Research in Gerontological Nursing

Focus on Methods 

Causal Inference in Cross-Lagged Panel Analysis: A Reciprocal Causal Relationship Between Cognitive Function and Depressive Symptoms

Ju Young Yoon, PhD, RN; Roger L. Brown, PhD

Abstract

Cross-lagged panel analysis (CLPA) is a method of examining one-way or reciprocal causal inference between longitudinally changing variables. It has been used in the social sciences for many years, but not much in nursing research. This article introduces the conceptual and statistical background of CLPA and provides an exemplar of CLPA that examines the reciprocal causal relationship between depression and cognitive function over time in older adults. The 2-year cross-lagged effects of depressive symptoms (T1) on cognitive function (T2) and cognitive function (T1) on depressive symptoms (T2) were significant, which demonstrated a reciprocal causal relationship between cognitive function and depressive mood over time. Although CLPA is a methodologically strong approach to examine the reciprocal causal inferences over time, it is necessary to consider potential sources of spuriousness to lead to false causal relationship and a reasonable time frame to detect the change of the variables.

[Res Gerontol Nurs. 2014; 7(4):152–158.]

Dr. Yoon is Assistant Professor, and Dr. Brown is Professor, School of Nursing, University of Wisconsin-Madison, Madison, Wisconsin.

The authors have disclosed no potential conflicts of interest, financial or otherwise.

Address correspondence to Ju Young Yoon, PhD, RN, Assistant Professor, School of Nursing, University of Wisconsin-Madison, Clinical Science Center, H6/234, 600 Highland Avenue, Madison, WI 53792; e-mail: yoon26@wisc.edu.

Received: October 03, 2013
Accepted: February 03, 2014
Posted Online: March 18, 2014

Abstract

Cross-lagged panel analysis (CLPA) is a method of examining one-way or reciprocal causal inference between longitudinally changing variables. It has been used in the social sciences for many years, but not much in nursing research. This article introduces the conceptual and statistical background of CLPA and provides an exemplar of CLPA that examines the reciprocal causal relationship between depression and cognitive function over time in older adults. The 2-year cross-lagged effects of depressive symptoms (T1) on cognitive function (T2) and cognitive function (T1) on depressive symptoms (T2) were significant, which demonstrated a reciprocal causal relationship between cognitive function and depressive mood over time. Although CLPA is a methodologically strong approach to examine the reciprocal causal inferences over time, it is necessary to consider potential sources of spuriousness to lead to false causal relationship and a reasonable time frame to detect the change of the variables.

[Res Gerontol Nurs. 2014; 7(4):152–158.]

Dr. Yoon is Assistant Professor, and Dr. Brown is Professor, School of Nursing, University of Wisconsin-Madison, Madison, Wisconsin.

The authors have disclosed no potential conflicts of interest, financial or otherwise.

Address correspondence to Ju Young Yoon, PhD, RN, Assistant Professor, School of Nursing, University of Wisconsin-Madison, Clinical Science Center, H6/234, 600 Highland Avenue, Madison, WI 53792; e-mail: yoon26@wisc.edu.

Received: October 03, 2013
Accepted: February 03, 2014
Posted Online: March 18, 2014

Causal inference between concepts is an important research issue for nursing and health science studies. Randomized controlled trials (RCTs) are regarded as the gold standard for yielding reliable evidence for causes and effects. However, many nursing studies are impossible or difficult to conduct using a true experimental design for practical or ethical reasons. Nonexperimental, longitudinal studies, also referred to as quasi-experimental designs, can be used to examine causal inferences, controlling for confounding factors, despite being less rigorous than RCTs. Data measured longitudinally at two or more points on the same individual are referred to as panel data, which are designed to explore the causal or antecedent factors leading to different outcomes over time and also to examine the effects of the conditions or predictive characteristics at the first measured time on those of second measurement based on the concept of quasi-experimental design (Frees, 2004).

