Use of change scores in redundancy analyses of multivariate psychological inventories

Transcription

1 Bond University From the SelectedWorks of Gregory J. Boyle 1987 Use of change scores in redundancy analyses of multivariate psychological inventories Gregory J. Boyle, Bond University Available at:

2 Use of Change Scores in Redundancy Analyses of Multivariate Psychological Inventories Gregory J. Boyle University of Melbourne This research was supported by a Research Development Grant awarded to the author by the University of Melbourne. Address requests for reprints to Gregory J. Boyle, University of Melbourne, Parkville, Victoria 3052, Australia.

3 Abstract Both canonical and multiple-regression redundancy analyses were computed on the 20 separate subscale change-scores for the Eight State Questionnaire (8SQ) and the Differential Emotions Scale (DES-IV), using a sample of 212 undergraduate students. In comparing the measurement overlap of the two measures, it was important, since state-change dimensions were of interest, that across occasions difference scores be used rather than single-occasion absolute scores. Viability of this approach was demonstrated and only minor redundancy was evident for the 8SQ and DES-IV instruments. On the present evidence, it appears that both inventories are tapping essentially discrete psychological variance (allowing for trait contamination) and that probably neither instrument alone is an adequate measure of the total 'mood-state sphere'.

4 Introduction In the area of transient, fluctuating emotional states, the use of multivariate self-report inventories has become popular in recent years. Boyle (1985b) reviewed the psychometric adequacy of a number of such measures and concluded that two of the better instruments presently available are the Differential Emotions Scale (DES- IV; Izard, Dougherty, Bloxom and Kotsch, 1974) and the Eight State Questionnaire (8SQ; Curran and Cattell, 1976). Both instruments are purported to index the major human fundamental emotions/source states respectively. Accordingly, it might be expected that both inventories should exhibit significant measurement redundancy. Previous factor analysis of the change-score intercorrelations (Boyle, 1986a) failed to reveal any significant overlap of the DES-IV and 8SQ subscales even though a number of the subscales across both instruments appear to index essentially the same mood states. In order to investigate such inter-inventory overlap more concisely, it is necessary to quantify as precisely as possible the actual measurement redundancy across both scales. One way of quantifying the measurement overlap of different instruments is to employ canonical correlation analysis together with Stewart and Love's (1968) redundancy index. This method has been employed usefully in previous studies of psychological inventories (e.g. Boyle, Stanley and Start, 1985; Krug, 1978). Thus in comparing the Sixteen Personality Factor Questionnaire (16PF), the Motivation Analysis Test (MAT) and the 8SQ, Boyle et al., reported a marginal overlap in measurement variance between the 16PF and 8SQ, but only very slight redundancy for the 16PF/MAT and 8SQ/MAT intersections. All three instruments therefore appeared to measure essentially discrete psychological domains. In each instance,

5 the canonical-redundancy calculation allowed precise quantification of the measurement overlap. Although other methods such as discriminant function analysis or even bipartial canonical analysis (cf. Timm and Carlson, 1976) might have been employed, Stewart and Love's method provided a clearcut numerical estimation of the actual redundancies. As an isolated procedure, Tatsuoka (in Cattell, 1978) has questioned the adequacy of substantive interpretation of canonical analysis, referring to the method as "double-barrelled principal components analysis" having little conceptual value despite its mathematical elegance. However, while the interpretation of canonical variates is ambiguous (even when rotated as per Cliff and Krus, 1976), its use with Stewart and Love's (1968) redundancy index provides a useful method of quantifying interset measurement overlap (Harris, 1985, pp ). As Krug (1978, p. 201) pointed out, the method avoids controversial issues involved in factor analytic extraction and rotation. As the substantive interpretation of the content similarities and differences between instruments is conceptually dubious (Cattell, 1978, pp ) there is little point in rotating the canonical vectors prior to calculation of Stewart and Love's redundancy index. Even though some reservations concerning Stewart and Love's index have been noted (cf. Amick and Walberg, 1975, pp ), the general consensus has been favourable as indicated in Gleason (1976), Van den Wollenberg (1977), De Sarbo (1981), Johansson (1981), Muller (1981), Harris (1985). Another way of quantifying the measurement overlap of different scales is to employ multiple regression procedures to ascertain the inter-inventory redundancy. This approach also has the advantage of permitting estimation of subscale scores across instruments using the resultant cross-inventory prediction equations (cf.

