Estimating and interpreting latent variable interactions: A tutorial for applying the latent moderated structural equations method

Latent variables are common in psychological research. Research questions involving the interaction of two variables are likewise quite common. Methods for estimating and interpreting interactions between latent variables within a structural equation modeling framework have recently become available. The latent moderated structural equations (LMS) method is one that is built into Mplus software. The potential utility of this method is limited by the fact that the models do not produce traditional model fit indices, standardized coefficients, or effect sizes for the latent interaction, which renders model fitting and interpretation of the latent variable interaction difficult. This article compiles state-of-the-science techniques for assessing LMS model fit, obtaining standardized coefficients, and determining the size of the latent interaction effect in order to create a tutorial for new users of LMS models. The recommended sequence of model estimation and interpretation is demonstrated via a substantive example and a Monte Carlo simulation. Finally, extensions of this method are discussed, such as estimating quadratic effects of latent factors and interactions between latent slope and intercept factors, which hold significant potential for testing and advancing developmental theories.

The analysis of multivariate longitudinal data: a review

Longitudinal experiments often involve multiple outcomes measured repeatedly within a set of study participants. While many questions can be answered by modeling the various outcomes separately, some questions can only be answered in a joint analysis of all of them. In this article, we will present a review of the many approaches proposed in the statistical literature. Four main model families will be presented, discussed and compared. Focus will be on presenting advantages and disadvantages of the different models rather than on the mathematical or computational details.

Psychosocial stress predicts future symptom severities in children and adolescents with Tourette syndrome and/or obsessive-compulsive disorder

BACKGROUND

The goals of this prospective longitudinal study were to monitor levels of psychosocial stress in children and adolescents with Tourette syndrome (TS) and/or obsessive-compulsive disorder (OCD) compared to healthy control subjects and to examine the relationship between measures of psychosocial stress and fluctuations in tic, obsessive-compulsive (OC), and depressive symptom severity.

METHODS

Consecutive ratings of tic, OC and depressive symptom severity were obtained for 45 cases and 41 matched healthy control subjects over a two-year period. Measures of psychosocial stress included youth self-report, parental report, and clinician ratings of long-term contextual threat. Structural equation modeling for unbalanced repeated measures was used to assess the temporal sequence of psychosocial stress with the severity of tic, OC and depressive symptoms.

RESULTS

Subjects with TS and OCD experienced significantly more psychosocial stress than did the controls. Estimates of psychosocial stress were predictive of future depressive symptoms. Current levels of psychosocial stress were also a significant predictor of future OC symptom severity, but not vice versa. Current OC symptom severity was a predictor of future depressive symptom severity, but not vice versa. Current levels of psychosocial stress and depression were independent predictors of future tic severity, even after controlling for the effect of advancing chronological age.

CONCLUSIONS

The impact of antecedent psychosocial adversity is greater on future depressive symptoms than for tic and/or OC symptoms. Worsening OC symptoms are also a predictor of future depressive symptoms. Advancing chronological age is robustly associated with reductions in tic severity.

A NEW MULTIVARIATE MEASUREMENT ERROR MODEL WITH ZERO-INFLATED DIETARY DATA, AND ITS APPLICATION TO DIETARY ASSESSMENT

In the United States the preferred method of obtaining dietary intake data is the 24-hour dietary recall, yet the measure of most interest is usual or long-term average daily intake, which is impossible to measure. Thus, usual dietary intake is assessed with considerable measurement error. Also, diet represents numerous foods, nutrients and other components, each of which have distinctive attributes. Sometimes, it is useful to examine intake of these components separately, but increasingly nutritionists are interested in exploring them collectively to capture overall dietary patterns. Consumption of these components varies widely: some are consumed daily by almost everyone on every day, while others are episodically consumed so that 24-hour recall data are zero-inflated. In addition, they are often correlated with each other. Finally, it is often preferable to analyze the amount of a dietary component relative to the amount of energy (calories) in a diet because dietary recommendations often vary with energy level. The quest to understand overall dietary patterns of usual intake has to this point reached a standstill. There are no statistical methods or models available to model such complex multivariate data with its measurement error and zero inflation. This paper proposes the first such model, and it proposes the first workable solution to fit such a model. After describing the model, we use survey-weighted MCMC computations to fit the model, with uncertainty estimation coming from balanced repeated replication.The methodology is illustrated through an application to estimating the population distribution of the Healthy Eating Index-2005 (HEI-2005), a multi-component dietary quality index involving ratios of interrelated dietary components to energy, among children aged 2-8 in the United States. We pose a number of interesting questions about the HEI-2005 and provide answers that were not previously within the realm of possibility, and we indicate ways that our approach can be used to answer other questions of importance to nutritional science and public health.

