Missing Patterns Research Articles

Odontocete spatial patterns and temporal drivers of detection at sites in the Hawaiian islands.

Successful conservation and management of marine top predators rely on detailed documentation of spatiotemporal behavior. For cetacean species, this information is key to defining stocks, habitat use, and mitigating harmful interactions. Research focused on this goal is employing methodologies such as visual observations, tag data, and passive acoustic monitoring (PAM) data. However, many studies are temporally limited or focus on only one or few species. In this study, we make use of an existing long-term (2009-2019), labeled PAM data set to examine spatiotemporal patterning of at least 10 odontocete (toothed whale) species in the Hawaiian Islands using compositional analyses and modeling techniques. Species composition differs among considered sites, and this difference is robust to seasonal movement patterns. Temporally, hour of day was the most significant predictor of detection across species and sites, followed by season, though patterns differed among species. We describe long-term trends in species detection at one site and note that they are markedly similar for many species. These trends may be related to long-term, underlying oceanographic cycles that will be the focus of future study. We demonstrate the variability of temporal patterns even at relatively close sites, which may imply that wide-ranging models of species presence are missing key fine-scale movement patterns. Documented seasonal differences in detection also highlights the importance of considering season in survey design both regionally and elsewhere. We emphasize the utility of long-term, continuous monitoring in highlighting temporal patterns that may relate to underlying climatic states and help us predict responses to climate change. We conclude that long-term PAM records are a valuable resource for documenting spatiotemporal patterns and can contribute many insights into the lives of top predators, even in highly studied regions such as the Hawaiian Islands.

A Novel Nonconvex Low-Rank Tensor Completion Approach for Traffic Sensor Data Recovery From Incomplete Measurements

Complete traffic sensor data is considered to be one of the critical ingredients for intelligent transportation systems (ITS). However, the traffic measurements prevalently suffer from the inevitable and ubiquitous missing values. Current missing data completion algorithms are difficult to leverage the global low-rank property and the fine-grained spatial-temporal structure simultaneously. To circumvent this problem, this work presents a novel collaborative nonconvex low-rank spatial-temporal data tensor completion model that can take full advantage of the inherent spatial-temporal characteristics of traffic measurement data. First, the tensor Schatten p-norm, as an effective nonconvex surrogate of rank function, is used to exploit the global multi-dimensional correlation of traffic data. Then, we present an elastic net self-representation method and utilize an autoregression model in order to simultaneously capture the self-similarity and the temporal continuity of traffic data acquired in the same sensor network. By integrating the above elements in a unified nonconvex learning model, our method can explore the inherent structure of traffic data from the viewpoints of both global multi-dimensional correlation and fine-grained spatial and temporal dependency. Then, in the view of the general framework of the alternating directions method of multipliers (ADMM), an efficient iterative algorithm is designed to solve our model. Besides, to optimize the parameter combination of the model, a Bayesian optimization-based parameter selection algorithm is developed, which avoids manual parameter adjustment. Extensive experiments and analyses on two real-world traffic datasets are carried out. The results demonstrate the advantages of our model under diverse missing patterns and missing ratios.

Causal Inference for Social and Engineering Systems

What will happen to Y if we do A? A variety of meaningful social and engineering questions can be formulated this way: What will happen to a patient's health if they are given a new therapy? What will happen to a country's economy if policy-makers legislate a new tax? What will happen to a data center's latency if a new congestion control protocol is used? We explore how to answer such counterfactual questions using observational data-which is increasingly available due to digitization and pervasive sensors-and/or very limited experimental data. The two key challenges are: (i) counterfactual prediction in the presence of latent confounders; (ii) estimation with modern datasets which are high-dimensional, noisy, and sparse. The key framework we introduce is connecting causal inference with tensor completion. In particular, we represent the various potential outcomes (i.e., counterfactuals) of interest through an order-3 tensor. The key theoretical results presented are: (i) Formal identification results establishing under what missingness patterns, latent confounding, and structure on the tensor is recovery of unobserved potential outcomes possible. (ii) Introducing novel estimators to recover these unobserved potential outcomes and proving they are finite-sample consistent and asymptotically normal. Finally, we discuss connections between matrix/tensor completion and time series analysis and reinforcement learning; we believe this could serve as a basis to do counterfactual forecasting, and building data-driven simulators for reinforcement learning.

Appropriately estimating the standardized average treatment effect with missing data: A simulation and primer.

