With rapid advances in technology, patients' health-care needs are constantly becoming more community based, individualized, and technology integrated. To keep pace with these changes, continuing education (CE) for nurses is more important than ever.
Empirical studies on CE have emphasized its role in nursing. However, an understanding of the effectiveness of CE in nursing still remains fragmented due to a focus on determining the efficacy of isolated CE programs. Such an approach ultimately fails to provide a unified picture of CE in nursing (Griscti & Jacono, 2006). Above all, a lack of analyses underpinning CE programs that use nurses' competency as the outcome measure was noted (Griscti & Jacono, 2006).
So far, randomized controlled trials (RCTs) have been used as the main research methodology to determine the efficacy of the nursing intervention (Park, Park, & Ocak, 2016). RCTs can produce strong evidence by directly comparing two groups (National Evidence-Based Healthcare Collaborating Agency, 2013). However, the RCT's design approach is limited in evaluating the actual trajectory of the nursing outcome due to the following flaws: (a) the rigorously controlled conditions and short research durations cannot fuslly reflect reality; (b) RCTs cannot virtually explain the process by which the outcome indicator changes as predictors change; (c) selective and fragmented reports about a trend are commonly reported in RCTs; and (d) if results of the RCTs are not statistically significant, it is difficult to publish the study findings (National Evidence-Based Healthcare Collaborating Agency, 2013; Park et al., 2016). Given the limitations of RCTs, this phenomenon needs to be reexamined using an analysis of change, which may fill the gaps left by the weaknesses associated with RCTs.
Growth curve modeling (GCM) provides an effective analysis of change for characterizing overall change for a sample, describing interindividual differences in change and predicting those interindividual differences (Singer & Willett, 2003). This method can provide answers that are difficult to obtain from an RCT's design, namely why some people show better outcomes than others and which contextual factors explain some of those interindividual differences, both in level and in rate of change.
Intraindividual variability refers to transient within-person fluctuations in the outcome measure (Allaire & Marsiske, 2005). The intraindividual variability index (IVI) is a reliable trait-like indicator of a within-person consistency in the outcome measure (Walls & Schafer, 2006). The learning process involves practice-related improvements over time, leading to the inflation of intraindividual variability (Allaire & Marsiske, 2005). Thus, it is necessary to detrend the data before computing IVI to gain an uncontaminated IVI by the learning effect. For detrending, GCM first needs to be performed with independent variables, including the linear and quadratic effects in the rate of change, which controls the intraindividual differences in learning (Allaire & Marsiske, 2005). The detrended IVI offers an insightful analysis of change in nursing, which can reveal new knowledge that existing traditional statistical analyses cannot, thereby highlighting possible solutions to unanswered questions in nursing research.
These methods are particularly meaningful to nursing education research because they can track the effectiveness of nursing education over time beyond confirming its efficacy to ensure a reasonable quality of nursing care and education. In addition, research evidence on the analysis of change of the effectiveness of nursing education over time is very limited, although the efficacy of the education has been widely reported. For example, from 2006 to 2016, the number of research reports using GCM and IVI were just two and zero, respectively. In conrast, approximately 500 studies determined a onetime statistical significance on the efficacy of nursing education in a cross-sectional way. This literature search was performed in PubMed®, CINAHL® and Web of Science® during February 2016. The key words were continuing education in nursing, growth curve modeling, intra-individual variability, and efficacy.
A lack of knowledge about the trajectory depicting changes in effectiveness may prevent nurse educators from determining the optimal point in time to provide educational boosters or to operationalize predictors that can significantly improve the effectiveness of nursing education. This study thus addressed the research gap by exploring the trajectory of the effectiveness of CE using both GCM and IVI. To demonstrate specific step-by-step procedures and the application of GCM and IVI, secondary analysis was performed using the data collected by Yun, Lim, and Park (2012) in the setting of case management (CM) between May 2008 and August 2009, where the analysis of change studies are particularly rare in the literature. Detailed procedures articulated in this article will help future nurse scientists to use GCM and IVI to facilitate an analysis of change in nursing education research.
This study is a secondary analysis of CE in nursing data that uses GCM and IVI to introduce a new analysis of change uncontaminated by the learning trend.
The original study examined the effects of the three levels of CE for case managers through the equivalent nonparametric Friedman test (Yun et al., 2012). Yun et al. (2012) reported a significantly improved group level of knowledge, attitude, and skill across four occasions (i.e., the number of time points used in data analysis: the pre- and posttest of the first CE, the posttest of the second CE, and the posttest of the third CE).