Individual differences in childhood sleep problems predict later cognitive executive control

STUDY OBJECTIVE

To determine whether individual differences in developmental patterns of general sleep problems are associated with 3 executive function abilities-inhibiting, updating working memory, and task shifting-in late adolescence.

PARTICIPANTS

916 twins (465 female, 451 male) and parents from the Colorado Longitudinal Twin Study.

MEASUREMENTS AND RESULTS

Parents reported their children's sleep problems at ages 4 years, 5 y, 7 y, and 9-16 y based on a 7-item scale from the Child-Behavior Checklist; a subset of children (n = 568) completed laboratory assessments of executive functions at age 17. Latent variable growth curve analyses were used to model individual differences in longitudinal trajectories of childhood sleep problems. Sleep problems declined over time, with approximately 70% of children having > or = 1 problem at age 4 and approximately 33% of children at age 16. However, significant individual differences in both the initial levels of problems (intercept) and changes across time (slope) were observed. When executive function latent variables were added to the model, the intercept did not significantly correlate with the later executive function latent variables; however, the slope variable significantly (P < 0.05) negatively correlated with inhibiting (r = -0.27) and updating (r = -0.21), but not shifting (r = -0.10) abilities. Further analyses suggested that the slope variable predicted the variance common to the 3 executive functions (r = -0.29).

CONCLUSIONS

Early levels of sleep problems do not seem to have appreciable implications for later executive functioning. However, individuals whose sleep problems decrease more across time show better general executive control in late adolescence.

Directional data analysis under the general projected normal distribution

The projected normal distribution is an under-utilized model for explaining directional data. In particular, the general version provides flexibility, e.g., asymmetry and possible bimodality along with convenient regression specification. Here, we clarify the properties of this general class. We also develop fully Bayesian hierarchical models for analyzing circular data using this class. We show how they can be fit using MCMC methods with suitable latent variables. We show how posterior inference for distributional features such as the angular mean direction and concentration can be implemented as well as how prediction within the regression setting can be handled. With regard to model comparison, we argue for an out-of-sample approach using both a predictive likelihood scoring loss criterion and a cumulative rank probability score criterion.

Estimation of causal mediation effects for a dichotomous outcome in multiple-mediator models using the mediation formula

Mediators are intermediate variables in the causal pathway between an exposure and an outcome. Mediation analysis investigates the extent to which exposure effects occur through these variables, thus revealing causal mechanisms. In this paper, we consider the estimation of the mediation effect when the outcome is binary and multiple mediators of different types exist. We give a precise definition of the total mediation effect as well as decomposed mediation effects through individual or sets of mediators using the potential outcomes framework. We formulate a model of joint distribution (probit-normal) using continuous latent variables for any binary mediators to account for correlations among multiple mediators. A mediation formula approach is proposed to estimate the total mediation effect and decomposed mediation effects based on this parametric model. Estimation of mediation effects through individual or subsets of mediators requires an assumption involving the joint distribution of multiple counterfactuals. We conduct a simulation study that demonstrates low bias of mediation effect estimators for two-mediator models with various combinations of mediator types. The results also show that the power to detect a nonzero total mediation effect increases as the correlation coefficient between two mediators increases, whereas power for individual mediation effects reaches a maximum when the mediators are uncorrelated. We illustrate our approach by applying it to a retrospective cohort study of dental caries in adolescents with low and high socioeconomic status. Sensitivity analysis is performed to assess the robustness of conclusions regarding mediation effects when the assumption of no unmeasured mediator-outcome confounders is violated.

Variable Selection for Nonparametric Gaussian Process Priors: Models and Computational Strategies

This paper presents a unified treatment of Gaussian process models that extends to data from the exponential dispersion family and to survival data. Our specific interest is in the analysis of data sets with predictors that have an a priori unknown form of possibly nonlinear associations to the response. The modeling approach we describe incorporates Gaussian processes in a generalized linear model framework to obtain a class of nonparametric regression models where the covariance matrix depends on the predictors. We consider, in particular, continuous, categorical and count responses. We also look into models that account for survival outcomes. We explore alternative covariance formulations for the Gaussian process prior and demonstrate the flexibility of the construction. Next, we focus on the important problem of selecting variables from the set of possible predictors and describe a general framework that employs mixture priors. We compare alternative MCMC strategies for posterior inference and achieve a computationally efficient and practical approach. We demonstrate performances on simulated and benchmark data sets.

