teachers’ efficacy beliefs about their students’ language learning, and learning and teaching style differences along the dimension of preference for silence. Second, the observed variables indicating language anxiety were tested whether they indeed explain this latent variable in a reliable and valid way. The next group of factors comprised two latent components of coping strategies: problem-focused strategies as measured by the aggregate of problem-focused coping and tension control; and emotion-focused coping strategies as measured by the aggregate variables of self-punishment and letting out emotions.
In the second part of the chapter, the results of testing the full structural model are presented. The full model consisted of the above listed four latent variables as defined by their constituents, three additional observed variables of language learning attitude, motivated language learning behavior, and self-efficacy beliefs and the hypothesized paths that represent the variables’ influence on one another (see also Figure 2).
7.1.1 Conflict
The first measurement model to be evaluated comprised the variables that were theorized to represent the conflicts or stressors learners encounter in the language classroom (cf Chapter 3). Accordingly, the measurement model of ‘conflict’
was hypothesized to include the observed variables in form of composite scores derived from the scales measuring fear of negative evaluation of peers, fear of negative evaluation of teacher, fear of participating in speaking tasks in a language class, lack of self-confidence, to/own and actual self discrepancy, ought-to/other and actual self difference, learning and teaching style discrepancy involving preference for silence, and the difference between teachers’ and learners’ beliefs about students’ efficacy. The scales the aggregates were derived from have been demonstrated to possess acceptable levels of reliability. The missing values in case of these variables were substituted by the means of the respective composite scores.
Thus, the model was specified to include eighteen variables: eight observed and ten unobserved; nine endogenous (dependent) and nine exogenous (independent) variables. For a visual representation of the measurement model see Figure 5 below.
0 conflict
speakin gtask
0;
err1
1
f earo f p
0;
err2
1
f earo f t
0;
err3
1
1
lackc o nf
0;
err4
1
0;
res1
1
o ug hto wnactualdiff
0;
err5
1
o ug hto theractualdiff
0;
err6
1
effdiff
0;
err7
1
stsilencediff
0;
err8
1
Figure 5. The measurement model of the latent variable of ‘conflict’.
Conflict
speakingtask: participating in speaking tasks fearofp: fear of negative evaluation from peers fearoft: fear of negative evaluation from teacher lackconf: lack of self-confidence
oughtownactualdiff: ought-to self/own and actual self difference oughtotheractualdiff: ought-to self/other and actual self difference effdiff: difference in how teachers and learners perceive learners’ efficacy
stsilencediff: difference between learners’ and teachers’ preference for silent style of learning and teaching
The model was characterized by 44 sample moments, with 24 distinct parameters to be estimated, which yielded df = 20. The positive degrees of freedom suggests that (1) the model met the criteria of overidentification (i.e. “there is more than one way of estimating a parameter (or parameters) because there is more than enough information in the matrix S” (Schumacker & Lomax, 2004, p.64)) and (2) it “allows for the rejection of the model, thereby rendering it of scientific use” (Byrne, 2001, p.35).
Addressing model estimation issues, maximum likelihood estimation with standardized factor loadings was used. This is a scale free fitting function to minimize the difference between the implied matrix and the sample matrix (Byrne, 2001;
Shumacker & Lomax, 2004). In the case of using standardized factor loadings the variance of the latent variables was fixed at 1.
The overall fit of the model is characterized by χ2 = 87.21 p < .01. Alongside the chi square statistic, the normed fit index (NFI) and the comparative fit index (CFI) are used to reflect the comparison of the hypothesized model with a baseline or independence model (where all the components are independent of one another). Both of their threshold values are set around .95, and any higher obtained values suggest a good fit (Byrne, 2001). Here the indicators did not reach the threshold (NFI = .88, CFI
= .90) which questioned the validity of the model.
The root mean square error of approximation index (RMSEA) is said to be
“one of the most informative criteria in covariance structure modeling” (Byrne, 2001, p.84) which takes into account the error of approximation and is dependent on the number of parameters to be estimated. Therefore, beside the NFI and CFI, this is also a model fit index of interest. RMSEA values of less than .05 are considered to be evidence for a good fitting model, values above .10 indicating poor fit (Byrne, 2001).
The latter held true for this model with RMSEA = .13.
Thus, it can be concluded that overall the model does not describe the sample data adequately. By looking at the significance of the estimates and the standardized regression weights that characterize the loading of the observed variables onto the latent variable, it can be noted that ought-to/other and actual self differences and the difference between learners’ and teachers’ beliefs about students’ efficacy explain only a very small portion of the latent variable of conflict. Furthermore, their loadings are not considered significant. As a result of poor fit, weak loadings of two items, and a lack of significance, the model was revised by dropping the two observed variables of ought-to/other and actual self difference and efficacy difference.