The original data were collected from the 22 case managers affiliated with the Korean National Health Insurance Corporation that attended three levels of CE to improve the managers' competency. Data collection was performed immediately before and immediately after each CE, using a total of three sets of pre- and posteducation questionnaires (Yun et al., 2012). Data collection intervals were approximately 1 year between the first and second sets and 2 months between the second and third tests.
GCM was executed first, followed by the generation of a detrended intraindividual standard deviation for IVI. Finally, Pearson's correlation analysis was conducted using the IVIs (Figure 1). Data analysis was performed using IBM® SPSS® Statistics version 21.0 for Windows® from June to September 2014 and from January to February 2016.
Analytic procedure process. * Case management.
Growth Curve Modeling
Dependent Measure. Case managers' competency, which was assessed after each education session, is an outcome measure for this study. The instrument, developed with Level 1: Reaction and Level 2: Learning and based on Kirkpatrick's and Kirkpatrick's (1998) four steps evaluation model, is composed of three domains: knowledge (e.g., sixth question: “I can articulate how to do medication counseling to patients with hypertension or diabetes mellitus”), attitude (e.g., tenth question, “Through case managers' contribution, patients' unreasonable [too much/too little] health care utilization can be controlled”), and skill (e.g., fifth question: “I can perform CM planning, implementing, and evaluation depending on the patient-individualized needs”). All domains were measured using a 5-level Likert scale questionnaire ranging from 1 = strongly disagree to 5 = strongly agree. The instrument consists of three domains that total 32 items: knowledge (10 items), attitude (10 items), and skill (12 items). The maximum score is 160, indicating higher competency, whereas the minimum is 32. The Cronbach's alpha coefficient of each domain was .951, .903, and .944 (Yun et al., 2012), respectively, indicating a satisfactory reliability of the instrument. The mean and SD of case managers' competency in the sample are presented in Table 1.
Mean and SD of Dependent Measure and Time-Varying Measures for Growth Curve Modeling
Time-Varying Measures and Time-Invariant Measures. Time-varying measures were assessed to reduce variability between occasions within each case manager in estimating the growth of case managers' competency over time. These include pre-knowledge, pre-attitude, and pre-skill scores, which were assessed immediately before each education session. These three time-varying predictors were then broken into person means (Level 2) and time-varying, mean-centered values (Level 1) (Figure 2). Table 1 describes the mean and SD of pre-knowledge, pre-sttitude, and pre-skills in the sample. Time-invariant measures were explored to determine whether they explain variances between case managers in their competency growth trajectories. These include education level and the working period in CM.
Composition of measures. * Case management.
Centering. Before analysis, all predictor variables and the outcome measure were centered into a Z score to (a) minimize multicollinearity between predictors; (b) ensure better stability for the estimation procedures (Hadley & Holt, 2006); and (c) obtain pseudostandardized beta weights (Singer & Willett, 2003). An estimation of standardized coefficients in the model with random effects is impossible due to the uncertainty of the standard deviation in the dependent measure (Hoffman, 2015). Z scores are by definition centered at zero and are in a standardized metric format, which enables the effect sizes across predictors to be scale free and comparable (Singer & Willett, 2003).
Modeling. Hierarchical Linear Modeling (HLM), adapted as the mixed-model modeling (MMM) approach, was used to model intercept, linear, and quadratic growth overall. Yun et al. (2012) excluded two participants in their article due to considerable missing values; however, for this study, all participants were analyzed because MMM is flexible in handling (a) unequal spacing of occasions, (b) missing occasions, and (c) people with varying numbers of occasion (Singer & Willett, 2003). Parameterizations of random and repeated error structures were also applied to find the best fitting model in the estimation of growth in case managers' competency over time. Finally, maximum likelihood estimation was applied throughout the study.
Intraindividual Variability Index
Indexing. Case managers' individual competency inconsistency was indexed using IVI. The purified residual T scores were used, which were computed to (a) save residuals generated by MMM using the best fitting model (i.e., Model E) in the estimation of case managers' competency growth trajectory; (b) standardize residuals to be centered into the Z score; and 3) linearly transform them as T scores. This process makes IVIs uncontaminated by the learning trend. It also regresses out predictors, which were identified as significant time-varying and invariant measures to explain within-and between-variability in their competency growth trajectories. Because those predictors might contribute to individual differences in case managers' competency inconsistency, it is advisable to covary them out (Dixon, Bäckman, & Nilsson, 2004). In addition, it makes IVIs comparable with each other by equating IVIs across participants and variables (Hultsch, MacDonald, Hunter, Levy-Bencheton, & Strauss, 2000).