Longitudinal data analysis is commonly conducted using one of several statistical analyses; analysis of covariance (ANCOVA) and repeated measures analysis of variance (ANOVA) have traditionally been used. Recently, the mixed models including multilevel analysis and latent growth modeling have become popular (Preacher, Wichman, MacCallum, & Briggs, 2008). These methods allow researchers to examine the treatment effects or change over time and to explore different change patterns. However, if the research is interested in the causal inference between longitudinally changing variables, a cross-lagged panel analysis (CLPA) is the most appropriate longitudinal analysis based on the quasi-experimental design. CLPA is intuitive for researchers to understand causal relationships and is effectively applicable to examine not only one-way causal inferences (i.e., Does A cause B?) but also to examine reciprocal causal inferences (i.e., Does A cause B and/or does B cause A?). The CLPA model has been widely used to examine causal inferences in psychology and educational studies (Cacioppo, Hawkley, & Thisted, 2010; Rogosa, 1980; Watkins, Lei, & Canivez, 2007). However, since cross-lagged panel correlation analysis was first published in 1988 by Reed and Verran, investigations using CLPA in the nursing research literature have ceased during the past two decades (van der Heijden, Demerouti, & Bakker, 2008). The purpose of this article is to illustrate the use of CLPA for exploring potential reciprocal causal relationships over time. This article first introduces the conceptual and statistical background of CLPA and then provides an exemplar of CLPA that examines the reciprocal causal relationship between depression and cognitive function over time in older adults.

Conceptual and Statistical Background of CLPA

CLPA is “a method for making causal inferences from temporal precedence over fixed intervals for two or more variables” (Shingles, 1985, p. 220). The simplest case is the two waves and two variables CLPA model, although there is no limit on the number of variables or the number of measurements. At the operational level, the CLPA model is a specific application of structural equation modeling (Kline, 2011). As Figure 1 presents, the variables X1 and Y1 are treated as exogenous variables, and X2 and Y2 are considered to be endogenous variables. In addition, the u and v are the residual variances of endogenous variables.

Operational diagram and configurations of the cross-lagged panel analysis model.Note. X1 = X variable at Time 1; X2 = X variable at Time 2; Y1 = Y variable at Time 1; Y2 = Y variable at Time 2.

Figure 1.

Operational diagram and configurations of the cross-lagged panel analysis model.

Note. X1 = X variable at Time 1; X2 = X variable at Time 2; Y1 = Y variable at Time 1; Y2 = Y variable at Time 2.

The CLPA model is a quasi-experimental design (Kenny, 1975). For a causal inference to exist from A to B, three important conditions should be met: “(a) A and B must covary; (b) A must precede B in time; and (c) the relationship between A and B must not be spurious or produced by the association of A and B with a third variable or set of variables” (Menard, 1991, p. 17). Regarding the first condition, autocorrelations in the CLPA model indicate the level of covariance of two variables. The second condition of the causal inference that cause precedes effect means that the state of one variable at Time 2 cannot have produced the prior state of the other variable at Time 1 in CLPA. The main assumption of CLPA is that all causal influences are lagged (Rogosa, 1980). In the example of X1 and Y2, if a causal relationship exists between X1 and Y2, the direction is from X1 to Y2 not from Y2 to X1. If the coefficient ß2 in Figure 1 is statistically significant, it is evident that X1 is a cause of Y2 (Shingles, 1985). However, several empirical procedures are necessary to rule out spurious causal inferences between X1 and Y2. A basic procedure is to control for the effects of outside variables that may influence the relationship between X1 and Y2 partially or fully. In addition, as most concepts of interest to health scientists are measured using survey tools or direct observations, it is necessary to control for confounding factors and measurement errors of the observed variables for successful causal inferences (Finkel, 1995).

Application of CLPA for Depressive Symptoms and Cognitive Function In Community-Dwelling Older Adults

Background of Research Questions

It is well known that depression is associated with cognitive impairment in older adults (Barnes, Alexopoulos, Lopez, Williamson, & Yaffe, 2006), and the two phenomena are often exhibited together. Recent prospective studies suggest that depression is an independent risk factor for developing dementia (Saczynski et al., 2010; Wilson et al., 2010). One major hypothesis is that depressive symptoms have a detrimental effect on level of cognitive function that might increase the likelihood of reaching the threshold where dementia is clinically evident in older adults (Wilson, Mendes De Leon, Bennett, Bienias, & Evans, 2004). On the other hand, some studies suggest an opposite effect, that depression is the consequence of and predicted by poorer cognitive function. One explanation offered is that older adults who experience cognitive decline might perceive an associated decrease in control over their lives and consequently experience more depressive symptoms (Bierman, Comijs, Jonker, & Beekman, 2007; Perrino, Mason, Brown, Spokane, & Szapocznik, 2008). Given this ambiguous causal association of depressive symptoms and cognitive function, the exemplar study reported herein was designed to examine the reciprocal causal association between depressive symptoms and cognitive decline in community-dwelling older adults using CLPA.