Reporting standardized effects in randomized treatment studies aids interpretation and facilitates future meta-analyses and policy considerations. However, when outcome data are missing, achieving an unbiased, accurate estimate of the standardized average treatment effect, sATE, can pose challenges even for those with general knowledge of missing data handling, given that the sATE is a ratio of a mean difference to a (within-group) standard deviation. Under both homogeneity and heterogeneity of variance, a Monte Carlo simulation study was conducted to compare missing data handling strategies in terms of bias and accuracy in the sATE, under specific missingness patterns plausible for randomized pretest posttest studies. Within two broad missing data handling approaches, maximum likelihood and multiple imputation, modeling choices were thoroughly investigated including the analysis model, variance estimator, imputation algorithm, and method of pooling results across imputed datasets. Results demonstrated that although the sATE can be estimated with little bias using either maximum likelihood or multiple imputation, particular attention should be paid to the model and variance estimator, especially at smaller sample sizes (i.e., N = 50). Differences in accuracy were driven by differences in bias. To improve estimation of the sATE in practice, recommendations and a software demonstration are provided. Moreover, a pedagogical explanation of the causes of bias, described separately for the numerator and denominator of the sATE is provided, demonstrating visually how and why bias occurs with certain methods.

ASSESSING NONSAMPLING BIAS ERROR AMONG SEXUAL MINORITY OLDER ADULTS IN THE CENSUS' HOUSEHOLD PULSE SURVEY

Abstract Previous research shows data quality and nonsampling bias error reduce accuracy of COVID-19 vaccination coverage in the Census' Household Pulse Survey. However, it is unclear how these issues relate to older sexual minority populations. Moreover, previous research has shown that sexual minority older adults survey nonparticipation rates are similar to their heterosexual older adult peers. Yet, it is less clear whether racial/ethnic variability in nonparticipation rates and patterns of missingness among sexual minority older adults exist. The current investigation utilizes repeated pooled data from the Census' Household Pulse Survey (N=329,078) to fill these gaps. Findings reveal nonsampling bias error contributing to inflated racial/ethnic inequities in vaccination coverage among older sexual minorities, with distinct racial/ethnic variability in missingness patterns among sexual minority older adults. The paper concludes with recommendations for improving survey-based research and details suggestions to improve recruitment strategies that minimize nonsampling bias.

A Realistic Evaluation of Methods for Handling Missing Data When There is a Mixture of MCAR, MAR, and MNAR Mechanisms in the Same Dataset

The impact of missing data on statistical inference varies depending on several factors such as the proportion of missingness, missing-data mechanism, and method employed to handle missing values. While these topics have been extensively studied, most recommendations have been made assuming that all missing values are from the same missing-data mechanism. In reality, it is very likely that a mixture of missing-data mechanisms is responsible for missing values in a dataset and even within the same pattern of missingness. Although a mixture of missing-data mechanisms and causes within a dataset is a likely scenario, the performance of popular missing-data methods under these circumstances is unknown. This study provides a realistic evaluation of methods for handling missing data in this setting using Monte Carlo simulation in the context of regression. This study also seeks to identify acceptable proportions of missing values that violate the missing-data mechanism assumed by the method used to handle missing values. Results indicate that multiple imputation (MI) performs better than other principled or ad-hoc methods. Different missing-data methods are also compared via the analysis of a real dataset in which mixtures of missingness mechanisms are created. Recommendations are provided for the use of different methods in practice.

Dynamic graph convolutional recurrent imputation network for spatiotemporal traffic missing data

In real-world intelligent transportation systems, the spatiotemporal traffic data collected from sensors often exhibit missing or corrupted data, significantly hindering the development of traffic data research. Missing data imputation is a classic research topic that encompasses a wide range of methods. However, these methods are typically underdeveloped in two aspects: the dynamic spatial dependencies of the road network over time, and the information extraction and utilization of diverse data. In this study, we design a novel deep learning architecture – Dynamic Graph Convolutional Recurrent Imputation Network (DGCRIN) – as a tool to impute missing traffic data. The DGCRIN employs a graph generator and dynamic graph convolutional gated recurrent unit (DGCGRU) to perform fine-grained modeling of the dynamic spatiotemporal dependencies of road network. Additionally, an auxiliary GRU learns the missing pattern information of the data, and a fusion layer with a decay mechanism is introduced to fuse a diverse range of information. This architecture enables the DGCRIN to be highly adaptable to complex scenarios involving missing data. Extensive experiments on two datasets demonstrate the superiority of DGCRIN over multiple baseline models.