Measurement invariance within and between individuals: a distinct problem in testing the equivalence of intra- and inter-individual model structures

We address the question of equivalence between modeling results obtained on intra-individual and inter-individual levels of psychometric analysis. Our focus is on the concept of measurement invariance and the role it may play in this context. We discuss this in general against the background of the latent variable paradigm, complemented by an operational demonstration in terms of a linear state-space model, i.e., a time series model with latent variables. Implemented in a multiple-occasion and multiple-subject setting, the model simultaneously accounts for intra-individual and inter-individual differences. We consider the conditions—in terms of invariance constraints—under which modeling results are generalizable (a) over time within subjects, (b) over subjects within occasions, and (c) over time and subjects simultaneously thus implying an equivalence-relationship between both dimensions. Since we distinguish the measurement model from the structural model governing relations between the latent variables of interest, we decompose the invariance constraints into those that involve structural parameters and those that involve measurement parameters and relate to measurement invariance. Within the resulting taxonomy of models, we show that, under the condition of measurement invariance over time and subjects, there exists a form of structural equivalence between levels of analysis that is distinct from full structural equivalence, i.e., ergodicity. We demonstrate how measurement invariance between and within subjects can be tested in the context of high-frequency repeated measures in personality research. Finally, we relate problems of measurement variance to problems of non-ergodicity as currently discussed and approached in the literature.

Two-Step Estimation of Models Between Latent Classes and External Variables

We consider models which combine latent class measurement models for categorical latent variables with structural regression models for the relationships between the latent classes and observed explanatory and response variables. We propose a two-step method of estimating such models. In its first step, the measurement model is estimated alone, and in the second step the parameters of this measurement model are held fixed when the structural model is estimated. Simulation studies and applied examples suggest that the two-step method is an attractive alternative to existing one-step and three-step methods. We derive estimated standard errors for the two-step estimates of the structural model which account for the uncertainty from both steps of the estimation, and show how the method can be implemented in existing software for latent variable modelling.

Causal inference with multiple time series: principles and problems

I review the use of the concept of Granger causality for causal inference from time-series data. First, I give a theoretical justification by relating the concept to other theoretical causality measures. Second, I outline possible problems with spurious causality and approaches to tackle these problems. Finally, I sketch an identification algorithm that learns causal time-series structures in the presence of latent variables. The description of the algorithm is non-technical and thus accessible to applied scientists who are interested in adopting the method.

Longitudinal Relationships Between Family Functioning and Identity Development in Hispanic Adolescents: Continuity and Change

The present study was designed to investigate trajectories of identity development and their relationship to family functioning in a sample of Hispanic adolescents and their primary caregivers. Two hundred fifty adolescents completed measures of identity coherence and confusion and of family functioning, and parents completed measures of family functioning. Significant variability over time and across individuals emerged in identity confusion, but not in identity coherence. As a result, the present analyses focused on identity confusion. Changes in adolescent-reported, but not parent-reported, family functioning were significantly related to changes in identity confusion. Follow-up analyses suggested that family functioning primarily influences identity confusion in early adolescence, but that identity confusion begins to exert a reciprocal effect in middle adolescence. Exploratory latent growth mixture modeling (LGMM) analyses produced three classes of adolescents based on their baseline values and change trajectories in identity confusion. The potential for family-strengthening interventions to affect identity development is discussed.

The Psychometrics of the Mini-K

Many published studies have employed the Mini-K to measure a single fast-slow life history dimension. However, the internal structure of the Mini-K has not been determined and it is not clear that a single higher order K-factor fits the data. It is also not clear that the Mini-K is measurement invariant across groups such as the sexes. To establish the construct validity of K as well as the broader usefulness of applying life history theory to humans, it is crucial that these psychometric issues are addressed as a part of measure validation efforts. Here we report on three studies that used latent variable modeling and data drawn from two college student samples ( ns = 361 and 300) to elucidate the psychometrics of the Mini-K. We found that (a) the Mini-K had a six dimensional first-order structure, (b) the K-factor provided a parsimonious explanation of the associations among the lower order factors at no significant cost to fit, (c) the Mini-K measured the same K-factor across the sexes, (d) K-factor means did not have the same meaning across the sexes and thus the first-order factors should be used in studies of mean sex differences, and finally, (e) the K-factor was only associated with environment and aspects of mating competition in females. Implications and future directions for life history research are discussed.