Data Source

The data source for this study is the Korean Longitudinal Study of Ageing (KLoSA), which is a longitudinal panel study that surveys a nationally representative community sample of adults older than 45 (Korea Labor Institute, 2012). Since its launch in 2006, the KLoSA has collected information about demographics, family, health and functional levels, employment, income and assets, and life satisfaction every 2 years. This panel study was based on a multistage stratified probability sampling method using area and households. All questionnaires were administered in Korean.

Study Sample

Two waves of data collected in 2006 (T1) and 2008 (T2) are publicly available for use by researchers. The number of adults older than 65 included in this study was 4,165 in 2006 and 3,511 in 2008.

Variables

Cognitive Function. The Korean Mini-Mental State Examination (K-MMSE; Kang, Na, & Hahn, 1997) was used to measure cognitive function. It ranges from 0 to 30, with higher scores indicating better cognitive function.

Depressive Symptoms. The Center for Epidemiological Studies-Depression (CES-D; Irwin, Artin, & Oxman, 1999) short form scale was used to assess depressive symptoms experienced within the past 7 days. The CES-D short form consists of 10 items. The total score ranges from 0 to 30, with higher scores indicating a more depressed status. The Korean version of the CES-D short form demonstrated good levels of psychometric properties including internal consistency (Cronbach’s alpha >0.7), concurrent validity with the original CES-D, and discriminant validity significantly differentiating depression from non-depression (Shin, 2011).

Covariates. Based on the previous studies, age, gender, years of education, location, living with spouse, living with children, and satisfaction with income were identified as influencing factors to depression and cognitive function and included as covariates in the model.

Analysis Process

A CLPA path model was built to test reciprocal causal relationship between cognitive function and depressive symptoms. To control for spuriousness of causal inference between cognitive function and depressive symptoms in the CLPA path model, several covariates that may influence cognitive function and depression were included in the model: age, gender, years of education, location, living with spouse, living with children, and satisfaction with income.

Measurement errors of the main variables—depressive symptoms and cognitive function—were then taken into account. Despite the importance of measurement errors in the model, many studies using CLPA have not incorporated measurement errors in the models, known as path models (Brown et al., 2009; Cacioppo et al., 2010). One commonly used technique to handle measurement errors is multiple indicator structural equation (MISE) modeling, which is an analytic technique for simultaneously estimating measurement errors and regression parameters in the context of the measurement error theory (Jöreskog & Sörbom, 1996). Despite the strengths of MISE modeling, it has a disadvantage, in which specification errors or estimation errors in one part of the model may produce biased parameter estimates in the whole model and convergence problems (McDonald, Behson, & Seifert, 2005). To overcome this problem with the MISE method, the composite indicator structural equation (CISE) alpha model was introduced (Hayduk, 1987). CISE modeling is not a simultaneous estimation method; therefore, measurement errors for the composite indicator calculated from an estimate of reliability are fixed ([1–Cronbach’s alpha]*variance of composite indicator), and regression coefficients are estimated in the presence of errors in measurement (McDonald et al., 2005). If the instruments that measured concepts in the study are valid and reliable, the CISE alpha model is more attractive than the MISE model because fewer parameters to be estimated decrease complexity and estimation demands in the model. In the current study, a CISE model was used because of its relative simplicity and the reliability of the measures already made.

Finally, the CLPA with CISE alpha model was developed to examine the reciprocal causal association between depressive symptoms and cognitive decline in the current study, as both main measures have been widely used with good psychometric properties. Regarding handling missing data, available data from all participants were included in analysis with full information maximum likelihood estimation with robust standard errors. Mplus 6.1 was used to run the CLPA model.