Person-Level Variables. The following variables were explored to determine the relationship with case managers' IVIs:
- Education level.
- Working period in CM.
- Person mean pre-knowledge.
- Person mean pre-attitude.
- Person mean pre-skill.
All predictors were centered into a Z score to obtain standardized estimates of correlation coefficients.
This study was approved by the Institutional Review Board of the University of Florida. In addition to the official permission to use data from the principal investigator of the original study, deidentified data were obtained.
A total of 22 participants included more male case managers (n = 18, 81.8%) than female case managers (n = 4, 18.2%), with no significant age difference between them (p > .05), and with the mean (SD) of men = 46.06 (4.36) versus women = 44.00 (3.65). Participants' highest education levels were college (n = 6, 27.3%), university (n = 11, 50%), and graduate school (n = 5, 22.7%). No statistically significant differences in pre-knowledge, pre-attitude, and pre-skills for CE 1 by education level were presented, p > .05 (F = .033, .193, .318, respectively). The overall average working period in CM was 4 (0.69) years.
Growth Curve Modeling
A total of five models of individual growth in case managers' competency were tested:
- Model A, unconditional means model.
- Model B, unconditional linear growth model.
- Model C, unconditional linear and quadratic growth model.
- Model D, conditional intercept model (allowing interactions between education level and quadratic growth in case managers' competency).
- Model E, conditional intercept model (parameterizations of random and repeated error structures [“Variance Components” and “Diagonal,” respectively] were applied to Model D).
Table 2 summarizes the results of the HLM analyses, and Table 3 describes how much each model fit had been improved, compared with Model A.
Fixed and Random Effects between Growth Models
Comparisons of Model Fit Statistics
Individual Differences in Case Managers' Competency Growth Trajectory. A significant correlation was found between person variability in both the starting level and the linear time slope. It was not until Model E was examined that individual differences in linear time slope in case managers' competency were clearly apparent (β = .087, p = .006). Significant individual variations between case managers in their average competency standard initial scores were also presented (β = .073, p = .016). However, individual differences of quadratic growth in case managers' competency had not been estimated throughout the analyses because of terminated iteration or the Hessian problem, which occurs when a random error structure of the mixed model does not have the same positive diagonal variances (Gill & King, 2004). The statistical software can then no longer work out to create stable estimates because no available variation exists in the data for that effect to exist, which suggests the need to remove the random effect of the mixed model (Gill & King, 2004). (Table 2).
Predictors Explaining Within- or Between-Variability. Model E also revealed significant fixed effects of linear and quadratic growth over time (β = 1.037, p = .015 and β = −.834, p = .041). However, case managers' average competency standard initial score was not statistically significant (β = .007, p = .992), indicating that it was marginally different from zero. These indicate that the average person began with a standard initial score of .007 and gained 1.037 standard units in the linear growth, leveling off at −.834 standard units in the negative quadratic curvilinear per every 1 standard unit increase in occasion, which was statistically significant (p < .05) (Table 2).
Among the individual predictors, person mean pre-attitude, person mean pre-skill, and education level had statistical significance in the overall estimates of growth in competency (β = .285, p = .020; β = .357, p = .036; and β = −.154, p = .049, respectively). This means that on average, person mean pre-attitude and person mean pre-skill were, by 1 standard unit, associated with higher competency by a beta weight of .285 and .357, which was statistically significant (p < .05). However, on average, an education level was, by 1 standard unit, significantly associated with lower competency by a beta weight of −.154 (p < .05).
Beyond that, an interaction between the education level and quadratic growth in competency approached statistical significance in the overall estimation of individual competency growth trajectories (β = −.126, p = .074). This means that as case managers' education level increased by 1 standard unit, the average person leveled off at −.126 standard units more in the overall time slope in the estimation of case managers' competency trajectory.