6 Goldberg, 1977). A review of studies in this area was provided by Campbell and Chun (1977). Clearly the magnitude of the multiple R 2 is a direct index of the amount of variance associated with a particular subscale in one inventory which is predictable from the various subscale scores of the other inventory. For example, Goldberg reported an average multiple R of 0.68 when predicting scores on Personality Research Form (PRF) scales from known scores on the California Personality Inventory (CPI). Accordingly, in Goldberg's study, the CPI subscale scores predicted an average 46% of the variance in the respective PRF subscales. Likewise, Goldberg reported an estimated multiple R of 0.70 (49% of variance) when predicting CPI subscale scores from PRF scores. With regard to crossinventory prediction equations, Goldberg (p. 352) pointed out that the reliability of these prediction equations depends not only on the sample size of the group from which the calculations are made, but also on particular idiosyncratic sampling characteristics such as homogeneity in age and education, as well as conditions under which psychological inventories are administered. While either the unstandardized or standardized (beta) coefficients can be used in such prediction equations, in practice, the standardized regression coefficient is more convenient to use in many instances. As Nie, Hull, Jenkins, Steinbrenner and Bent (1975, p. 325) correctly pointed out, "Working with beta weights enables one to simplify the linear regression equation, since the constant A (the Y intercept) is always equal to zero and therefore can be omitted. Furthermore, when there are two or more independent variables measured on different units... standardized coefficients may provide the only sensible way to compare the relative effect on the dependent variable of each independent variable. Moreover, a standardized regression coefficient is quite readily transformed to its unstandardized counterpart if standard deviations for the

7 original X and Y are available." Evidently, use of beta weights rather than unstandardized regression coefficients will be preferable when comparing psychological inventories which have different scaling properties and characteristics. When working with mood-state inventories rather than say personality trait inventories, it is important to base the various redundancy calculations on change scores rather than on absolute scores. In this regard, the use of difference scores removes the trait pattern variance which is inherent in absolute single-occasion scores. In the latter context, both kinds of dimensions (states and traits) will emerge from analyses and each will be 'frozen' at a given instant in time, just as a singleoccasion photograph is fixed in time. Unfortunately, the reliability of change scores has been seriously challenged (e.g. Cronbach and Furby, 1970) with the result that many investigators in the psychological measurement area have avoided using them. Despite these severe criticisms, many investigators have examined the issues and have concluded that change scores are extremely useful when undertaking multivariate analyses of state-change structures (e.g. Cattell, 1978, 1979, 1982; Lam, 1981; Nesselroade and Cable, 1974; Overall and Woodward, 1975). According to Nesselroade and Cable (p. 281), "from a structural point of view, difference scores offer one way of getting at the multidimensional nature of change..." Furthermore, Nesselroade and Cable contended that multivariate analysis of change scores, "is not misleading but actually rather precise in not only revealing change dimensions but in suppressing dimensions of stable interindividual differences." (p. 281). Nevertheless, as Cattell (1978, pp ) stated, "The sources of distortion of difference score correlations one needs to watch are (1) different reliabilities of before and after measures, (2) different variances of before

8 and after measures, (3) departure of scaling from equal interval properties, (4) the need for greater efforts for reduction of experimental error (with accompanying emphasis on larger samples..." Cattell (1982) has addressed this issue of the reliability of difference scores in considerable detail and he has shown that when the first and second measures are essentially uncorrelated (cf. Cattell, 1978, p. 343), the ratio of error to true variance is about the same for both absolute and change scores. This can be expressed algebraically as: However, when the two sets of measures are correlated, the ratio of error to true variance is increased as only the true variance is responsible for the correlation, while the error variance remains by definition uncorrelated. A simplified version of the corresponding equation given by Cattell (assuming equal across-occasion variances) is: wherein it is apparent that the true variance is reduced by the factor 2rσ t1 σ t2. It is possible to evaluate Eq. (2) given the immediate test-retest (dependability) coefficient and the observed score stability coefficient (retest after a reasonable period of time such as after one or several weeks). Fortunately in mood-state research as opposed to developmental research, the correlation between acrossoccasions measures is often very close to zero, so that the proportion of error variance to true variance is not greatly increased when working with change scores rather than absolute scores.