Results

Table 1 provides the sample statistics of the study participants at each time point. The final CLPA with CISE alpha model controlling for several confounding factors and measurement errors are presented in Table 2 and Figure 2. Model fit indices showed good fit. The 2-year cross-lagged effects of depressive symptoms (T1) on cognitive function (T2) and cognitive function (T1) on depressive symptoms (T2) were modest but statistically significant (ß3 = −0.049 and ß2 = −0.069, respectively).

Descriptive Statistics of Variables at Each Time Point

Table 1:

Descriptive Statistics of Variables at Each Time Point

Coefficients in the Final Cross–Lagged Panel Analysis With CISE Alpha Model

Table 2:

Coefficients in the Final Cross–Lagged Panel Analysis With CISE Alpha Model

Cross-lagged panel analysis results using the composite indicator structural equation alpha model.Note. RMSEA = root mean square error of approximation; CFI = comparative fit index; TLI = Tucker-Lewis index; SRMR = standardized root mean square residual. All coefficients are standardized values. Gender, education, and location were treated as time-invariant covariates, whereas age, living with spouse, living with children, and satisfaction with income were controlled as time-varying covariates.*p < 0.05, **p < 0.01.

Figure 2.

Cross-lagged panel analysis results using the composite indicator structural equation alpha model.

Note. RMSEA = root mean square error of approximation; CFI = comparative fit index; TLI = Tucker-Lewis index; SRMR = standardized root mean square residual. All coefficients are standardized values. Gender, education, and location were treated as time-invariant covariates, whereas age, living with spouse, living with children, and satisfaction with income were controlled as time-varying covariates.

*p < 0.05, **p < 0.01.

Discussion

The exemplar CLPA study demonstrated a modest reciprocal causal relationship between cognitive function and depressive symptoms for community-dwelling older adults, suggesting a possibility of both ways of causal inferences: (a) higher levels of depression are associated with late cognitive decline, and (b) poorer cognitive function among older adults may predict greater depressive symptoms at sequential time points. These reciprocal causal relationships between depressive symptoms and cognitive function may not be mutually exclusive, but instead may work together under different mechanisms. However, given the modest levels of effects, the reciprocal causal relationships between cognitive function and depressive symptoms need to be interpreted cautiously.

Methodologically, although CLPA is a strong approach to examine the reciprocal causal inferences over time, several important issues that might influence the true causal relationships in the CLPA model need to be noted with the exemplar study. First, as already noted, measurement errors and covariates controlling for main variables may influence examining whether those relationships are true effects. Although not shown in this article, we ran the CLPA path model without taking into account measurement errors of two main variables. Although overall model fit indices were shown to be appropriate (root mean square error of approximation = 0.039; comparative fit index = 0.983; Tucker-Lewis index = 0.936; and standardized root mean square residual = 0.015), they were not as good as the fit indices of the CISE alpha model. In addition, several estimated parameters in the CLPA model without consideration of measurement errors (ß1 = 0.458, ß4= 0.386) were attenuated. As already known, measurement error may create an attenuation bias, which may make estimated parameters underestimate the true parameter (Kenny, 1975) and bias standard error terms of parameters and increase the probability of detecting a spurious relationship by chance (McDonald et al., 2005). In addition, medical conditions that might influence depressive symptoms or cognitive function could not be included as covariates in this study. However, as Maruyama (1998) emphasized, it is important to specify proper covariates for adjustment to prevent the spuriousness of causal inferences when applying CLPA.

Although an exemplar study included two time measurement points, a CLPA can apply to the extended model with two waves or more. But it is necessary to consider that the time frame of measurement influences the significance of cross-lagged effects. The effects of some factors may take longer to manifest themselves in the second measurement. In the case of cognitive function and depression, although the current study’s comparative short follow-up period of 2 years showed significant reciprocal relationships, two other prospective studies failed to examine the significant relationship between depressive symptoms and cognitive function over 3 years (Dufouil, Fuhrer, Dartigues, & Alpérovitch, 1996; Henderson et al., 1997). Longer interval periods between the measurements are not always beneficial to detect the change of the variables, but the reasonable time frame should be considered in CLPA to yield trustworthy inferences about causal structures. Although causal effects require a finite amount of time (Kline, 2011), in reality, we cannot estimate the finite time to lead to causal effects. Because the choices of different time points and measurement occasions can produce different study results or even contradictory findings, it is important to decide an appropriate time period to expect the explicit representation of causal effects. To overcome the issue of different time intervals in discrete time CLPA models, continuous time CLPA models have recently been introduced (Voelkle, Oud, Davidov, & Schmidt, 2012).

