarized in Table 2.

Table 2 Summary of Intercorrelations, Means, and Standard Deviations of the Exogenous and Endogenous Variables Within Total Sample and Per Treatment Condition Separated by Dyad Members (Tutees vs. Tutors)

	Correlations							Means and standard deviations
	Total sample			Per treatment condition (reading strategy above, control group below main diagonal)				Total sample		Reading strategy		Control group
	1	2	3	1	2	3	4	M	SD	M	SD	M	SD
Tutees
1 ELFEpre					0.41*	0.58***	0.26	6.13	2.07	5.97	2.28	6.29	1.85
2 ELFEpost	0.31**			0.25		0.46**	0.29	8.35	3.17	8.85	3.14	7.85	3.16
Tutors
3 ELFEpre	0.42***	0.18		0.23^†	−0.13		0.69***	15.25	3.39	15.50	3.50	15.00	3.30
4 ELFEpost	0.20°	0.20°	0.60***	0.10	0.14	0.49**		16.12	3.45	15.85	4.01	16.38	2.83

Note. ELFE = subtest text comprehension (sum of correct answers, min = 0, max = 20).^†p <.20, °p <.10, *p <.05, **p <.01, ***p <.001 (two-tailed, liberal significance criterion for the test of nonindependence between dyad members (α =.20), as recommended by Cook & Kenny, 2005).

Partner Effects

First, we examined whether the pretest reading comprehension of tutees and tutors predict each other's reading comprehension score after the interventions. Consistent with our expectation, there was just one positive and significant average partner effect: from tutor to tutee within the reading strategy group (p₁₂, see Table 3 for the parameter estimates). The unconstrained model reached a better fit than a model with equal partner effects in both groups, (Δχ² (1, n = 68) = 4.41 and p <.05, see Table 4 for the parameter estimates) indicating that the partner effect in the strategy intervention group was greater than the effect in the control group. The estimated effect size for the partner effect is 0.40 (estimated as adjusted d; cf. Kenny et al., 2006, chap. 7). Thus, the pretest reading comprehension score of the tutors had a significant effect on the tutees' level of reading comprehension after the training, demonstrating that the tutees could benefit from their tutors' reading skills while implementing reading strategies.

Table 3 Estimates for the Saturated APIMs per Treatment Condition (Reading Strategy Training vs. Control Group, Unstandardized Regression Coefficients)

	Saturated models
	Reading strategy group			Control group
Effects	Estimate	SE	Z	Estimate	SE	Z
Tutees
Intercept c1	8.82	0.47	18.84***	7.73	0.51	15.07***
Actor effect a1	0.29	0.25	1.14	0.50	0.29	1.73*
Partner effect p12
tutor→tutee	0.31	0.17	1.86*	−0.19	0.16	−1.16
Tutors
Intercept c2	15.56	0.48	32.34***	16.49	0.42	39.32***
Actor effect a2	0.94	0.17	5.53***	0.43	0.13	3.24**
Partner effect p21
tutee→tutor	−0.38	0.26	−1.48	−0.02	0.23	−0.09

Note. Y = reading comprehension score measured with ELFE; 1 = tutees, 2 = tutors; arrows indicate the direction of the effects.*p <.05, **p <.01, ***p <.001 (one-tailed).

Table 4 Estimates for the Constrained APIMs per Treatment Condition (Reading Strategy Training vs. Control Group, Unstandardized Regression Coefficients)

	Constrained models (equal partner effects tutor-tutee)						Constrained models (equal actor effects tutees)						Constrained models (equal actor effects tutors)
	Reading strategy group			Control Group			Reading strategy group			Control group			Reading strategy group			Control group
Effects	Estimate	SE	Z	Estimate	SE	Z	Estimate	SE	Z	Estimate	SE	Z	Estimate	SE	Z	Estimate	SE	Z
Tutees
Intercept c1	8.92	0.48	18.51***	7.80	0.53	14.78***	8.85	0.47	18.93***	7.75	0.51	15.12***	8.82	0.47	18.84***	7.74	0.51	15.07***
Actor effect a1	0.51	0.24	2.16*	0.40	0.29	1.37	0.38	0.19	1.99*	0.38	0.19	1.99*	0.29	0.25	1.14	0.47	0.29	1.65*
Partner effect p12
tutor→tutee	0.05	0.12	0.45	0.05	0.12	0.45	0.27	0.15	1.78*	−0.17	0.16	−1.08	0.31	0.17	1.86*	−0.13	0.16	−0.82
Tutors
Intercept c2	15.56	0.48	32.34***	16.51	0.42	39.28***	15.56	0.48	32.34***	16.5	0.42	39.39***	15.69	0.50	31.17***	16.55	0.43	38.41***
Actor effect a2	0.94	0.17	5.53***	0.47	0.13	3.65***	0.94	0.17	5.53***	0.43	0.13	3.26***	0.61	0.11	5.68***	0.61	0.11	5.68***
Partner effect p21
tutee→tutor	−0.39	0.26	−1.48	−0.04	0.23	−0.17	−0.39	0.26	−1.48	−0.04	0.23	−0.19	−0.1	0.24	−0.39	−0.1	0.24	−0.41