9 Clearly though, apart from the ratio of error to true variance, it is important to minimise the distorting influence of the other confounding variables mentioned by Cattell (listed above). Examination of the raw data is therefore an essential requirement when undertaking analyses on difference scores. While the correlation between across-occasions measures is often not as problematic in state-change studies as in developmental research (Cattell, 1978, p. 344), it is nevertheless, important to minimise any correlation of the before and after measures in order not to reduce the proportion of true variance to error variance, as per Eq. (2) above. Cattell (1982, p. 89) suggested that any such across-occasions correlation could be minimised by, "(1) Using longer tests to raise the dependability coefficient of the single occasion measures themselves, (2) Keeping conditions such as to maintain pre- and post-dependabilities essentially equal, (3) Keeping pre- and post-variances equal, if necessary by putting them in standard scores, and (4) Obtaining both dependability (re-test without time for state change) coefficients and stability (re-test after psychological change) coefficients..." The relationship between dependability and stability coefficients (cf. Nesselroade, Pruchno and Jacobs, 1986) is a critical determinant of the reliability of difference scores. As Boyle (1985b) pointed out, while both dependability and stability coefficients should be reasonably high (0.8 or above) for trait measures, in contrast for state measures, dependability coefficients should be high, but stability estimates should be considerably lowered if the state measures are sensitive to situational variability and are reliable indicators of true measurement variance (cf. Boyle, 1985b, p. 53). In an empirical examination of dependability coefficients derived from values of dependability and stability coefficients of absolute scores, Cattell (1982, p. 92) demonstrated that, "When the stability coefficient rises to equal the depend ability

10 ... difference scores cease to have any dependability." On the assumption of equal across-occasions variances, Cattell (p. 96) further proposed the following formula for assessing the dependability of difference scores: r d(2-1) = r d r s / 1 r s (3) Cattell concluded therefore, that with dependability coefficients in the 0.8 to 0.9 range and stability coefficients in the 0 to 0.7 range, the resultant differencescore dependability estimates are quite acceptable. Under the unusual situation of zero stability (as in a pure state measure which only measures true variance) Cattell reported that the difference-score reliability is identical to the reliability of the absolute scores. For a more comprehensive discussion of these issues, the article by Cattell (1982) is essential reading. In the present study, in order to ascertain estimates of redundancy in measurement variance of the DES-IV and 8SQ mood-state inventories (with the aim of developing a more effective and efficient measure of the mood-state sphere), it was necessary to compute across-occasions difference scores for the 20 multiple regression analyses of redundancy. The importance of basing the calculations on change scores rather than on absolute scores was that it was desirable to examine the overlap in state-change (mood-state) dimensions as opposed to trait dimensions. The question under examination was, "How much measurement overlap is there between the DES-IV and 8SQ state-change dimensions?" Only computation of difference scores across separate measurement occasions would allow a precise answer to this question.

11 Method Subjects The 212 male and female students were all undergraduates attending either the Melbourne College of Advanced Education or the Institute of Catholic Education, Melbourne. The mean age of the sample was years (SD = 6.87 years). In the main, the students were predominantly Australian-born from middleclass socioeconomic backgrounds. The two instruments were administered during the students' regularly time-tabled classes and accordingly most seemed quite willing to answer the questions as best they could. A number of DES-IV and 8SQ protocols from the first measurement occasion were not included in the analysis, however, as some students were absent on the second occasion (and vice versa). As administration of both inventories took only about minutes, the effort required on the part of the students was minimal, thereby facilitating their co-operation. Instruments The two multivariate mood-state inventories employed (DES-IV and 8SQ) were selected on the basis of a review of several self-report psychometric instruments by Boyle (1985b). The 8SQ is purported to measure eight important source states labelled, Anxiety, Stress, Depression, Regression, Fatigue, Guilt, Extraversion and Arousal respectively, while the DES-IV is purported to measure Interest, Joy, Surprise, Sadness, Anger, Disgust, Contempt, Hostility (innerdirected), Fear, Shame, Shyness and Guilt in that order. While the 8SQ comprises 12 items per subscale which are presented cyclically in order to avoid spurious contiguity effects, the DES-IV generally has three items per subscale, except for the subscales of Sadness (four items), Hostility (seven items), and Shame (eleven