Dyadic retention in a phase 3 mild cognitive impairment clinical trial

AbstractBackgroundExiting a study early (dropout) may bias treatment effect estimates, while dropout and missing visits reduces study power. Simply increasing planned sample sizes cannot remove bias due to non‐ignorable missingness (Fleming, 2011). Preventing missing data is best (National Research Council, 2010). Hence, quantifying associations with missingness may identify ways to improve retention. Alzheimer’s disease (AD) clinical trials require study participation by a participant and study partner. Previous research examined dyadic retention in AD dementia trials (Grill et al., 2013; Bernstein, Grill & Gillen, 2021), yet less is understood in mild cognitive impairment (MCI) trials. Here, we examined MCI trial dropout rates and missingness patterns by dyad type.MethodWe performed retrospective analyses of the Alzheimer’s Disease Cooperative Study phase 3 MCI trial of donepezil and vitamin E. Scheduled study visits occurred at baseline, month 3, and semi‐annually until month 36. Study completion included the progression to a possible or probable AD diagnosis or month 36 visit. Dropout was withdrawal of consent or lost‐to‐follow‐up. Deaths and study completions were censored. Dyad types were spousal, adult child, or other. We estimated Kaplan‐Meier‐based dropout rates and summarized frequencies of on‐study missing visit patterns by baseline dyad type and stratified by randomized treatment (placebo, donepezil, vitamin E).ResultFigure 1 displays cumulative dropout rates by dyad type and treatment (panels A, B, C). Among 259 participants randomized to placebo, estimated study dropout rates were 24% for spousal, 16% for adult child, and 14% for other dyads. Table 1 summarizes on‐study missing visit patterns by dyad type and treatment; Figure 2 displays placebo data for specific patterns of missing data. While on study, 21% of spousal, 23% of adult child, and 27% of other dyads missed at least one scheduled visit, primarily monotonic missingness.ConclusionDyad type may be associated with some types of missingness in MCI clinical trials. Implementing dyad‐type‐specific strategies that encourage staying on study and attending all scheduled visits may improve retention, thus reducing bias, in future MCI trials.

Implementing Multiple Imputation for Missing Data in Longitudinal Studies When Models are Not Feasible: An Example Using the Random Hot Deck Approach.

Researchers often use model-based multiple imputation to handle missing at random data to minimize bias. However, constraints within the data may sometimes result in implausible values, making model-based imputation infeasible. In these contexts, we illustrate how random hot deck imputation can allow for plausible multiple imputation in longitudinal studies. Our motivating example is the Childhood Health, Activity, and Motor Performance School Study Denmark (CHAMPS-DK), a prospective cohort study that measured weekly sports participation for 1700 Danish schoolchildren. Using observed data on 4 variables (pain, activity frequency, sport, sport counts), we created a gold-standard data set without missing data. We then created a synthetic data set by setting some variable values to missing based on a prediction model that mimicked real-data missingness patterns. To create 5 imputed data sets, we matched each record with missing data to several fully observed records, generated probabilities from matched records, and sampled from these records based on the probability of each occurring. We assessed variability and agreement (kappa) between the imputed data sets and the gold-standard data set. We compare results to common model-based imputation methods. Variability across data sets appeared reasonable. The range of kappa for the random hot deck approach was moderate for activity frequency (0.65 to 0.71) and sport (0.59 to 0.85), and poor for common model-based approaches (range 0.00 to 0.11). The range of kappas for sport count was strong (0.87 to 0.97) for random hot deck imputation and weak to moderate (0.55 to 0.71) for common model-based imputation. Agreement was higher when more information was present, and when prevalence was higher for our binary variable sport. Random hot deck imputation should be considered as an alternative method when model-based approaches are infeasible, specifically where there are constraints within and between covariates.

To Explore What Isn't There-Glyph-Based Visualization for Analysis of Missing Values.