Parameterizations of Random and Repeated Error Structures. Three types of repeated error structures, which refers to the matrix of the variances and covariances of the population average (fixed) effects (i.e., types include AR1, diagonal, and unstructured), and two types of random error structures, which refers to the matrix of variances and covariances of the subject-specific (random) effects (i.e., types include variance components and unstructured), were separately examined using Model D. All structures were not converged, excluding the diagonal repeated error structure and the variance components random error structure, which demonstrated Model E as the best fitting model in this study (−2LL, 91.870; AIC, 119.870; BIC, 149.874). A diagonal repeated error structure presents a different estimate of variance at each occasion because it is no longer imposing homogeneous variance terms. For Model E, the within-person variance of the second occasion was statistically significant with an estimate of .229 (p = .005), whereas the first and third occasion had insignificant within-person variability with estimates of .135 (p = .172) and .000 (p = .997). This suggests that the second occasion has meaningful fluctuations to explain case managers' individual differences in competency variability.
Testing Deviance Between Models. Compared with Model A, Model E dramatically improved the model fit (χ2  = 63.822, p = .001, 68.1%) of the explainable variation between occasions within each case manager in estimating a growth in competency was explained; further, statistically significant within-person variability was no longer detected at the first and third series with β = .135 (p = .172) and β = .000 (p = .997). In addition, Model E explained 88% of the explainable variation between case managers in their average competency growth trajectory, compared with Model A. However, significant individual differences still existed between case managers in their average competency standard initial scores, worth about .073 variance points (Tables 2–3).
Intraindividual Variability Index
Correlation coefficients between nine person-level variables and case managers' IVIs ranged from −.501 (education level, p = .017) to .342 (gender, p = .119). Of note, education level was only significantly associated with case managers' IVIs (p = −.501, p < .05), indicating that the higher the education level, the less intraindividual variability in the overall estimates of growth in competency. Gender also approached statistical significance (p = .119). However, all other person-level variables were not statistically significant (p > .05).
Nursing research on CE using both GCM and IVI is limited. Most prior research on CE in nursing addressed efficacy in a fragmented way and contained methodological and statistical limitations (Griscti & Jacono, 2006). In fairness, GCM and IVI approaches are not antithetical to the RCTs mainly used in previous studies. However, these hybrids seldom exist in nursing literature, despite their ability to address unanswered questions in nursing research. This study was meaningful in that it introduced how using GCM and IVI can create an advanced analysis of change, highlighted detailed procedures about GCM and IVI, facilitated planning studies, and provided significant findings that have not been addressed in previous studies.
Specifically, GCM revealed (a) that individual differences existed in case managers' competency growth trajectory; (b) significant predictors explaining that the differences within and between subjects were person mean pre-attitude, person mean pre-skill, and case managers' education level; and (c) the overall slope in case managers' competency growth trajectory was quadratic curvilinear, as well as linear (i.e., it improves initially, but the rate of improvement decreases as improvement continues over time). Yun et al. (2012) reported that case managers had a significantly improved competency level in knowledge, attitude, and skill at the group level across all series of CE. However, because ANOVA pooled random effects and errors, the study by Yun et al. (2012) contains a methodological limitation in revealing the various dynamics in their improvement process (i.e., reliable individual differences both in the level and in the rate of change in a case manager's competency level) (Kristjansson, Kircher, & Webb, 2007).
Second, the inclusion of person mean pre-attitude, person mean pre-skill, and level of education led to greater precision in the estimation of case managers' individual competency growth trajectories, which were core foundations for the emergence and distinctive growth of competency. These suggest that weighting the domain of attitude and skill in the composition of CE could be more effective in improving a case manager's competency level over time.
Third, a significant negative parameter of the education level was presented (β = −.154, p = .049), indicating that for all case managers, the higher the education level, the lower the competency level over time. A significant negative correlation also existed between educational level and intraindividual competency inconsistency (r = −.501, p < .05), indicating that the higher the education level, the less intraindividual variability in their competency growth trajectory (i.e., the less they learned compared with case managers with a lower education level). That is to say, for case managers with a higher education level, fewer improvements in their competency level were observed over time, compared with case managers with a lower education level. The interaction between education level and quadratic growth in case managers' competency even approached statistical significance in the overall estimation of the model (β = −.126, p = .074), indicating that, for case managers with a higher education level, a greater decrease in competency level was observed over time, compared with case managers with a lower education level.
