Autoregressive Latent Trajectory Research Articles

Parenting Behavior and Adolescent Conduct Problems

ABSTRACT This research examined the relationship between parenting practices and adolescent conduct problems and the mediation of these relationships by two parent-adolescent relationship variables, conflict and psychological autonomy. Autoregressive latent trajectory (ALT) analyses were used to assess relationships over time between parent practices and adolescent conduct problems. Participants were 2,453 students recruited from 7 public middle schools and assessed 5 times between fall of 6th and 9th grades on the following measures: Parent Monitoring; Parent Knowledge; adolescent Psychological Autonomy; parent-adolescent Conflict; and adolescent Conduct Problems. Adolescent Conduct Problems and parenting practices were associated in both cross-sectional and prospective analyses. In time-lagged autoregressive modeling as a part of ALT analyses, adolescent Conduct Problems and parenting practices were reciprocally related from Time 1 to Time 2, but there after only Parent Monitoring was consistently associated with adolescent Conduct Problems over time. Adolescent Psychological Autonomy positively mediated the relationships between adolescent Conduct Problems and Parent Monitoring, but not the relationship between Parental Knowledge and Conduct Problems; while Conflict partially mediated the relationships between the slope of Conduct Problems and the slopes of both parenting behaviors and the relationship between the slopes of Conduct Problems and Psychological Autonomy. The findings provide evidence of reciprocal relationships between Conduct Problems and parenting behaviors and parent-teen relationship variables. Mediational analyses indicated relationships with Conduct Problems unmediated by Autonomy and partially mediated by Conflict. The findings provide support for the hypothesis that associations over time between parenting practices and adolescent Conduct Problems depend in part on the parent-adolescent relationship.

Analyzing reciprocal relationships by means of the continuous‐time autoregressive latent trajectory model

Over the past decades, several analytic tools have become available for the analysis of reciprocal relations in a non‐experimental context using structural equation modeling (SEM). The autoregressive latent trajectory (ALT) model is a recently proposed model [BOLLEN and CURRAN Sociological Methods and Research (2004) Vol. 32, pp. 336–383; CURRAN and BOLLEN New Methods for the Analysis of Change (2001) American Psychological Association, Washington, DC], which captures features of both the autoregressive (AR) cross‐lagged model and the latent trajectory (LT) model. The present article discusses strengths and weaknesses and demonstrates how several of the problems can be solved by a continuous‐time version: the continuous‐time autoregressive latent trajectory (CALT) model. Using SEM to estimate the exact discrete model (EDM), the EDM/SEM continuous‐time procedure is applied to a CALT model of reciprocal relations between antisocial behavior and depressive symptoms.

Job performance over time is a function of latent trajectories and previous performance.

Previous literature addressing job performance over time notes that past performance can affect future performance and that individuals often have distinct latent performance trajectories. However, no research to date has modeled these 2 aspects of job performance in tandem. Drawing on previous literature, the authors note that current performance may act as performance feedback, influencing future performance directly (i.e., autoregression), and that individuals differ in their performance trajectories due to individual-difference factors (i.e., latent trajectories). The authors demonstrate an autoregressive latent trajectory (ALT) model to show how both autoregressive and latent trajectory parameters may be incorporated in modeling job performance over time. Also discussed are the implications of the ALT model for future studies examining job performance longitudinally.

Predictors of Resident Outcome Improvement in Nursing Homes

The effects of contextual characteristics and nursing-related factors on the overall quality improvement of resident outcomes, measured by a weighted index in incidents of pressure ulcers, physical restraints, and catheter use in nursing homes, were investigated by autoregressive latent trajectory modeling of panel data (1997-2003). Findings show that in the initial study period, nursing homes with a smaller bed size, being for-profit, caring for more Medicare residents, having residents with lower acuity levels, being located elsewhere than the South, having a high level of nurse staffing, and certified with lower frequencies of nursing care deficiencies had better quality. The intercept factor, representing the baseline of quality, was well predicted by six of the eight contextual and facility characteristics variables, and the slope trajectory of quality was only weakly predicted by them. The improved quality in resident outcomes was associated with facilities having fewer nursing care deficiency citations than their counterparts.