This article contributes a novel visualization method, Missingness Glyph, for analysis and exploration of missing values in data. Missing values are a common challenge in most data generating domains and may cause a range of analysis issues. Missingness in data may indicate potential problems in data collection and pre-processing, or highlight important data characteristics. While the development and improvement of statistical methods for dealing with missing data is a research area in its own right, mainly focussing on replacing missing values with estimated values, considerably less focus has been put on visualization of missing values. Nonetheless, visualization and explorative analysis has great potential to support understanding of missingness in data, and to enable gaining of novel insights into patterns of missingness in a way that statistical methods are unable to. The Missingness Glyph supports identification of relevant missingness patterns in data, and is evaluated and compared to two other visualization methods in context of the missingness patterns. The results are promising and confirms that the Missingness Glyph in several cases perform better than the alternative visualization methods.

Using missing dispersion patterns to detect determinism and nonlinearity in time series data

Using missing dispersion patterns to detect determinism and nonlinearity in time series data

Performance of LTMLE in the Presence of Missing Data in Control-Matched Longitudinal Studies

Conventional controlled trials employ randomization and blinding to ensure the balance of baseline covariates between study arms. Treatment effect is formally tested via a pre-specified hypothesis reflecting trial’s primary objective defined by the primary efficacy endpoint, such as, is experimental treatment effective in slowing cognitive decline at a pre-specified landmark time in a neurologic therapeutic development? To address the same clinical question, but, as a safety endpoint in an observational study post radiopharmaceutical imaging drug approval due to concerns of radiation retention in the brain after accumulated real-world use over time, the targeted minimum loss-based estimation (TMLE) method has been suggested. Overall, for a longitudinal control-matched cohort study, assessing treatment effect (efficacy or safety) in the presence of missingness can be very challenging, which depends also on trial duration and missingness pattern of outcome data between study arms. TMLE is a two-step procedure to estimate a target parameter and has been shown to be doubly robust. The objectives of our research are a few folds. First, we investigate the performance of the TMLE method using longitudinal structure (LTMLE) in a prospective control-matched longitudinal cohort study. Second, we evaluate the performance of LTMLE and a few methods that are often proposed in regulatory submissions for longitudinal data analysis or in the presence of missing data with various missing data mechanisms. Third, we assess the impacts of various missing data mechanisms to treatment effect estimation via extensive simulation studies. Finally, we discuss the results of the simulation studies and their implications to conducting a feasible real-world control-matched longitudinal cohort study.

Imputation of Missing SST Observation Data Using Multivariate Bidirectional RNN

The data of the missing section among the vertex surface sea temperature observation data was imputed using the Bidirectional Recurrent Neural Network(BiRNN). Among artificial intelligence techniques, Recurrent Neural Networks (RNNs), which are commonly used for time series data, only estimate in the direction of time flow or in the reverse direction to the missing estimation position, so the estimation performance is poor in the long-term missing section. On the other hand, in this study, estimation performance can be improved even for long-term missing data by estimating in both directions before and after the missing section. Also, by using all available data around the observation point (sea surface temperature, temperature, wind field, atmospheric pressure, humidity), the imputation performance was further improved by estimating the imputation data from these correlations together. For performance verification, a statistical model, Multivariate Imputation by Chained Equations (MICE), a machine learning-based Random Forest model, and an RNN model using Long Short-Term Memory (LSTM) were compared. For imputation of long-term missing for 7 days, the average accuracy of the BiRNN/ statistical models is 70.8%/61.2%, respectively, and the average error is 0.28 degrees/0.44 degrees, respectively, so the BiRNN model performs better than other models. By applying a temporal decay factor representing the missing pattern, it is judged that the BiRNN technique has better imputation performance than the existing method as the missing section becomes longer.

Sequential Multiple Imputation for Real-World Health-Related Quality of Life Missing Data after Bariatric Surgery.

One of the main challenges for the successful implementation of health-related quality of life (HRQoL) assessments is missing data. The current study examined the feasibility and validity of a sequential multiple imputation (MI) method to deal with missing values in the longitudinal HRQoL data from the Scandinavian Obesity Surgery Registry. All patients in the SOReg who received bariatric surgery between 1 January 2011 and 31 March 2019 (n = 47,653) were included for the descriptive analysis and missingness pattern exploration. The patients who had completed the short-form 36 (SF-36) at baseline (year 0), and one-, two-, and five-year follow-ups were included (n = 3957) for the missingness pattern simulation and the sequential MI analysis. Eleven items of the SF-36 were selected to create the six domains of SF-6D, and the SF-6D utility index of each patient was calculated accordingly. The multiply-imputed variables in previous year were used as input to impute the missing values in later years. The performance of the sequential MI was evaluated by comparing the actual values with the imputed values of the selected SF-36 items and index at all four time points. At the baseline and year 1, where missing proportions were about 20% and 40%, respectively, there were no statistically significant discrepancies between the distributions of the actual and imputed responses (all p-values > 0.05). In year 2, where the missing proportion was about 60%, distributions of the actual and imputed responses were consistent in 9 of the 11 SF-36 items. However, in year 5, where the missing proportion was about 80%, no consistency was found between the actual and imputed responses in any of the SF-36 items. Relatively high missing proportions in HRQoL data are common in clinical registries, which brings a challenge to analyzing the HRQoL of longitudinal cohorts. The experimental sequential multiple imputation method adopted in the current study might be an ideal strategy for handling missing data (even though the follow-up survey had a missing proportion of 60%), avoiding significant information waste in the multivariate analysis. However, the imputations for data with higher missing proportions warrant more research.