Note. Y = reading comprehension score measured with ELFE; 1 = tutees, 2 = tutors; arrows indicate the direction of the effects.*p <.05, **p <.01, ***p <.001 (one-tailed).

Actor Effects

Second, we examined whether the pretest reading comprehension score of dyad members predict their comprehension score after the treatment by testing the average actor effects. For the tutees (a₁), only the actor effect within the control group became positive and significant (effect size d = 0.44). However, constraining the actor effects of the tutees to be equal in both treatment conditions failed to result in a worse model fit compared to the unconstrained model (Δχ² (1, n = 68) = 0.29 and p =.59), suggesting that no differences exist between the two conditions. For the tutors (a₂), the actor effects were positive and significant in both treatment conditions with an estimated effect size of 0.69 in the reading strategy group and an effect size of 0.60 in the control group. Thus, unexpectedly, the reading comprehension skills of the good readers remained stable over the course of the study. This effect was even larger in the reading strategy group (Δχ² (1, n = 68) = 5.43 and p <.01), compared to the control group.

Average Treatment Effects

The effectiveness of the reading strategy training compared to the control group was estimated separately for tutees and tutors by testing the differences between the intercepts (i.e., the mean reading comprehension levels per treatment condition according to the posttest). Within the group of tutees, the treatment effect failed to reach statistical significance marginally (B = 1.10, SE =.69, Z = 1.58, p =.057, one-tailed). However, the positive estimate and the effect size (d =.32, estimated with pooled posttest standard deviations) give a hint that poor readers in the reading strategy group tended to reach higher comprehension scores than the control group after the treatment.

In addition, the mean comprehension score of the tutors taking part in the reading strategy training did not differ from those participating in the control treatment (B = −0.93, SE =.64, Z = −1.46, ns, one-tailed).

DISCUSSION

The aim of this study was to demonstrate how the Actor-Partner Interdependence Model (APIM) can be used to analyze interpersonal and individual effects in peer-tutored reading interventions controlled for the interdependence that arises in peer-tutored learning settings. In the APIM, the effects of both dyad members can be assessed simultaneously within one structural equation model. This offers the opportunity to explicitly test the assumption that the tutees' reading comprehension after the treatment is affected by the tutors' reading abilities. The APIM was applied to data from an experimental intervention study that assessed the effects of a peer-tutored reading strategy intervention by comparing this intervention to a control condition. In this study, fourth-graders with reading skills below the class average (tutees) and above the class average (tutors) were paired and matched between the two treatment conditions. A multigroup APIM was estimated with the dyads as the units of analysis.

In line with the assumption that tutors act as models for their tutees, a significant partner effect within the strategy group from the tutors' pretest reading comprehension score to the tutees' reading comprehension after the intervention occurred. Thus, the tutees benefited from the reading comprehension skills that their tutors brought into the dyad, indicating that the collaboration within the dyad seems to help the tutees to implement the strategies effectively (see also Van Keer & Verhaeghe, 2005). Although the average treatment effect for the tutees marginally failed to reach statistical significance, the positive estimate and the effect size hints at the effectiveness of the reading strategy training in order to reach this goal. The mean reading comprehension of the tutees after the treatment, controlled for actor and partner effects, was higher in the strategy group than in the control condition. Thus, consistent with previous research, poor readers could apparently improve their reading comprehension skills after attending a reading strategy treatment. The prompting of inferences by questions while reading is more effective in producing a coherent text representation than questioning after reading, as discussed by McMaster et al. (2012). Therefore, it might be informative to examine whether the treatment effect for the tutees could be increased by implementing prompts of formative questioning and summarizing in the reading process.