12 items). Hence, nine of the DES-IV subscales have only three items each and accordingly from the Spearman-Brown prophecy formula, it is obvious that the reliability of these DES-IV subscales would probably be lower than for the 8SQ subscales. Nevertheless, both inventories have received considerable support for their construct validity in the extant literature (e.g. Boyle, 1984, 1986b; Fuenzalida, Erode, Pannabecker and Stenberg, 1981; Izard, Blumberg and Oyster, 1985; Kotsch, Gerbing and Schwartz, 1982; Schwartz, 1982, for the DES-IV; Barton and Flocchini, 1985; Boyle, 1985a, c, 1986a; Boyle and Cattell, 1984; Boyle et al., 1985, for the 8SQ). Both inventories have been subjected to extensive factor analytic investigation and there seems to be support for the subscale structure of each instrument in general. Results and Discussion The means and standard deviations for the first- and second-occasion absolute scores as well as for the change scores are presented in Table 1. Inspection of this table suggests that the variances across the two measurement occasions were essentially stable for each instrument. Indeed, the across-occasions correlations for the standard deviations of the 8SQ and DES-IV were 0.92 and 0.75 respectively. For the combined 8SQ/DES-IV scales, the across-occasions correlation increased to 0.99, clearly suggesting that the variances of the absolute scores on each occasion were virtually the same. This is an important finding as it provides evidence that the change scores were reasonably reliable, in accord with Cattell's (1982) requirements above for minimising the across-occasions correlation of the initial raw scores themselves.

13 Using Eq. (3) above, it was possible to estimate the dependability coefficients for the 8SQ and DES-IV change scores, from both the stability and dependability coefficients calculated for the absolute scores respectively. Table 2 presents the estimated reliability coefficients for the 8SQ and DES-IV change scores. Since Eq. (3) is based on the assumption of equal variances across measurement occasions, there is good reason to accept the dependability coefficients in Table 2 for the 8SQ and DES-IV change scores. Table I Means and standard deviations for the DES-IV and 8SQ (N=212) Occasion I Occasion 2 Change-scores 8SQ M so M SD M SD Anxiety Stress Depression Regression Fatigue Guilt Extraversion Arousal DES-IV Interest Joy Surprise Sadness Anger Disgust Contempt Hostility Fear Shame Shyness Guilt The variances for the 20 separate subscales for the 8SQ and DES-IV do not differ significantly across occasions as indicated by their product-moment correlation of (calculated on the before and after standard deviations). Evidently, the reliability estimates for the 8SQ are all fairly high, with the lowest coefficient being 0.80 for the Guilt subscale. In accord with the Spearman-Brown prophecy formula though, the estimated reliabilities for the various DES-IV subscales were generally a little lower than those for the 8SQ (the averages were 0.85 and 0.89 respectively). In particular, the dependability estimates for the subscales labelled, Interest, Joy, Surprise and Sadness all seemed less than optimally desirable. Taken overall however, 14 of the combined DES-IV and 8SQ subscales

14 exhibited reliability estimates of 0.80 or higher. This finding further supports the view that the change scores in the present study were reliable, thereby enabling the redundancy analyses to be undertaken with confidence that the results obtained would be justifiable. Table 2 Estimation of dependability coefficients for change scores (N=212) 8SQ Single-scale stabilities Single-scale dependabilities Change-score dependabilities Anxiety Stress Depression Regression Fatigue Guilt Extraversion Arousal DES.IV Interest Joy Surprise Sadness Anger Disgust Contempt Hostility Fear Shame Shyness Guilt Notes. Stability coefficients (for all 212 subjects) were calculated across an interval of at least 1week's duration (most often the interval was about 4weeks). The average stability coefficients for the 8SQandDES-IVwere 0.38 and 0.41 respectively. The average single-scale dependability coefficients were 0.94 and 0.76 respectively, while the average estimated dependability coefficients for the change scores were 0.89 and 0.85 respectively. Table 3 Significant roots for DES-IV /8SQ measures (N=212) Roots Rl Chi-square df. p < ' I Occasion I Changescores The intercorrelation matrix for the combined DES-IV/8SQ change score data is reported in Boyle (1986a).