The revised model (see Figure 6) had 27 distinct sample moments, 18 distinct parameters to be estimated and a positive degrees of freedom df = 9. From the standardized regression weights it can be noted that the difference in preference of silent learning style and teaching style and the variable of discrepancy between the ought-to/own and actual/own selves did not load onto the latent variable and thus do not explain much of its variance.
0 conflict
speakingtask
0;
err1
1
f earo f p
0;
err2
1
f earo f t
0;
1 1 err3
lackco nf
0;
err4
1
stsilencediff
0;
err5
1
oughtownactualdiff
0;
err6
1 0;
res1
1
Figure 6. The first revised version of the measurement model of ‘conflict’.
Conflict
speakingtask: participating in speaking tasks fearofp: fear of negative evaluation from peers fearoft: fear of negative evaluation from teacher lackconf: lack of self-confidence
stsilencediff: difference between learners’ and teachers’ preference for silent style of learning and teaching
oughtownactualdiff: ought-to self/own and actual self difference oughtotheractualdiff: ought-to self/other and actual self difference effdiff: difference in how teachers and learners perceive learners’ efficacy
Table 33
Standardized Regression Weights of the First Revised Measurement Model of
‘Conflict’
Observed independent variable Estimate
Participating in speaking tasks .93
Fear of negative evaluation of peers .92
Fear of negative evaluation of teacher .80
Lack of self-confidence .77
Differences in preference for silent learning and teaching styles .20 Ought-to self/own and actual self difference .15
Note: All estimates are significant at p < .05.
The overall model fit indices (χ2 = 14.88, df = 9, p = 0.09; NFI = .98, CFI = .99; RMSEA = .06) suggest an acceptable model. From the PCLOSE = 0.38 value we cannot accept the hypothesis that the RMSEA indicates a good fit as the value does not supersede .50 (based on Byrne, 2001). All factor loadings had a an associated significance p < .05, but not all standardized regression weights suggested high loadings (see Table 33 above). Thus, the two observed variables with the weakest estimates (oughtownactualdiff and stsilcencediff) were deleted from the measurement model. The final revised confirmatory factor model is depicted in Figure 7.
0 conflict
sp eaking task
0;
err1
1
f earo f p
0;
err2
1
f earo f t
0;
1 1 err3
lack c o nf
0;
err4
1
0;
res1
1
Figure 7. Final measurement model of the latent variable of ’conflict’.
Conflict
speakingtask: participating in speaking tasks fearofp: fear of negative evaluation from peers fearoft: fear of negative evaluation from teacher lackconf: lack of self-confidence
The third model was successfully identified. Its indices read as follows: (χ2 = 0.96, df
= 2, p = 0.62; NFI = .99, CFI = 1.00; RMSEA = .00). The high p value implies that the departure of the data from the model is not significant. PCLOSE = .75 indicates a good fit and the RMSEALO = .00 and RMSEAHI = .11 values depict the low and upper boundaries of a two-sided 90% confidence interval for RMSEA. The standardized estimates in Table 34 are acceptably high.
Table 34
Standardized Regression Weights of the Final Revised Measurement Model of
‘Conflict’
Observed independent variable Estimate Participating in speaking tasks .92 Fear of negative evaluation of peers .92 Fear of negative evaluation of teacher .80
Lack of self-confidence .77
Note: All estimates are significant at p < .05.
There is, however, one more question to address which involves the issue of normal distribution. Although SEM is said to be robust in carrying out statistical analyses, for the meaningful interpretation of model fit indices it does require the distribution of the data to be multivariate normal with special emphasis on kurtosis (Schumacker & Lomax, 2004). The multivariate kurtosis of the variables in this model was 3.9 and the corresponding critical ratio was 4.14. These figures may be negligible if we consider that multivariate kurtosis values up to 10 and critical ration
up to 20 are generally indicative of moderate non-normality. Thus, the model fit indices can be interpreted meaningfully.
In conclusion, the latent variable of conflict, comprising the possible stressors learners may encounter in the language classroom, is determined by learners’ fear of participating in speaking tasks, their fear of negative evaluation from their teachers and peers, and their lack of self-confidence. The difference between learners’ and teachers’ beliefs and styles was not demonstrated in this study to be a key element of the conflicts learners’ experience. The remaining four components are identical to the ones that were measured by the FLCAS as key sources of language anxiety.