Fitting a bivariate measurement error model for episodically consumed dietary components

There has been great public health interest in estimating usual, i.e., long-term average, intake of episodically consumed dietary components that are not consumed daily by everyone, e.g., fish, red meat and whole grains. Short-term measurements of episodically consumed dietary components have zero-inflated skewed distributions. So-called two-part models have been developed for such data in order to correct for measurement error due to within-person variation and to estimate the distribution of usual intake of the dietary component in the univariate case. However, there is arguably much greater public health interest in the usual intake of an episodically consumed dietary component adjusted for energy (caloric) intake, e.g., ounces of whole grains per 1000 kilo-calories, which reflects usual dietary composition and adjusts for different total amounts of caloric intake. Because of this public health interest, it is important to have models to fit such data, and it is important that the model-fitting methods can be applied to all episodically consumed dietary components.We have recently developed a nonlinear mixed effects model (Kipnis, et al., 2010), and have fit it by maximum likelihood using nonlinear mixed effects programs and methodology (the SAS NLMIXED procedure). Maximum likelihood fitting of such a nonlinear mixed model is generally slow because of 3-dimensional adaptive Gaussian quadrature, and there are times when the programs either fail to converge or converge to models with a singular covariance matrix. For these reasons, we develop a Monte-Carlo (MCMC) computation of fitting this model, which allows for both frequentist and Bayesian inference. There are technical challenges to developing this solution because one of the covariance matrices in the model is patterned. Our main application is to the National Institutes of Health (NIH)-AARP Diet and Health Study, where we illustrate our methods for modeling the energy-adjusted usual intake of fish and whole grains. We demonstrate numerically that our methods lead to increased speed of computation, converge to reasonable solutions, and have the flexibility to be used in either a frequentist or a Bayesian manner.

A general non-linear multilevel structural equation mixture model

In the past 2 decades latent variable modeling has become a standard tool in the social sciences. In the same time period, traditional linear structural equation models have been extended to include non-linear interaction and quadratic effects (e.g., Klein and Moosbrugger, 2000), and multilevel modeling (Rabe-Hesketh et al., 2004). We present a general non-linear multilevel structural equation mixture model (GNM-SEMM) that combines recent semiparametric non-linear structural equation models (Kelava and Nagengast, 2012; Kelava et al., 2014) with multilevel structural equation mixture models (Muthén and Asparouhov, 2009) for clustered and non-normally distributed data. The proposed approach allows for semiparametric relationships at the within and at the between levels. We present examples from the educational science to illustrate different submodels from the general framework.

Truth and Memory: Linking Instantaneous and Retrospective Self-Reported Cigarette Consumption

Studies of smoking behavior commonly use the time-line follow-back (TLFB) method, or periodic retrospective recall, to gather data on daily cigarette consumption. TLFB is considered adequate for identifying periods of abstinence and lapse but not for measurement of daily cigarette consumption, thanks to substantial recall and digit preference biases. With the development of the hand-held electronic diary (ED), it has become possible to collect cigarette consumption data using ecological momentary assessment (EMA), or the instantaneous recording of each cigarette as it is smoked. EMA data, because they do not rely on retrospective recall, are thought to more accurately measure cigarette consumption. In this article we present an analysis of consumption data collected simultaneously by both methods from 236 active smokers in the pre-quit phase of a smoking cessation study. We define a statistical model that describes the genesis of the TLFB records as a two-stage process of mis-remembering and rounding, including fixed and random effects at each stage. We use Bayesian methods to estimate the model, and we evaluate its adequacy by studying histograms of imputed values of the latent remembered cigarette count. Our analysis suggests that both mis-remembering and heaping contribute substantially to the distortion of self-reported cigarette counts. Higher nicotine dependence, white ethnicity and male sex are associated with greater remembered smoking given the EMA count. The model is potentially useful in other applications where it is desirable to understand the process by which subjects remember and report true observations.

