This study used a three-year panel dataset obtained from the central computerized management systems for the smoking cessation programs of the community health centers in the nation. Data were stored from July 16, 2005 until July 15, 2008. 711,862 smokers were registered and re-registered for the programs for the period. 860 of those who were retained for three years in the programs were finally included in the dataset. For the study, success in smoking cessation means smokers did not smoke cigarettes for the past consecutive six months. The rate of success in smoking cessation each year is as follows: 32.7% (1st), 29.7% (2nd), 12.9% (3rd). The majority of the smokers were men (n = 800, 93%). Average age of the smokers was 49.2 years (standard deviation = 12.8 years). About 90% (n = 770) had health insurance. Half (n = 369) lived in smaller cities (Table 1). The reliability of the variables such as nicotine dependence and average smoking, which was measured each year for the three-year period of the study, showed high internal consistency (Cronbach's α = 0.780 and 0.788, respectively).

To measure nicotine dependence, a revised Fagerström Test for Nicotine Dependence (FTND) was used, which is currently in wide use on a global level [18,19]. The FTND is consisted of the following six items: 1) 'How many cigarettes do you smoke a day?' (0-10, score 0; 11-20, score 1; 21-30, score 2; >31, score 3); 2) 'How soon after you wake up do you smoke your first cigarette?' (≤5 minutes, score 3; 6-30 minutes, score 2; 31-60 minutes, score 1; >60 minutes, score 0); 3) 'Do you find it difficult to refrain from smoking in places where it is forbidden?' (yes, score 1; no, score 0); 4) 'Do you smoke if you are so ill that you are in bed most of the day?' (yes, score 1; no, score 0); 5) 'Do you smoke more frequently during the first hours of waking than the rest of the day?' (yes, score 1; no, score 0); and 6) 'Which cigarette would you hate most to give up?' (morning cigarette, score 1; other cigarette, score 0). In scoring the revised FTND, the items are summed to yield a total score of 0 (very low) to 10 (very high) [19]. The community health centers in Korea also used this questionnaire to measure nicotine dependence of smokers [4,18].

In the study, average smoking was operationalizing as the number of cigarettes smoked a day for the entire smoking period until the smokers visited the smoking cessation clinic in the community health centers.

To examine the longitudinal relationships between nicotine dependence and smoking, an autoregressive cross-lagged (ARCL) model was explored. The core of the ARCL is that the value at the time of [t] is explained by the value at the time of the previous point, [t-1] [20,21]. In order to explore the ARCL model, the order of analyses should be followed by homogeneity of measurements, paths, and error covariance.

Homogeneity means that "statistical properties of any one part of an overall dataset are the same as any other part" [22,23]. Homogeneity of measurements is conducted to test whether the concept is measured at each time point for a longitudinal study or measuring the changes on the concept over time. Therefore, factor loadings of the same questions (study variables) should be constrained equally [21]. Because this study employed only one observed variable, homogeneity of measurements was not examined.

Homogeneity of paths is conducted to test the regression coefficients for each observed variable is stable over time. It can be tested by comparing if the impact of the variable (regression coefficient) at the time of [t-1] on the variable at the time of [t] is same with the impact of the variable (regression coefficient) at the time of [t] on the variable at the time of [t+1]. The regression coefficient can be labeled as stability coefficient [21].

To test homogeneity of error covariance is to equally constrain covariance between the errors of the variables. In order to evaluate the goodness-of-fit, χ² tests and the goodness-of-fit indices were considered. Among the various fit indices, incremental fit indices such as Comparative Fit Index (CFI), Normed Fit Index (NFI), Tucker-Lewis Index (TLI), and absolute indices such as Goodness Fir Index (GFI), Root Mean Square Error of Approximation (RMSEA) were used for the study [24-26].

In general, if the values of incremental fit indices such as the CFI are larger than 0.9, it means that the model fit is good [24,25]. The GFI has a value between 0 and 1, and the value should be greater than 0.9 for a model that fits well. The RMSEA was developed to correct the issue of statistics arising from χ² tests which include many observed variables. The value of RMSEA should be less than 0.05 for a model that fits well. Values of 0.06 to 0.08 indicate mediocre fit, and values greater than 0.1 indicate poor fit [25-28].

For the analyses of this study, SPSS ver. 19.0 was used for descriptive statistics and average analysis. To analyze the ARCL model, AMOS ver. 20.0 (IBM, New York, USA) for the structural equation modeling was employed.

The research questions (RQ) of this study are as follows:

The ARCL model was employed to test the above research questions (Figure 1).