Piloting and validating the linkage of routine ART and laboratory records in an HIV endemic setting.

ObjectivesIntegrating clinical and laboratory data systems offers opportunities to understand disease aetiology and improve patient outcomes. We developed and piloted a data linkage algorithm to link HIV patient treatment records with routine laboratory service records in an HIV endemic setting in rural South Africa. ApproachWe used data from the South Africa’s National Health Laboratory Service (NHLS) and Three Integrated Electronic Registers (TIER.Net) databases for 17 primary healthcare clinics from uMkhanyakude district, South Africa. The two databases contained data on key demographic variables such as patient first name, surname, date of birth, sex, and health facility, and national ID numbers for a subset of the data. We adapted a probabilistic record linkage algorithm we previously developed for linkage of laboratory results. We trained and validated our algorithm using two approaches: 1) firstly, we constructed a quasi-gold standard based on manual review of potential matches for 1,061 randomly selected patients; 2) secondly, we constructed a quasi-gold standard based on records that contained national ID numbers. We calculated the probabilities that the algorithm could correctly identify a true match (sensitivity) and the probabilities that the match identified by the algorithm was truly a match (positive predictive value) using the two approaches. ResultsBetween 2015 and 2020, 55,077 patients were recorded in the HIV treatment database and 386,577 laboratory tests were recorded in the laboratory service database. The sensitivity and positive predictive value in the manually reviewed data were estimated to be 94.4% and 81.2% respectively. The sensitivity and positive predictive value in the matched individual identifiers were estimated to be 99.6% and 99.7% respectively. ConclusionsRecords can be linked successfully, but estimated performance of record linkage depends on the validation set used. Manually reviewed data contain noise and may underestimate performance, while national ID numbers may overestimate performance due to non-random patterns of missingness.

Exploiting Missing Value Patterns for a Backdoor Attack on Machine Learning Models of Electronic Health Records: Development and Validation Study.

BackgroundA backdoor attack controls the output of a machine learning model in 2 stages. First, the attacker poisons the training data set, introducing a back door into the victim’s trained model. Second, during test time, the attacker adds an imperceptible pattern called a trigger to the input values, which forces the victim’s model to output the attacker’s intended values instead of true predictions or decisions. While backdoor attacks pose a serious threat to the reliability of machine learning–based medical diagnostics, existing backdoor attacks that directly change the input values are detectable relatively easily.ObjectiveThe goal of this study was to propose and study a robust backdoor attack on mortality-prediction machine learning models that use electronic health records. We showed that our backdoor attack grants attackers full control over classification outcomes for safety-critical tasks such as mortality prediction, highlighting the importance of undertaking safe artificial intelligence research in the medical field.MethodsWe present a trigger generation method based on missing patterns in electronic health record data. Compared to existing approaches, which introduce noise into the medical record, the proposed backdoor attack makes it simple to construct backdoor triggers without prior knowledge. To effectively avoid detection by manual inspectors, we employ variational autoencoders to learn the missing patterns in normal electronic health record data and produce trigger data that appears similar to this data.ResultsWe experimented with the proposed backdoor attack on 4 machine learning models (linear regression, multilayer perceptron, long short-term memory, and gated recurrent units) that predict in-hospital mortality using a public electronic health record data set. The results showed that the proposed technique achieved a significant drop in the victim’s discrimination performance (reducing the area under the precision-recall curve by at most 0.45), with a low poisoning rate (2%) in the training data set. In addition, the impact of the attack on general classification performance was negligible (it reduced the area under the precision-recall curve by an average of 0.01025), which makes it difficult to detect the presence of poison.ConclusionsTo the best of our knowledge, this is the first study to propose a backdoor attack that uses missing information from tabular data as a trigger. Through extensive experiments, we demonstrated that our backdoor attack can inflict severe damage on medical machine learning classifiers in practice.