Our study yielded no evidence for the assumption that the tutors could improve their reading comprehension after the strategy intervention. This result is consistent with the additional finding that the tutors' actor effects indicate stable comprehension skills in both treatment conditions. Possibly, the strategy intervention offered too little learning opportunities for students with above-average reading comprehension skills given that all exercises were conceptualized to be managed for the tutors within their zone of actual development. Moreover, tutors monitored their peers' text comprehension and gave feedback while they also read the text for comprehension, which is likely to have been a novel and challenging task associated with cognitive costs. Contrary to the tutees, the tutors received no support during the training. The reading strategy intervention might have been more fruitful for them if they had received previous tutor training (e.g., Bentz & Fuchs, 1996; Van Keer & Verhaeghe, 2005) as opposed to simply introducing the reading strategies in the peer-learning setting of the present study. As a consequence, the tutors had the sole responsibility for providing the training from the start. One way to support the tutors would be to divide the intervention into three phases: (1) a whole-group modeling of the strategies (cf. Rosenshine & Meister, 1994), (2) an instruction involving how to deal with the strategies by working in dyads, and (3) peer-tutored practicing of the strategies (cf. Spörer, Brunstein, & Kieschke, 2009). This stepwise procedure would possibly increase the treatment effect for the tutees as well. As Connor, Morrison, and Petrella (2004) showed, third-graders with below-average reading skills achieved a lower level of comprehension gain from peer-assisted reading instructions than from teacher-led instruction (see Van Keer & Verhaeghe, 2005, for similar results). In the same vein, Webb and Palincsar (1996) suggest that learning a new strategy might be perhaps best attained by working with an adult, while learning how to apply an already known strategy to new material works best with peers.

The analyses presented here only illustrate the application of the basic version of the APIM. However, typical research questions might involve additional variables—for example, moderating variables that can account for differential effects of the reading strategy intervention such as gender or first language (for relevant moderator variables in peer-assisted learning, see Rohrbeck et al., 2003). Basic reading skills on the word level are likely candidates as well, because these processes must be routinized to a certain degree to release the cognitive resources that are needed to effectively implement reading strategies (e.g., Perfetti, 1985; Richter, Isberner, Naumann, & Neeb, 2013). Such potential moderating variables can be added to the APIM either as actor or as partner effects (cf. Cook & Kenny, 2005). In addition, interaction effects (nonadditive, combined effects of the exogenous variables) can be tested. For instance, it might be of importance whether the partner effect occurs in all possible combinations of tutees and tutors. In our study, the differences between the pretest reading comprehension scores of the tutees and tutors were kept roughly the same to realize Vygotsky's idea of learning with a more knowledgeable partner whose reading skills are above the actual developmental zone but not too far above the tutee's skill level. However, given that tutees and tutors with variable differences in their pretest scores are paired, interaction effects can be estimated to analyze whether the partner effect depends on the composition of the tutor-tutee dyad.

Additionally, it might be interesting to shed more light on the processes that mediate the interpersonal and individual effects of the strategy intervention. Among others, the quality of the interaction within the dyads (cf. model of processes in peer-assisted learning, Topping, 2005), especially the way tutors offer support to their tutees to apply the strategies, are potential mediators of peer-tutored reading instruction's effectiveness. According to Webb (1989), tutees learn from elaborated feedback and explanations provided by the tutors. Elaborated support in a reading strategy training requires that tutors assist their tutees in using the strategies to construct text meaning instead of just providing a summary of the text based on the tutor's own comprehension. However, several studies report that tutors experience problems in giving elaborated feedback in peer-assisted learning (see Roscoe & Chi, 2007, for an overview). Further plausible mediators are the awareness of reading strategies and the actual use of these strategies (cf. Pressley, Forrest-Pressley, Elliot-Faust, & Miller, 1985; Van Keer & Vanderlinde, 2010) and the tutees' standards of coherence while reading (Van den Broek, Risden, & Husebye-Hartmann, 1995), given that deep comprehension can be achieved only if the readers also endorse this goal (Oakhill & Cain, 2007). Examples and explanations of how the standard APIM can be extended to an Actor-Partner Interdependence Mediation Model are given by Ledermann, Macho, & Kenny (2011).