Nicotine dependence and average smoking over the time period are described in Table 2. The value of skewness and kurtosis of nicotine dependence and average smoking supported the assumption of normal distribution of the data; the absolute value of skewness is less than 3, and the absolute value of kurtosis is less than 10 [29]. Therefore, there was no statistical problem in testing the ARCL model of structural equation modeling. Because structural equation models assume multivariate normal distribution, analyses were conducted under the assumption that observed variables are normally distributed.

Prior to analyzing the ARCL model, correlations between nicotine dependence and average smoking were analyzed. Table 3 presents strongly positive (+) correlations between variables.

To test homogeneity of paths and error covariance, the following six competitive models were developed:

To ascertain the optimal model of the above six models, statistical analyses were sequentially conducted, and its results were compared. Each model was nested; therefore, χ² tests were viewed as appropriate for the analyses. However, to increase the reliability of the statistical results, other goodness-of-fit indices such as CFI, GFI, NFI, TLI, RMSEA were applied because χ² tests has been recognized as problematic when related to sample size sensitivity [21,30]. Thus, as applied herein, if the fit indices were not more adverse when any constraint was applied, it was concluded homogeneity was established.

Although homogeneity constraints were added to the paths A-E, the fit indices were not getting worse (Table 4). The impact of the time of [t-1] on the time of [t] proved to be the same with the impact of the time of [t] on the time of [t+1] on all paths. Model 6 did not show a big difference with Model 5; therefore, considering model simplicity, Model 6 was selected as a final model for this study.

Table 5 presents path coefficients of the finally selected models: Model 6 and a base model. Path coefficients of Model 6 presented in Table 5 indicate that nicotine dependence and average smoking had strongly positive relations over time. Cross-relations flowing from nicotine dependence to average smoking over time were strongly static and vice versa. The impact of average smoking on nicotine dependence (β = 0.109, 0.101) was higher than the impact of nicotine dependence on average smoking (β = 0.085, 0.089). Therefore, it was concluded that it is possible to verify statistical causality by applying the ARCL model of nicotine dependence and average smoking.

A latent growth curve model was developed to explore trajectory changes of nicotine dependence and average smoking. It was noted that both nicotine dependence and average smoking were proved to be linear transformation models (Figures 2, 3).

In Table 6, the goodness-of-fit of nicotine dependence remained suitable for all other indices except the value of χ². In case of average smoking, all except the values of χ² and RMSEA were suitable.

Trajectory changes of nicotine dependence showed a linear model which had decreased for the three-year period. The mean intercept of nicotine dependence was 5.454, and it showed a steady decline of 0.247 on average over the period (Table 6). The values of the intercept and the variance of slope were statistically significant. The mean intercept of nicotine dependence had a significant difference between individuals. The slope also had a significant difference between individuals. In addition, the coefficient of correlation between the intercept and the slope was -0.288 indicating that the higher the intercept of nicotine dependence, the lower rate of decline.

Trajectory changes of average smoking also showed a linear model which had decreased for the three-year period. The mean intercept of average smoking was 21.758, and it showed a steady decline of 0.817 on average over the period. The values of the intercept and the variance of slope were statistically significant. The mean intercept of average smoking had a significant difference between individuals. The slope also had a significant difference between individuals. In addition, the coefficient of correlation between the intercept and the slope was -0.398 indicating that the higher the intercept of average smoking, the lower rate of smoking decline.

Figure 4 was proposed as a conditional model in this study. The model was developed based on the results of previous studies [4,13] and the correlation analysis between nicotine dependence and average smoking. In the study, it was specifically analyzed whether attempts for smoking cessation was successful or not and the impact of average smoking on behavior change that lower the level of nicotine dependence over time. A result from the analysis of the conditional model reported that all other fit indices except the value of χ² (55.410, df = 3) showed suitable fit (NFI = 0.952, CFI = 0.957, TLI = 0.909, RMSEA = 0.090) in the model.

Table 7 presented regression coefficients which affect the impact of whether attempts for smoking cessation was successful or not and average smoking on the intercept and the slope. The first success in smoking cessation had a negative (-) effect on the intercept of nicotine dependence (β = -0.085, p < 0.05). It showed a negative (-) effect on the slope (β = -0.183, p < 0.01) as well. In case of the person who was successful in smoking cessation (1st), the intercept of nicotine dependence was low, and nicotine dependence was decreased over time. Success in smoking cessation (2nd) had a negative (-) effect on the slope of nicotine dependence (β = -0.194, p < 0.05). The person who was successful in smoking cessation (2nd) also showed that nicotine dependence was decreased over time. The average smoking (1st) had a positive (+) effect on the intercept of nicotine dependence (β = -0.684, p < 0.01) and a negative (-) effect on the slope (β = -0.425, p < 0.01). Even though a person who had large amount of average smoking showed high nicotine dependence at the initial point measured, and nicotine dependence was decreased over time.