Memory-augmented dynamic graph convolution networks for traffic data imputation with diverse missing patterns

Missing data is an inevitable and ubiquitous problem for traffic data collection in intelligent transportation systems. Recent research has employed graph neural networks (GNNs) for spatiotemporal data imputation and achieved promising performance. However, there still exist two limitations to be addressed: first, existing approaches are generally limited in directly leveraging global spatiotemporal information from different nodes at different time; second, most of these approaches do not consider the unique characteristics of transportation systems or traffic data, including dynamic spatial dependencies and correlated missing patterns. To fill these research gaps, we propose a novel deep learning framework called Memory-augmented Dynamic Graph Convolution Networks (MDGCN) to impute missing traffic data. The model uses a recurrent layer to capture temporal information and a graph convolution layer to capture spatial information. To address the first research gap, we introduce an external memory network to store and share the global spatiotemporal information across the traffic network. For the second research gap, a graph structure estimation technique is proposed to learn dynamic spatial dependencies directly from traffic data. In addition, four types of missing patterns with various missing ratios are considered in model evaluation. Extensive experiments based on two public traffic speed datasets are conducted. The results show that our proposed model outperforms existing state-of-the-art deep learning approaches in all kinds of missing scenarios, and both the proposed external memory network and graph structure estimation technique contribute to the model performance. The model performance is competitive in most cases even without complete training data.

Graph Spectral Regularized Tensor Completion for Traffic Data Imputation

In intelligent transportation systems (ITS), incomplete traffic data due to sensor malfunctions and communication faults, seriously restricts the related applications of ITS. Recovering missing data from incomplete traffic data becomes an important issue for ITS. Existing works on traffic data imputation cannot achieve satisfactory accuracy due to inefficiently exploiting the underlying topological structure of the traffic data. In this paper, we model the topology of the road network as a graph and introduce graph Fourier transform (GFT) to process the traffic data. Then we utilize an algebraic framework termed as graph-tensor singular value decompositions (GT-SVD) to extract the hidden spatial information of traffic data. Furthermore, we propose a novel graph spectral regularized tensor completion algorithm based on GT-SVD and construct temporal regularized constraints to improve the recovery accuracy. The extensive experimental results on real traffic datasets demonstrate that the proposed algorithm outperforms the state-of-the-art methods under different missing patterns.

An exact test for equality of two normal mean vectors with monotone missing data

The problem of testing equality of two normal mean vectors with incomplete data when the covariance matrices are equal is considered. For data matrices with monotone missing pattern, an exact test is proposed as an alternative one to the traditional likelihood ration test. Numerical power comparisons show that the powers of the proposed test and the likelihood ration test are comparable. However, the proposed test is an exact one. It is easy to use and useful to identify the component that caused the rejection of null hypothesis. It is illustrated using an example.

Children's use of egocentric reference frames in spatial language is related to their numerical magnitude understanding.

Numerical magnitude information is assumed to be spatially represented in the form of a mental number line defined with respect to a body-centred, egocentric frame of reference. In this context, spatial language skills such as mastery of verbal descriptions of spatial position (e.g., in front of, behind, to the right/left) have been proposed to be relevant for grasping spatial relations between numerical magnitudes on the mental number line. We examined 4- to 5-year-old’s spatial language skills in tasks that allow responses in egocentric and allocentric frames of reference, as well as their relative understanding of numerical magnitude (assessed by a number word comparison task). In addition, we evaluated influences of children’s absolute understanding of numerical magnitude assessed by their number word comprehension (montring different numbers using their fingers) and of their knowledge on numerical sequences (determining predecessors and successors as well as identifying missing dice patterns of a series). Results indicated that when considering responses that corresponded to the egocentric perspective, children’s spatial language was associated significantly with their relative numerical magnitude understanding, even after controlling for covariates, such as children’s SES, mental rotation skills, and also absolute magnitude understanding or knowledge on numerical sequences. This suggests that the use of egocentric reference frames in spatial language may facilitate spatial representation of numbers along a mental number line and thus seem important for preschoolers’ relative understanding of numerical magnitude.