A simpler but suboptimal approach to assess partner effects in peer tutoring is by using a traditional linear model. In order to fit a similar model using a traditional approach one would need to compute two separate ordinary least square regressions: First, the tutees' posttest reading comprehension are regressed on the tutees' pretest reading comprehension, tutors' pretest reading comprehension, treatment condition, and the interactions between pretest scores and treatment condition; and second, the tutors' posttest reading comprehension scores are regressed on the same set of predictors (see the Appendix for the R code of both OLS-regressions). Running the traditional approach yields the same unstandardized regression estimates as the APIM. However, there are important differences: The traditional approach cannot account for the nonindependence between tutees and tutors after controlling for the predictors. As a consequence, the standard errors of the test statistics are biased. In the example presented here, the standard errors obtained from the traditional approach are higher than those obtained from the APIM. This indicates that the significance test is too conservative and the probability of rejecting a true alternative hypothesis increases (see Kenny et al., 2006, chap. 2, for a detailed discussion). Another crucial difference is that the APIM offers the opportunity to compare the tutees' treatment effect with those of the tutors. Moreover, the APIM allows for analyzing latent variables, which is not possible in the traditional regression approach. Finally, the APIM provides an estimate of the covariance between the tutees' and the tutors' pretests in both treatment groups. This estimate is particularly informative when tutees and tutors are assigned to ability-based dyads before the intervention. Thus, if the composition of the dyads is based on a rank order of students (e.g., by combining the best reader above the class average with the best reader below the average, the second best above with the second best below, and so forth) and if the composition of the dyads is not changed during the intervention, nonindependence of the data is likely and should be investigated. If nonindependence occurs, using the APIM (rather than a traditional approach with separate OLS regressions) is indicated. Extending the analyses presented here, the APIM can even be estimated using multilevel modeling (see Cook & Kenny, 2005, or Kenny et al., 2006, chap. 4). In contrast, if peers are randomly assigned to dyads and if the dyads and/or the roles within the dyads are changed several times during the intervention, the traditional approach studying treatment effects separately for each dyad member or with aggregated data might be feasible.

In sum, by analyzing the data of tutees and tutors simultaneously, we were able to show that tutees might benefit from collaboration with a tutor whose reading comprehension skill surpasses the tutee’s. Beyond those interpersonal effects, tutees in the strategy training outperformed tutees with comparable pretest reading skills in the control condition. In contrast, no treatment effects occurred for the tutors. From a methodological point of view, our study emphasizes the importance to estimate effects in a dyadic learning setting with distinguishable roles by using the dyads as units of analysis. The Actor-Partner Independence Model proposed by Kenny (1996) provides an excellent means to account for the nonindependence of data obtained in such learning settings.

ACKNOWLEDGMENTS

The authors are grateful to Janin Brandenburg for conceptualizing the control treatment and to Susanne Jurkowski for helpful comments on prior versions of the manuscript. We would like to thank all the students, teachers, and student assistants taking part in this study. Researchers who are interested in the materials of the training are invited to send an e-mail to the first author.

FUNDING

The research reported in this article was supported by the German Ministry of Education and Research (Bundesministerium für Bildung und Forschung, BMBF, grant 01GJ1004).

AUTHOR NOTES

Bettina Müller and Tobias Richter are affiliated with the Department of Psychology at the University of Kassel in Kassel, Germany. Ana Križan, Teresa Hecht, and Marco Ennemoser are affiliated with the Department of Psychology at Justus Liebig University of Giessen in Giessen, Germany.

APPENDIX

Full Statistical Model

The SEMs for the two groups were estimated as saturated models with four manifest variables per treatment condition (see Figure A1 for the path diagram of the APIM): the ELFE-scores at the pretest t-1 as two exogenous variables (tutees: Y_1,t-1; tutors: Y_2,t-1), and the ELFE-scores at the posttest t as two endogenous variables (tutees: Y_1,t; tutors: Y_2,t). The model for the reading strategy training group r can be summarized as follows: (1) (2)

Figure 2 The path diagram of the actor-partner interdependence model (APIM). Note. Y₁ = tutees' reading comprehension at pretest (t-1) and posttest (t); Y₂ = tutors' reading comprehension at pretest (t-1) and posttest (t); a = actor effects; p = partner effects; the triangle indicates the intercept c; e = residual variables; single-headed arrows indicate the direction of the effects; double-headed arrows indicate correlations.

Equation 1(1) models the reading comprehension skill of tutee Y₁ of dyad i in the reading strategy training group r at the posttest t as a linear combination of the intercept c_1i,r, the actor effect a_1i,r (the stability of the tutee's reading comprehension between pre- and posttest), the partner effect p_12i,r (the influence of the tutor's reading comprehension at pretest on the tutee's posttest score), and the residuum e_1ti,r. Likewise, Equation 2(2) models the posttest reading comprehension of tutor Y₂ of dyad i as a linear combination of the intercept c_2i,r, the actor effect a_2i,r, the partner effect p_21i,r, and the residuum e_2ti,r. The equations for the dyads within the control group are structured analogously with the group index c instead of r.