Subscale structure for the Positive and Negative Syndrome Scale (PANSS): a proposed solution focused on clinical validity

Although the items of the Positive and Negative Syndrome Scale (PANSS) are ordinal, continuous data methods are consistently used to analyze them. The current study addresses this issue by applying a categorical method and critically examining the ideas of item inclusion and goodness of fit. Data from 1527 subjects were used to test a proposed solution to the factor structure of the PANSS using a categorical factor analytic method. The model was made more generalizable by setting a minimum level of association between the item and the factor, and the results were then compared to existing solutions. The model was also tested for consistency in a first-episode sample. Use of categorical methods indicated similar results to previous analyses; however, it is demonstrated that the strength of the estimates can be unstable when items are shared across factors. The current study demonstrates that solutions can change substantially when a model is over-fitted, and therefore use of measures of fit as the criterion for an acceptable model can mask important relationships and decrease clinical validity.

Research on Individual Differences in Executive Functions: Implications for the Bilingual Advantage Hypothesis

Executive functions (EFs), such as response inhibition, interference control, and set shifting, are general-purpose control mechanisms that enable individuals to regulate their thoughts and behaviors. Because bilingual individuals use EF-like processes during language control, researchers have become interested in the hypothesis that this use might train EFs, resulting in better performance on non-linguistic EF tasks. Although this bilingual advantage hypothesis seems straightforward to test, it involves a number of important decisions in terms of how to assess bilingualism and EFs. In this article, I focus on the complexity of measuring EFs, drawing on individual differences research (conducted with participants not selected for bilingualism). Specifically, I discuss issues related to (1) the measurement of EFs (particularly the effects of task impurity and unreliability) and (2) the multicomponent nature of EFs. Within each of these topics, I elaborate on consequences for research on bilingual advantages and provide some recommendations.

Emerging ideas and tools to study the emergent properties of the cortical neural circuits for voluntary motor control in non-human primates

For years, neurophysiological studies of the cerebral cortical mechanisms of voluntary motor control were limited to single-electrode recordings of the activity of one or a few neurons at a time. This approach was supported by the widely accepted belief that single neurons were the fundamental computational units of the brain (the “neuron doctrine”). Experiments were guided by motor-control models that proposed that the motor system attempted to plan and control specific parameters of a desired action, such as the direction, speed or causal forces of a reaching movement in specific coordinate frameworks, and that assumed that the controlled parameters would be expressed in the task-related activity of single neurons. The advent of chronically implanted multi-electrode arrays about 20 years ago permitted the simultaneous recording of the activity of many neurons. This greatly enhanced the ability to study neural control mechanisms at the population level. It has also shifted the focus of the analysis of neural activity from quantifying single-neuron correlates with different movement parameters to probing the structure of multi-neuron activity patterns to identify the emergent computational properties of cortical neural circuits. In particular, recent advances in “dimension reduction” algorithms have attempted to identify specific covariance patterns in multi-neuron activity which are presumed to reflect the underlying computational processes by which neural circuits convert the intention to perform a particular movement into the required causal descending motor commands. These analyses have led to many new perspectives and insights on how cortical motor circuits covertly plan and prepare to initiate a movement without causing muscle contractions, transition from preparation to overt execution of the desired movement, generate muscle-centered motor output commands, and learn new motor skills. Progress is also being made to import optical-imaging and optogenetic toolboxes from rodents to non-human primates to overcome some technical limitations of multi-electrode recording technology.

Modeling Disease Progression with Longitudinal Markers

In this paper we propose a Bayesian natural history model for disease progression based on the joint modeling of longitudinal biomarker levels, age at clinical detection of disease and disease status at diagnosis. We establish a link between the longitudinal responses and the natural history of the disease by using an underlying latent disease process which describes the onset of the disease and models the transition to an advanced stage of the disease as dependent on the biomarker levels. We apply our model to the data from the Baltimore Longitudinal Study of Aging on prostate specific antigen (PSA) to investigate the natural history of prostate cancer.

A new threshold regression model for survival data with a cure fraction

Due to the fact that certain fraction of the population suffering a particular type of disease get cured because of advanced medical treatment and health care system, we develop a general class of models to incorporate a cure fraction by introducing the latent number N of metastatic-competent tumor cells or infected cells caused by bacteria or viral infection and the latent antibody level R of immune system. Various properties of the proposed models are carefully examined and a Markov chain Monte Carlo sampling algorithm is developed for carrying out Bayesian computation for model fitting and comparison. A real data set from a prostate cancer clinical trial is analyzed in detail to demonstrate the proposed methodology.