Over time relationships between early adolescent and peer substance use

Peer and adolescent substance use are highly correlated, but this relationship is not fully understood. In particular, the relative contributions of selection and socialization to substance use progression have not been established. Students ( n = 2453) in the seven middle schools in one school district were assessed at school at the beginning and end of the sixth, seventh, eighth grade and beginning of the 9th grade. Self-reported smoking and drinking and the number of substance using friends were assessed 5 times over 3 years. The relationship between peer and adolescent substance use were assessed in parallel processes as part of an autoregressive latent trajectory model. Substance use and the number of substance using friends increased in linear fashion from T1 to T5. Initial substance use predicted an increase in the number of substance using friends over time, indicating an effect of selection, and the initial number of substance using friends predicted substance use progression, providing evidence of socialization. The magnitudes of these relationships were similar. Bivariate, lagged autoregressive analyses of the successive relationships from one assessment to the next showed consistent, significant associations from peer use to adolescent substance use. The association from adolescent to peer use was significant only from 7th to 8th grade. The findings provide evidence of reciprocal influences, but socialization was a more consistent influence than selection.

Conditions for the Equivalence of the Autoregressive Latent Trajectory Model and a Latent Growth Curve Model With Autoregressive Disturbances

Curran and Bollen combined two models for longitudinal panel data: the latent growth curve model and the autoregressive model. In their model, the autoregressive relationships are modeled between the observed variables. This is a different model than a latent growth curve model with autoregressive relationships between the disturbances. However, when the autoregressive parameter is invariant over time and lies between-1 and 1, it can be shown that these models are algebraically equivalent. This result can be shown to generalize to the multivariate case. When the autoregressive parameters in the autoregressive latent trajectory model vary over time, the equivalence between the autoregressive latent trajectory model and a latent growth curve model with autoregressive disturbances no longer holds. However, a latent growth curve model with time-varying autoregressive parameters for the disturbances could be considered an interesting alternative to the autoregressive latent trajectory model with time-varying autoregressive parameters.

Autoregressive Latent Trajectory (ALT) Models A Synthesis of Two Traditions

Although there are a variety of statistical methods available for the analysis of longitudinal panel data, two approaches are of particular historical importance: the autoregressive (simplex) model and the latent trajectory (curve) model. These two approaches have been portrayed as competing methodologies such that one approach is superior to the other. We argue that the autoregressive and trajectory models are special cases of a more encompassing model that we call the autoregressive latent trajectory (ALT) model. In this paper we detail the underlying statistical theory and mathematical identification of this model, and demonstrate the ALT model using two empirical data sets. The first reanalyzes a simulated repeated measures data set that was previously used to argue against the autoregressive model, and we illustrate how the ALT model can recover the true latent curve model. Second, we apply the ALT model to real family income data on N=3912 adults over a seven year period and find evidence for both autoregressive and latent trajectory processes. Extensions and limitations are discussed.

Expectancy of panic in the maintenance of daily anxiety in panic disorder with agoraphobia: A longitudinal test of competing models

Although panic expectancy and the experience of anxiety are clearly related, their causal relationship remains unclear. A series of autoregressive latent trajectory models was used to evaluate the relationship between the highest level of daily anxiety and panic expectancy over time. Participants (N = 45) who met criteria for panic disorder with agoraphobia filled out daily diary measures over a 10-day period. It was hypothesized that expectation of panic (measured in the morning) would be primarily responsible for the maintenance of daily anxiety (measured in the evening). Daily anxiety was found to be influenced by a traitlike anxiety component, anxiety from the previous day, and morning expectation of panic. Panic expectancy was found to be influenced by a traitlike expectancy component, but not by the previous day's anxiety. Limitations of the model and future applications are discussed.