R Code for Running the Models

#the data set can be required from the first author

library(lavaan)

d ←read.csv2(“filename.csv”)

summary(d)

attach(d)

######saturated APIM-Modell#####

#explanation of the variable names:

#S = tutees, T = tutors

#a_ELFE_text_z = pretest reading comprehension (group-mean centered)

# b_ELFE_text = posttest reading comprehension

#beta0 = difference of the tutees' intercepts (i.e., treatment effect tutees)

#beta4 = difference of the tutors' intercepts (i.e., treatment effect tutors)

#GroupRole = group variable (group + role in dyad, 3: reading strategy group, 4: control group)

model ← '

b_ELFE_text_S ∼ c(ga41,ga31)*a_ELFE_text_S_z + c(ga42,ga32)*a_ELFE_text_T_z

b_ELFE_text_T ∼ c(ga43,ga33)*a_ELFE_text_S_z + c(ga44,ga34)*a_ELFE_text_T_z

b_ELFE_text_S ∼ c(ga40,ga30)*1

b_ELFE_text_T ∼ c(ga400,ga300)*1

b_ELFE_text_S ∼∼ b_ELFE_text_T

a_ELFE_text_S_z ∼∼ a_ELFE_text_T_z

beta0 : = ga30 − ga40

beta4 : = ga300 − ga400

'

m5 ← sem(model, data = d, meanstructure = T, group = “GroupRole_S”, fixed.x = F)

summary(m5, standardized = T)

anova(m5)

######comparison of the saturated model (m5) vs. constrained models#####

###actor effects of the tutees (m5_equal_actorS)

model ← '

b_ELFE_text_S ∼ c(ga31,ga31)*a_ELFE_text_S_z + c(ga42,ga32)*a_ELFE_text_T_z

b_ELFE_text_T ∼ c(ga43,ga33)*a_ELFE_text_S_z + c(ga44,ga34)*a_ELFE_text_T_z

b_ELFE_text_S ∼ c(ga40,ga30)*1

b_ELFE_text_T ∼ c(ga400,ga300)*1

b_ELFE_text_S ∼∼ b_ELFE_text_T

a_ELFE_text_S_z ∼∼ a_ELFE_text_T_z'

m5_equal_actorS ← sem(model, data = d, meanstructure = T, group = “ GroupRole_S”, fixed.x = F)

summary(m5_equal_actorS, standardized = T)

anova(m5,m5_equal_actorS)

###actor effects of the tutors (m5_equal_actorT)

model ← '

b_ELFE_text_S ∼ c(ga41,ga31)*a_ELFE_text_S_z + c(ga42,ga32)*a_ELFE_text_T_z

b_ELFE_text_T ∼ c(ga43,ga33)*a_ELFE_text_S_z + c(ga34,ga34)*a_ELFE_text_T_z

b_ELFE_text_S ∼ c(ga40,ga30)*1

b_ELFE_text_T ∼ c(ga400,ga300)*1

b_ELFE_text_S ∼∼ b_ELFE_text_T

a_ELFE_text_S_z ∼∼ a_ELFE_text_T_z'

m5_equal_actorT ← sem(model, data = d, meanstructure = T, group = “ GroupRole_S”, fixed.x = F)

summary(m5_equal_actorT, standardized = T)

anova(m5,m5_equal_actorT)

###partner effects tutor→tutee (m5_equal_partnerT)

model ← '

b_ELFE_text_S ∼ c(ga41,ga31)*a_ELFE_text_S_z + c(ga32,ga32)*a_ELFE_text_T_z

b_ELFE_text_T ∼ c(ga43,ga33)*a_ELFE_text_S_z + c(ga44,ga34)*a_ELFE_text_T_z

b_ELFE_text_S ∼ c(ga40,ga30)*1

b_ELFE_text_T ∼ c(ga400,ga300)*1

b_ELFE_text_S ∼∼ b_ELFE_text_T

a_ELFE_text_S_z ∼∼ a_ELFE_text_T_z'

m5_equal_partnerT ← sem(model, data = d, meanstructure = T, group = “ GroupRole_S”, fixed.x = F)

summary(m5_equal_partnerT, standardized = T)

anova(m5,m5_equal_partnerT)

##### compare the APIM with traditional approaches: how to compute as ordinary least square regression#####

###regression of tutees' posttest reading comprehension on tutees' pretest comprehension, tutors' pretest comprehension, group variable, and interactions group*tutee pre and group*tutor pre

d$treat ← as.numeric(d$GroupRole_S = = 31)

m_OLS_S ← lm(b_ELFE_text_S ∼ a_ELFE_text_S_z*treat + a_ELFE_text_T_z*treat, data = d)

summary(m_OLS_S)

###regression of tutors' posttest reading comprehension on tutors' pretest comprehension, tutees' pretest comprehension, group variable, and interactions group*tutee pre and group*tutor pre

m_OLS_T ← lm(b_ELFE_text_T ∼ a_ELFE_text_S_z*treat + a_ELFE_text_T_z*treat, data = d)

summary(m_OLS_T)