15 Canonical analyses As the 8SQ comprised the smaller number of subscales, a total of eight canonical vectors was extracted. Of these, only the first three roots were statistically significant for the change-score data (Table 3). Clearly, these three roots accounted for most of the variance involved in the intersection of the 8SQ and DES-IV measures. Comparison with the canonical analyses performed on the first-occasion scores also indicated three canonical vectors as being significant, while for the second-occasion scores, four canonical vectors had significant roots. The strength of each canonical vector was given by the canonical roots (the squares of the canonical correlations, the later ranging from 0.67 down to 0.39 for the change-score data; from 0.83 down to 0.50 for the first-occasion data; and from 0.88 down to 0.33 for the second-occasion data). The number of multivariate relationships between the two inventories was clearly suggested by the vectors with significant roots. As for the nature of the canonical relationships, it is important to note that there was no point in rotating the canonical variates given the uncertainties about their interpretation discussed above (cf. Tatsuoka in Cattell, 1978, p. 393). Furthermore, the purpose of conducting the canonical analyses was to estimate the redundancy across the DES-IV and the 8SQ, rather than to examine the content similarities and differences, per se. As Tabachnick and Fidell (1983, p. 148) stated, "Canonical correlation has several important theoretical limitations that may explain its rarity in the literature. Perhaps the most critical limitation involves interpretability..." Undoubtedly, the interpretation of content similarities and differences based on orthogonal canonical variates is potentially ambiguous. While computation of total redundancy requires the extraction of the complete set of canonical variates (eight in the present instance), it would seem unjustified,

16 however, to include more than the significant variates in the redundancy calculations, given the measurement error in most psychological data (cf. Weiss, 1976). This seems all the more important when calculations are based on change scores as in the present context. As Boyle et al. (1985, p. 116) pointed out, "The test of significance is one of equality of the remaining roots. Conceptually this is similar to Bartlett's test for principal components, and hence it is unclear what meaning can be drawn from the total redundancy values or the later roots". Table 4 presents the calculation of the redundancy indices on the changescore data for the three significant DES-IV/8SQ variates only. As is evident, the DES-IV accounted for approximately 26% of the measurement variance contained in the 8SQ, while the 8SQ explained about 17% of the variance in the DES-IV. In pan, the difference in these two estimates of redundancy was due to the different number of subscales in each instrument. Since all calculations were based on subscale scores instead of individual items (necessitated by the limited sample size of 212 subjects), the 12 subscales of the D2S-IV explained more of the 8SQ variance than did the eight subscale scores of the 8SQ in relation to the DES-IV. Had items been used as the basis for the canonical-redundancy calculations, it is likely that the proportions of variance predicted for each measure would have been reversed in order of magnitude. Nevertheless, while it is apparent that these two Table 4 Canonical-redundancy calculations for change-score data Root CanonicalR (R,) RSquared (}.) Variance extracted(vc) Redundancy (l VC) I I DES-TV Redundancy calculated for significant roots only. Redundancy of 8SQ given DES-IV= Redundancy of DES-.IV given 8SQ=0.174.