A two-level structural equation model approach for analyzing multivariate longitudinal responses

The analysis of longitudinal data to study changes in variables measured repeatedly over time has received considerable attention in many fields. This paper proposes a two-level structural equation model for analyzing multivariate longitudinal responses that are mixed continuous and ordered categorical variables. The first-level model is defined for measures taken at each time point nested within individuals for investigating their characteristics that are changed with time. The second level is defined for individuals to assess their characteristics that are invariant with time. The proposed model accommodates fixed covariates, nonlinear terms of the latent variables, and missing data. A maximum likelihood (ML) approach is developed for the estimation of parameters and model comparison. Results of a simulation study indicate that the performance of the ML estimation is satisfactory. The proposed methodology is applied to a longitudinal study concerning cocaine use.

Theoretical and Methodological Implications of Associations between Executive Function and Mathematics in Early Childhood

Despite agreement about the importance of executive function (EF) for children's early math achievement, its treatment in correlational studies reflects a lack of agreement about the theoretical connection between the two. It remains unclear whether the association between EF and math operates through a latent EF construct or specific EF components. Specifying the correct measurement model has important theoretical implications for the predicted effects of EF interventions on children's math achievement. In the current study, we tested whether associations between EF and math operate via a latent EF factor, or via specific EF components using data from a large, nationally representative sample. We then replicated these same analyses with a meta-analytic database drawn from ten studies that collected measures of children's EF and math achievement. Our results lend support to explanations that a single EF factor accounts for most of the EF component-specific associations with math achievement. We discuss theoretical and methodological implications of these findings for future work.

Data driven model discovery and interpretation for CAR T-cell killing using sparse identification and latent variables

In the development of cell-based cancer therapies, quantitative mathematical models of cellular interactions are instrumental in understanding treatment efficacy. Efforts to validate and interpret mathematical models of cancer cell growth and death hinge first on proposing a precise mathematical model, then analyzing experimental data in the context of the chosen model. In this work, we present the first application of the sparse identification of non-linear dynamics (SINDy) algorithm to a real biological system in order discover cell-cell interaction dynamics in in vitro experimental data, using chimeric antigen receptor (CAR) T-cells and patient-derived glioblastoma cells. By combining the techniques of latent variable analysis and SINDy, we infer key aspects of the interaction dynamics of CAR T-cell populations and cancer. Importantly, we show how the model terms can be interpreted biologically in relation to different CAR T-cell functional responses, single or double CAR T-cell-cancer cell binding models, and density-dependent growth dynamics in either of the CAR T-cell or cancer cell populations. We show how this data-driven model-discovery based approach provides unique insight into CAR T-cell dynamics when compared to an established model-first approach. These results demonstrate the potential for SINDy to improve the implementation and efficacy of CAR T-cell therapy in the clinic through an improved understanding of CAR T-cell dynamics.

Coding of latent variables in sensory, parietal, and frontal cortices during closed-loop virtual navigation

We do not understand how neural nodes operate and coordinate within the recurrent action-perception loops that characterize naturalistic self-environment interactions. Here, we record single-unit spiking activity and local field potentials (LFPs) simultaneously from the dorsomedial superior temporal area (MSTd), parietal area 7a, and dorsolateral prefrontal cortex (dlPFC) as monkeys navigate in virtual reality to 'catch fireflies'. This task requires animals to actively sample from a closed-loop virtual environment while concurrently computing continuous latent variables: (i) the distance and angle travelled (i.e., path integration) and (ii) the distance and angle to a memorized firefly location (i.e., a hidden spatial goal). We observed a patterned mixed selectivity, with the prefrontal cortex most prominently coding for latent variables, parietal cortex coding for sensorimotor variables, and MSTd most often coding for eye movements. However, even the traditionally considered sensory area (i.e., MSTd) tracked latent variables, demonstrating path integration and vector coding of hidden spatial goals. Further, global encoding profiles and unit-to-unit coupling (i.e., noise correlations) suggested a functional subnetwork composed by MSTd and dlPFC, and not between these and 7a, as anatomy would suggest. We show that the greater the unit-to-unit coupling between MSTd and dlPFC, the more the animals' gaze position was indicative of the ongoing location of the hidden spatial goal. We suggest this MSTd-dlPFC subnetwork reflects the monkeys' natural and adaptive task strategy wherein they continuously gaze toward the location of the (invisible) target. Together, these results highlight the distributed nature of neural coding during closed action-perception loops and suggest that fine-grain functional subnetworks may be dynamically established to subserve (embodied) task strategies.