Conclusion

The current article introduced CLPA to examine the reciprocal causal inferences over time, which have been a major research interest for health scientists. Although findings from a CLPA study cannot claim a causal relationship in a strict sense compared to those from a RCT, CLPA offers a good alternative to explore the causal inferences in many social and health science studies that are limited to using a RCT design. Given the increase of longitudinal studies and publicly available panel survey studies, the use of CLPA with consideration of several important issues addressed in this article may help researchers examine the causal inferences in many nursing research areas.

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Descriptive Statistics of Variables at Each Time Point

VariableTime 1 (N = 4,165)Time 2 (N = 3,511)
Mean (SD)
Depressive symptomsa8.1 (5.7)9.2 (6.1)
Cognitive functionb21.4 (7.1)20.6 (7.6)
Age (years)73.0 (6.3)74.8 (6.1)
n (%)
Gender
  Female2,426 (58)2,048 (58)
  Male1,739 (42)1,463 (42)
Education
  <6 years2,941 (71)2,494 (71)
  ≥6 years1,222 (29)1,015 (29)
Location
  Urban2,962 (71)2,416 (69)
  Rural1,203 (29)1,095 (31)
Living with spouse
  Yes2,606 (63)2,172 (62)
  No1,557 (37)1,339 (38)
Living with children
  No2,326 (57)2,126 (62)
  Yes1,744 (43)1,318 (38)
Satisfaction with income
  Yes2,093 (50)1,905 (54)
  No2,072 (50)1,605 (46)

Coefficients in the Final Cross–Lagged Panel Analysis With CISE Alpha Model

Depressive Symptoms (T1)Cognitive Function (T1)Depressive Symptoms (T2)Cognitive Function (T2)
VariableB (SE)95% CIßB (SE)95% CIßB (SE)95% CIßB (SE)95% CIß
Cognitive function (T1)−0.059** (0.021)[−0.099, −0.018]−0.069**0.587** (0.028)[0.531, 0.642]0.538**
Depressive symptoms (T1)0.504** (0.025)[0.455, 0.553]0.463**−0.068** (0.025)[−0.118, −0.019]−0.049**
Age0.085** (0.015)[0.056, 0.114]0.103**−0.421** (0.017)[−0.454, −0.387]−0.396**0.063** (0.018)[0.028, 0.097]0.070**−0.172** (0.020)[−0.212, −0.132]−0.148**
Gendera0.587** (0.204)[0.187, 0.987]0.055**−2.081** (0.223)[−2.519, −1.644]−0.153**0.789** (0.216)[0.365, 1.213]0.068**−0.133 (0.255)[−0.632, 0.366]−0.09
Locationa−0.265 (0.186)[−0.630, 0.100]−0.0230.678** (0.205)[0.277, 1.079]0.046**−0.064 (0.198)[−0.451, 0.324]−0.0050.228 (0.225)[−0.213, 0.668]0.014
Educationa−0.750** (0.197)[−1.136, −0.365]−0.065**2.645** (0.215)[2.225–3.069]0.180**−0.069 (0.219)[−0.498, 0.361]−0.0060.505 (0.282)[−0.047, 1.057]0.031
Living with spousea−1.114** (0.224)[−1.553, −0.675]−0.103**0.388 (0.236)[−0.075, 0.852]0.0280.113 (0.232)[−0.343, 0.568]0.0100.009 (0.236)[−0.453, 0.471]0.001
Living with childrena−0.450* (0.177)[−0.798, −0.103]−0.043*−0.317 (0.197)[−0.704, 0.069]−0.0230.005 (0.194)[−0.376, 0.386]0.000−0.900** (0.235)[−1.359, −0.440]−0.060**
Satisfaction with incomea−3.373** (0.167)[−3.701, −3.045]−0.323**1.981** (0.190)[1.609, 2.353]0.148**−2.224** (0.191)[−2.599, −1.850]−0.195**0.905** (0.214)[0.486, 1.324]0.062**

10.3928/19404921-20140310-01

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