It is important to note that here, in the model of the development of language anxiety an attempt was made to distinguish between the sources and the feeling of anxiety, and for this reason two latent variables were devised. The first latent variable is that of conflict, which incorporates the sources of language anxiety as shown in the measurement model above. The second latent variable is that of language anxiety, which sets out to measure the strength of the feeling itself, rather than its sources. The latter measurement model is described in the next section.
7.1.2 Language Anxiety
The second measurement model that was used as a building block for the structural model was a second-order confirmatory model of language anxiety, where the first order latent factors were explained by a higher order structure (Byrne, 2001).
More precisely, language anxiety, a higher order latent structure is seen as a composite of language classroom anxiety and language use anxiety. In anxiety research it has been widespread practice to employ these two measures when
assessing learners’ levels of anxiety (see MacIntyre’s research on anxiety). For this reason and for the theoretical consideration that language anxiety involves using the language in and outside the classroom, the measurement model of language anxiety as seen in Figure 8 was drawn up.
0
class mot24
0;
err4
1 1
mot34
0;
err5
1
mot44
0;
err6
1
0
language anxiety
0;
res2
1
0;
1 res3
0
use
1 0; 0
res1
1
mot22
0;
err1
1 1
mot32
0;
err2
1
mot42
0;
err3
1
mot54
0;
err7
1
Figure 8. The second-order confirmatory model of ‘language anxiety’.
Language anxiety use: language use anxiety
mot22: anxiety about communicating with native speakers mot32: anxiety about talking to foreigners in English mot42: anxiety about meeting native speakers of English class: language class anxiety
mot24: anxiety about volunteering in class
mot34: anxiety about others being better at English mot44: anxiety about speaking in English in class
mot54: anxiety about being laughed at when speaking in class
The model was identified with χ2 = 20.47, df = 13, p = .08; NFI = .98, CFI = .99;
RMSEA = .05). As previously, maximum likelihood estimation was used to derive standardized regression weights of the factors on the latent variables.
Table 35
Standardized Regression Weights for the Second-order Confirmatory Model of
‘Language Anxiety’
Observed/Latent variable - Latent dependent variable Estimate
Language class anxiety – Language anxiety .90
Language use anxiety – Language anxiety 1.00
mot24 – Language class anxiety .81
mot34 – Language class anxiety .70
mot44 – Language class anxiety .85
mot54 – Language class anxiety .68
mot22 – Language use anxiety .70
mot32 – Language use anxiety .81
mot42 – Language use anxiety .87
Note: All estimates are significant at p < .05.
The regression weight of Language use anxiety on language anxiety was set at 1.
The standardized regression weights are all above .70 (see Table 35) and the model fit indices are also moderately acceptable. The modification indices (M.I.) proposed a covariance relationship between error terms. After re-specifying the model by adding a covariance between ‘err6’ and ‘err3’ (M.I.= 11.22), a model of better fit was attained.
0
class mot24
0;
err4
1 1
mot34
0;
err5
1
mot44
0;
err6
1
0
language anxiety
0;
res2
1
0;
1 res3
0
use
1 0; 0
res1
1
mot22
0;
err1
1 1
mot32
0;
err2
1
mot42
0;
err3
1
mot54
0;
err7
1
Figure 9. The revised second-order confirmatory model of ‘language anxiety’.
The new model’s fit was characterized by the following as a good fit: χ2 = 5.95 df = 12, p = 0.92; NFI = .99, CFI = 1.00; RMSEA = .00 PCLOSE =.99. (For a graphic representation of the measurement model see Figure 9). Indicative of a non-normal distribution, the multivariate kurtosis of the model is 30.40. Consequently, in case of non-normal multivariate distribution, bootstrap maximum likelihood analysis with the help of the Bollen-Stine p value can suggest whether the model identified with the criteria of normal distribution has to be rejected when the distribution is non-normal.
In case of p > .05 the model can be assumed to be correct (Byrne, 2001). For this confirmatory model p = .97, indicating an acceptable model based on a 150 samples bootstrap.
These results suggest that the items of the motivation questionnaire adequately measure learners’ feelings of language anxiety when using the foreign language in general and in the context of the foreign language classroom. Thus, the latent variable of language anxiety will be incorporated in the final structural model as an indicator of learners’ level of language anxiety, a variable distinct from the variable of conflict that comprises the sources of language anxiety (i.e. the stressors).
7.1.3 Emotion-Focused Coping
The next two measurement models that were tested for inclusion in the final structural model were that of emotion-focused and problem-focused coping strategies.
First, the emotion-focused component was investigated.