17 multivariate mood-state inventories have some overlap in measurement variance, it is also apparent from the change-score data that this redundancy is only slight. In order to compare the canonical-redundancy findings for the change-score data with the estimates calculated from single-occasion scores, the DES-IV/8SQ scores for each separate measurement occasion were similarly subjected to the above procedures. The results of these calculations are presented in Tables 5 and 6 respectively. As is evident, for the first-occasion data, the DES-IV accounted for 47% of 8SQ variance, while the 8SQ explained 28% of the measurement variance in the DES-IV. For the second-occasion data, the DES-IV predicted 50% of the 8SQ variance, while the 8SQ accounted for 37% of DES-IV measurement variance. Averaged across both occasions, the DES-IV predicted 48% of 8SQ variance, while the 8SQ explained 32% of DES-IV variance. These redundancy estimates contrast markedly with the estimates derived from the change-score data. At first sight, it might appear that the use of change scores in canonical redundancy analysis leads to underestimates of the actual levels of redundancy. However, the question of probable "trait contamination" (Cattell, 1979, p. 320) must be raised as a likely causative agent in augmenting the redundancy estimates when the calculations were based on the single-occasion scores. According to Cattell, "it is very difficult indeed to find items for state measurement that do not also appreciably involve traits." In fact, in designing the 8SQ, Curran and Cattell (1976) used the personality trait sphere as a guide for deriving the major states incorporated in the measure. Accordingly, it is clear that the 8SQ contains significant trait variance.

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19 Table 7 Inter-inventory prediction equations from change-score data 8SQ No.of steps Anxiety Stress Depression Regression Fatigue Extraversion Arousal 0.18 DES-IV Interest Surprise 0.03 Sadness Anger Disgust Hostility Shame Shyness Equation 0.28Joy+0.31Sad+0.15Sha -0.26Joy+0.18Sad -0.30Joy+0.29Sad+0.14Shy 0.17Shy+0.24Sad -0.29Joy+0.22Sad -0.17Joy++0.17Sad+0.19Hos+0.19Shy+0.14Ang 0.34Joy-0.21Sad-0.28Sha-0.18Gui 0.32Joy-0.23Shy -0.19Ax -0.24Ax+0.22Ex-0.16Fa -0.17Gi 0.24Gi+0.19Ax+0.18De 0.29Gi+0.16Ax 0.30Gi-0.16Ar 0.26Gi 0.46Gi 0.28Gi+0.19Ax 0.25Gi-0.24Ex 0.41Gi-0.13Ar 0.40Gi-0.23Ex+0.20Ax Suggested equations are shown only for the number of significant steps in each instance. Standardized regression coefficients used for ease of interpretation. The average multiple R 2 for the 8SQ was 0.24, whereas that for the DES-IV was This suggests that the DES-IV accounted for 24% of 8SQ variance, while the 8SQ predicted 17% of DES-IV variance. The higher redundancy estimates from the single-occasion measures therefore partly reflect the communality of trait variance per se, quite apart from the overlap in the stage-change variance. However, as Cattell and Brennan (1986) have shown, when change scores are used, this trait contamination is not a problem, as it would not be expected to be. Stepwise regression analyses On the basis of the article by Goldberg (1977), forward stepwise regression analyses were conducted on each ofthe 20 separate subscales in the combined DES- IV and 8SQ inventories, using the subscales from the other inventory as independent variables. This approach to the estimation of measurement overlap between the two instruments not only provided an estimate of prediction accuracy (multiple R2 ), but also resulted in the best fitting linear prediction equation for each subscale in the two instruments. The findings based on analyses of the state-change

20 data are presented in Table 7. The average multiple R 2 for the 8SQ subscales was 0.24 whereas that for the DES-IV was This suggests that the DES-IV predicted 24% of the 8SQ measurement variance, while the 8SQ predicted 17% of DES-IV variance. These estimates support the corresponding estimates of redundancy from the canonical analyses. Examination of Table 7 also demonstrates that the DES-IV subscales, Joy and Sadness were the main predictors for most of the 8SQ subscales. As for the prediction of the DES-IV subscales, the 8SQ factor labelled Guilt was the major predictor for no less than 10 of the 12 subscales. For comparative purposes, the corresponding regression analyses were computed for the single-occasion data for both and before and after measures. These findings are presented in Tables 8 and 9 respectively. Including these additional analyses served the important goal of providing cross-validational evidence. For the before and after measures respectively, the average multiple R2 was 0.46 and 0.49 for the prediction of the 8SQ from the DES-IV, while for the prediction of the DES- IV from the 8SQ the average estimates of redundancy were 0.28 and 0.36, in tum. These redundancy estimates match those obtained for the canonical analyses of the respective single occasion data. Once again, it is clear that a few of the DES-IV subscales (notably Sadness and Joy) played a major role in predicting 8SQ measurement variance, while the 8SQ Guilt subscale was the main predictor of DES-IV subscales. In conclusion, it is likely that neither the DES-IV nor 8SQ inventories are adequate measures of the mood-state sphere (at least for the two instruments alone), given that in terms of state-change variance each measure seems to comprise essentially discrete measurement variance. It is possible though, that one of the two instruments might be a reasonable measure of the mood-state sphere