These findings were unexpected, considering that the positive relationship between participants' education level and outcome variables in nursing research has been statistically significant in most of the previous studies. GCM and IVI, a new analysis of change, revealed the noteworthy findings that various dynamics existed in participants' improvement process—reflecting participants' individual changes—while the overall significant improvement of competency level was observed (Yun et al., 2012). The authors think these novel results support the significance of this study.
However, these results were not surprising considering that CE for case managers focuses on maintaining a reasonable level of competency to meet patient-centered needs. These results may reflect case managers' dissatisfaction with CE, which could result from unmet educational needs, such as unaddressed content to encourage intellectual curiosity and meet current patients' needs (Griscti & Jacono, 2006). A careful needs assessment before CE and an implementation of various educational methods is necessary so that all case managers—regardless of their education level—can feel a sense of achievement.
Above all, the trajectory depicted a notable negative quadratic curvilinear, reflecting a leveling-off slope. This may indicate that the 2-month interval between the second and third training session was inadequate to make a continuous significant difference. Considering that CE operation is accompanied by considerable educational costs and requires high-quality human resources, an identification study on the optimal interval of CE is necessary.
Finally, it may be meaningful that female case managers had more competency inconsistency than male case managers (r = .342, p = .119), suggesting that female case managers learned more over time. Previous research suggests gender differences in the learning process, but the results of the current study may be the first to report gender differences in nursing education. The mode of teaching may be gender dependent, but this demands further investigation to examine which characteristics differentiate the competency inconsistency by gender.
However, the results from this study should be interpreted with a degree of caution because the effect size of each parameter for GCM and the magnitude of each correlation coefficient between predictors and case managers' IVIs was based on limited repeated measures and a small sample size. Hox (2002) suggested that 100 cases and at least 10 measures per case are required for models interested in variance. Salthouse, Nesselroade, and Berish (2006) also reported that more than 50 measures were required to achieve an asymptotic level of competency. Because only three measures were used for this study, further study is recommended to ensure reliable findings.
In addition, the sample size is also quite small (N = 22). Although power analysis for Pearson's correlation analysis supported a total of 22 cases to ensure statistical significance, given an alpha of .05, a power of .80, and a coefficient determination of .05, at least 30 cases are required for GCM (Snijders & Bosker, 1999). Because IVIs were generated from GCM using Model E, with a total of 22 cases, caution is advised in interpreting the current study's findings.
However, MMM accounts for sample-dependent random variance, as well as fixed effects, balancing the small sample size without losing valuable information (Zannella, 2009). MMM also provides good flexibility for handling a spare dataset (Singer & Willett, 2003). In addition, the current study primarily aimed to present a step-by-step analysis of change procedure so readers can apply this innovative methodology to their own research. The authors believe that the importance of the current study's new knowledge surpasses the limitation of the small sample size.
The threat of internal validity caused by the repeated measures of the same questionnaires may be another concern. However, the interval between the first and second education was 1 year, indicating that the duration was too long for participants to remember the questionnaires previously used. The difference in competency level between the second and third education was also not statistically significant (p > .05), suggesting that the testing effect was minimal (Yun et al., 2012).
- Allaire, J.C. & Marsiske, M. (2005). Intraindividual variability may not always indicate vulnerability in elders' cognitive performance. Psychology and Aging, 20, 390–401. doi:10.1037/0882-7918.104.22.1680 [CrossRef]
- Dixon, R.A., Bäckman, L. & Nilsson, L.-G. (2004). New frontiers in cognitive aging. New York, NY: Oxford University Press. doi:10.1093/acprof:oso/9780198525691.001.0001 [CrossRef]
- Gill, J. & King, G. (2004). What to do when your Hessian is not invertible: Alternatives to model respecification in nonlinear estimation. Sociological Methods & Research, 33, 54–87. doi:10.1177/0049124103262681 [CrossRef]
- Griscti, O. & Jacono, J. (2006). Effectiveness of continuing education programmes in nursing: Literature review. Journal of Advanced Nursing, 55, 449–456. doi:10.1111/j.1365-2648.2006.03940.x [CrossRef]
- Hadley, P.A. & Holt, J.K. (2006). Individual differences in the onset of tense marking: A growth-curve analysis. Journal of Speech, Language, and Hearing Research, 49, 984–1000. doi:10.1044/1092-4388(2006/071) [CrossRef]
- Hoffman, L. (2015). Longitudinal analysis: Modeling within-person fluctuation and change. New York, NY: Routledge, Taylor & Francis.