Based on Lazarus’ (1993) two factor approach, the components of self-punishment, seeking social support and letting out emotions were expected to load onto one factor which can be characterized as emotion focus strategies towards coping. The other components identified earlier were not included due to the reliability coefficients being lower than .70
0 punish
cope5
0;
err1
1 1
cope14
0;
err2
1
cope33
0;
err3
1
cope50
0;
err4
1
0 social
cope24
0;
err5
1 1
cope25
0;
err6
1
cope27
0;
err7
1
cope29
0;
err8
1
0 lettingout
0 emotion focus
cope17
0;
err10
1 1
cope22
0;
err11
1
cope23
0;
err12
1
1
cope35
0;
err13
1
cope46
0;
err14
1
cope44
0;
err9
1
0;
res1
1 0;
res2
1 0;
res3
1 0;
res4
1
Figure 10. Second-order confirmatory model of emotion-focused coping strategies.
Emotion focus: Emotion-focused coping punish: self-punishment
cope5: blaming oneself cope14: feeling guilty
cope33: putting the blame on oneself cope50: criticizing oneself
social: seeking social support
cope24: needs to talk to someone
cope25: asking others who have been in similar situation cope27: needs others’ comfort
cope29: sharing problems
cope44: seeking condolence with friends and family lettingout: letting out emotions
cope17: get angry cope22: break everything cope23: let feelings flow cope35: thinking about revenge cope46: get rid of anger
The second-order confirmatory model (see Figure 10) was identified. Letting out emotions seems to contribute to the latent variable emotion focus the least (see Table 36). What is more, the model fit indices do not suggest a strong model fit (χ2 = 156.40, df = 74, p < .00; NFI = .86, CFI = .92; RMSEA = .07)
Table 36
Standardized Regression Weights for the Second-order Confirmatory Model of
‘Emotion-focused Coping Strategies’
Observed/Latent variable - Latent dependent variable Estimate
Self-punishment – Emotion-focused coping .55
Seeking social support –Emotion-focused coping .90
Letting out emotions – Emotion-focused coping .46
cope5 – self-punishment .62
cope14 – self-punishment .64
cope33 – self-punishment .75
cope50 – self-punishment .63
cope24 – seeking social support .83
cope25 – seeking social support .67
cope27 – seeking social support .65
cope29 – seeking social support .69
cope44 – seeking social support .74
cope17 – letting out emotions .71
cope22 – letting out emotions .81
cope23 – letting out emotions .58
cope35 – letting out emotions .51
cope46 – letting out emotions .81
Note: All estimates are significant at p < .05.
Based on the above, the variable of letting out emotions was withdrawn from the model. The modification index of the re-specified model suggested a covariance between ‘err1’ and ‘err8’ (M.I.= 11.24) and ‘err4’and ‘err7’ (M.I.= 4.33) (For the modified model see Figure 11). In order to achieve an identified model, the variance of res1 was set at 0.
The model fit indices improved: χ2 = 27.60, df = 24, p = 0.28; NFI = .96, CFI = .99; RMSEA = .03, PCLOSE = .82) The standardized regression weights depict acceptable levels of loadings, albeit the loading of seeking social support is not as convincing as the other figures (see Table 37). All paths were significant at p < .05.
0
self-punish cope5
0;
err1
1 1
cope14
0;
err2
1
cope33
0;
err3
1
cope50
0;
err4
1
0
social cope24
0;
err5
1 1
cope25
0;
err6
1
cope27
0;
err7
1
cope29
0;
err8
1
cope44
0;
err9
1
0
emotion focus
0; 0 1
res1
1
0;
res2
1
0;
res3
1
Figure 11. Revised second-order confirmatory model of emotion-focused coping strategies.
Emotion focus: Emotion-focused coping punish: self-punishment
cope5: blaming oneself cope14: feeling guilty
cope33: putting the blame on oneself cope50: criticizing oneself
social: seeking social support
cope24: needs to talk to someone
cope25: asking others who have been in similar situation cope27: needs others’ comfort
cope29: sharing problems
cope44: seeking condolence with friends and family
Table 37
Standardized Regression Weights for the Revised Second-order Confirmatory Model of ‘Emotion-focused Coping Strategies’
Observed/Latent variable - Latent dependent variable Estimate
Self-punishment – Emotion-focused coping 1.00
Seeking social support –Emotion-focused coping .50
cope5 – self-punishment .63
cope14 – self-punishment .64
cope33 – self-punishment .75
cope50 – self-punishment .62
cope24 – seeking social support .83
cope25 – seeking social support .66
cope27 – seeking social support .64
cope29 – seeking social support .70
cope44 – seeking social support .74
Note: All estimates are significant at p < .05.