21 SSQ Anxiety Stress Depression Regression Fatique Guilt Extraversion Arousal DES-IV Interest Joy Surprise Sadness Anger Disgust Contempt Hostility Fear Shame Shyness Guilt Table 8 Inter-inventory prediction equations from Occasion I data No.of Mutt. steps R I 0.11 I I 0.09 I Equation 0.27Sad-0.29Joy+0.22Ang+0.21Fea+0.19Hos-0.16Shy-0.09Con 0.29Joy+0.I8Ang+0.26Fea-0.29Shy 0.35Sad-0.44Joy+0.18Ang 0.31Sad-0.29Joy+0.21Sha 0.20Sad-0.29Joy+0.17Ang 0.19Sad-0.25Joy+0.29Gui+0.31Hos-0.13Sur-0.13Shy+0.13Fea -0.27Sad+0.36Joy+0.21Fea-0.20Shy-0.19Sha+0.13Sur -0.25Sad+0.30Joy-0.19Hos+0.16Sur -0.33De -0.64De 0.17Gi+0.18Ar 0.42Gi +0.33De 0.24 Gi+0..3Ax 0.40Gi +0.19St 0.29Gi 0.63Gi 0.35Gi +0.39Ax+0.I7Ar 0.43Gi-0.22De -0.22Ex+0.20Rg 0.32 Gi-0.26Ex-0.17Fa 0.66Gi-0.15Fa Suggested equations are shown only for the number of significant steps in each instance. Standardized regression coefficients used for ease of interpretation. The average multiple R 2 for the 8SQ was 0.46, whereas that for the DES-IV was This suggests that the DES-IV accounted for 46% of 8SQ variance, while the 8SQ predicted 28% of DES-IV variance. These estimates include predicted variance due to trait contamination however.

22 Table 9. Inter-inventory prediction equations from Occasion 2 data 8SQ No.of steps Mult. R' Equation Anxiety Sad-0.16Joy+0.18Ang-.15lnt+O.I4Fea-0.13Shy Stress Sad-0.25Joy Depression Sad-0.27Joy0.19lnt Regression I Sad Fatigue Sad-0.20Joy-0.16Sur Guilt Sad-0.20Joy+0.16 Gui+0.15Fea-0.13/nt+0.12Dis Extraversion Sad+0.16Joy-0.17Shy+0.16Sur+O.IS!nt Arousal Sad+0.24lnt+0.14Con+0.14Sur DES-IV Interest I De Joy Gi-0.57De Surprise Gi +0.40Ar+0.32Rg Sadness Gi +0.49De+0.25Ax-0.11Fa Anger Gi+0.28De+0.35Ax-0.19Fa Disgust Gi+0.25Ax Contempt Ax+0.35Ar+0.34De Hostility Gi +0.43De-0.20Fa Fear Gi+0.27Ax Shame Gi-0.17Ar Shyness Gi-0.19Ex Guilt I Gi Suggested equations are shown only for the number of significant steps in each instance. Standardized regression coefficients used for ease of interpretation. The average multiple R 2 for the 8SQ was 0.49, whereas that for the DES-IV was.36. This suggests that the DES-IV accounted for 49% of 8SQ variance, while the 8SQ predicted 36% of DES-IV variance. These estimates include predicted variance due to trait contamination however. and that the other is inadequate. However, examination of external and construct validity characteristics of these two inventories (cf. Boyle, 1985b) suggests that this interpretation is not accurate. In this context, development of a more comprehensive mood-state instrument is clearly desirable. It should therefore be feasible to reduce the total number of subscales considerably from the 20 presently contained in both the DES-IV and 8SQ inventories combined.

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