- Hox, J.J. (2002). Multilevel analysis: Techniques and applications. Mahwah, NJ: Lawrence Erlbaum Associates.
- Hultsch, D.F., MacDonald, S.W., Hunter, M.A., Levy-Bencheton, J. & Strauss, E. (2000). Intraindividual variability in cognitive competency in older adults: Comparison of adults with mild dementia, adults with arthritis, and healthy adults. Neuropsychology, 14, 588–598. http://dx.doi.org/10.1037/0894-422.214.171.1248 doi:10.1037/0894-4126.96.36.1998 [CrossRef]
- Kirkpatrick, D.L. (1998). Evaluating training programs: The four levels. San Francisco, CA: Berrett-Koehler. Retrieved from https://www.amazon.co.uk/Evaluating-Training-Programs-Four-Levels/dp/1576750426
- Kristjansson, S.D., Kircher, J.C. & Webb, A.K. (2007). Multilevel models for repeated measures research designs in psychophysiology: An introduction to growth curve modeling. Psychophysiology, 44, 728–736. doi:10.1111/j.1469-8986.2007.00544.x [CrossRef]
- National Evidence-Based Healthcare Collaborating Agency. (2013). A summary of methods for comparative effectiveness research (Version 1). Retrieved from http://www.neca.re.kr/center/researcher/book_view.jsp?boardNo=CA&seq=6098&q=626f6172644e6f3d4341
- Park, C.S., Park, E.O. & Ocak, M.A. (2016). Comparative effectiveness research and its application to nursing education. Journal of Learning and Teaching in Digital Age, 1(2), 10–19. Retrieved from http://joltida.org/index.php/joltida/article/view/3
- Salthouse, T.A., Nesselroade, J.R. & Berish, D.E. (2006). Short-term variability in cognitive competency and the calibration of longitudinal change. Journal of Gerontology, 61, 144–151. doi:10.1093/geronb/61.3.P144 [CrossRef]
- Singer, J.D. & Willett, J.B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. London, UK: Oxford University Press. doi:10.1093/acprof:oso/9780195152968.001.0001 [CrossRef]
- Snijders, T.A. & Bosker, R.J. (1999). Multilevel analyses: An introduction to basic and advanced multilevel modeling. London, UK: Sage.
- Walls, T.A. & Schafer, J.L. (2006). Models for intensive longitudinal data. London, UK: Oxford University Press. doi:10.1093/acprof:oso/9780195173444.001.0001 [CrossRef]
- Yun, S.N., Lim, S.J. & Park, S.Y. (2012). Effects of CE for healthcare manager on knowledge, attitude, and skills. Korean Journal of Occupational Health Nursing, 21, 184–191. http://dx.doi.org/10.5807/kjohn.2012.21.3.184 doi:10.5807/kjohn.2012.21.3.184 [CrossRef]
- Zannella, K. (2009). Nonlinear mixed-effects modeling of population pharmacokinetics data. MATLAB Digest, 1–5.
Mean and SD of Dependent Measure and Time-Varying Measures for Growth Curve Modeling
|Continuing Education Session||Time-Varying Measure||Dependent Measure|
|Preknowledge||Preattitude||Preskills||Case Managers' Competency|
|First||4.30 (.48)||4.39 (.39)||4.31 (.43)||139 (13.62)|
|Second||4.24 (.46)||4.39 (.48)||4.37 (.46)||145 (12.48)|
|Third||4.34 (.48)||4.40 (.39)||4.42 (.42)||146 (12.85)|
Fixed and Random Effects between Growth Models
|Effects||Model A||Model B||Model C||Model D||Model E|
| Person mean pre-knowledge||.086||.195|
| Person mean pre-attitude||.309*||.285*|
| Person mean pre-skill||.432*||.357*|
| Education level||−.188*||−.154*|
| CM working period||.055||.045|
|Rate of change|
| Linear growth||.207*||1.021*||1.031*||1.037*|
| Quadratic growth × Education level||−.820*||−.829*||−.834*|
| Level 1|
| First occasion||.135|
| Second occasion||.229**|
| Third occasion||.000|
| Level 2|
| In rate of linear change||.064||.077||.052||.087**|
| In rate of quadric change||—a||—b||—b|
Comparisons of Model Fit Statisticsa
|Modelb||−2LL||AIC||BIC||df||χ2||Residual||Eta R2Withinc||Intercept||Eta R2Betweend|