The regression weight of self-punishment on emotion focus was set at 1.
Similarly to previous analysis, joint multivariate normality of the observed variables was checked by assessing the values of multivariate kurtosis (kurtosis = 11.20) and its corresponding critical ratio (c.r. = 5.82). These values were just above those indicating a normal distribution of the sample data. Using the Bollen-Stine bootstrap (Byrne, 2001), the p value was found to be p = .50, which meant that the null hypothesis of the model being correct could not be rejected taking into consideration the bootstrap sample of 150.
Interestingly, contrary to Oláh’s (2005) results, in the present sample only self-punishment and seeking social support were identified as indicators of emotion-focused coping strategies. This result may have arisen from the fact that in the specific context of the language learning situation certain coping strategies, such letting out emotions and showing aggressive behavior are normally not viable options to deal with language anxiety in the classroom. Moreover, learners may not be aware
of their choice to use diverting attention and resignation strategies as often coping strategies are not based on conscious considerations (Oláh, 2005) as opposed to the conscious decisions of using problem directed learning strategies (cf. Chamot, 2005).
7.1.4 Problem-Focused Coping
The final measurement model to be included in the full structural model was that of problem-focused coping. As results of Oláh’s (2005) study suggest, problem- focused coping comprises a problem-focused approach and tension control. Thus, a second order confirmatory factor model was devised which included the latent variables of problem and tension control as well as the latent variable problem focus, with the respective items of the questionnaire that have been demonstrated with the help of principal component analysis to adequately measure them. The model depicted in Figure 12 was set up and tested.
0 tension control cope4
0;
err1
1 1
cope18
0;
err2
1
cope28
0;
err3
1
cope30
0;
err4
1
cope37
0;
err5
1
0 problem cope3
0;
err6
1 1
cope7
0;
err7
1
cope38
0;
err8
1
cope40
0;
err9
1
cope49
0;
er10
1
cope51
0;
err11
1
0 problem focus 1
0; 0
res1
1 0;
res3
1
0;
res2
1
Figure 12. Second-order confirmatory model of problem-focused coping strategies.
Problem focus: Problem-focused coping tension control: tension control
cope4: be flexible
cope18: overcome obstacles
cope30: use all energy resources to overcome difficulties cope37: be determined
problem: problem-focused items cope3: think up solutions
cope7: try to understand the situation
cope38: try to learn through previous experience cope49: try to alter the situation
cope51: try to think up several alternative solutions
The factor model was identified (χ2 = 97.40, df = 43, p < 0.01) using maximum likelihood estimation. The standardized regression weights of the observed variables on the latent variables seemed acceptable with the exception of items cope4 and cope3. The overall model fit indices (NFI = .83, CFI = .90; RMSEA = .08) also suggested a mere mediocre fit.
Table 38
Standardized Regression Weights for the Second-order Confirmatory Model of
‘Problem-focused Coping Strategies’
Observed/Latent variable - Latent dependent variable Estimate
Tension control – Problem-focused coping .74
Problem – Problem-focused coping 1.00
cope18 – tension control .69
cope28 – tension control .54
cope30 – tension control .58
cope37 – tension control .65
cope4 –tension control .40
cope3 – problem .41
cope7 – problem .52
cope38 – problem .65
cope40 – problem .61
cope49 – problem .54
cope51 – problem .71
Note: All estimates are significant at p < .05.
The regression weight of problem on problem-focused coping was set at 1.
By disregarding items ‘cope3’ and ‘cope4’ due to low regression weights (see Table 38) and taking into account the modification index of M.I. = 30.91that suggests a covariance relationship between error measures err3 and err5, the following model was arrived at (see Figure 13).
0 tension control cope18
0;
err2
1
cope28
0;
err3
1
cope30
0;
err4
1
cope37
0;
err5
1 1
0 problem cope7
0;
err7
1 1
cope38
0;
err8
1
cope40
0;
err9
1
cope49
0;
er10
1
cope51
0;
err11
1
0 problem focus 1
0;
res1
1 0; 0
res3
1
0;
res2
1
Figure 13. Final second-order confirmatory model of problem-focused coping strategies.
Problem focus: Problem-focused coping tension control: tension control
cope18: overcome obstacles
cope30: use all energy resources to overcome difficulties cope37: be determined
problem: problem-focused items
cope7: try to understand the situation
cope38: try to learn through previous experience cope49: try to alter the situation
cope51: try to think up several alternative solutions
This factor model was also identified (χ2 = 33.52, df = 25, p =.12). The fit indices imply a better fitting model than the previous one: NFI = .93, CFI = .98; RMSEA =