Variance-covariance Structure Research Articles

Bayesian inference in arm posture perception.

To configure our limbs in space, the brain must compute their position based on sensory information provided by mechanoreceptors in the skin, muscles, and joints. Because this information is corrupted by noise, the brain is thought to process it probabilistically and integrate it with prior belief about arm posture, following Bayes' rule. Here, we combined computational modeling with behavioral experimentation to test this hypothesis. The model conceives the perception of arm posture as the combination of a probabilistic kinematic chain composed by the shoulder, elbow, and wrist angles, compromised with additive Gaussian noise, with a Gaussian prior about these joint angles. We tested whether the model explains errors in a virtual reality (VR)-based posture matching task better than a model that assumes a uniform prior. Human participants (N = 20) were required to align their unseen right arm to a target posture, presented as a visual configuration of the arm in the horizontal plane. Results show idiosyncratic biases in how participants matched their unseen arm to the target posture. We used maximum likelihood estimation to fit the Bayesian model to these observations and estimate key parameters including the prior means and its variance-covariance structure. The Bayesian model including a Gaussian prior explained the response biases and variance much better than a model with a uniform prior. The prior varied across participants, consistent with the idiosyncrasies in arm posture perception and in alignment with previous behavioral research. Our work clarifies the biases in arm posture perception within a new perspective on the nature of proprioceptive computations.NEW & NOTEWORTHY We modeled the perception of arm posture as a Bayesian computation. A VR posture-matching task was used to empirically test this Bayesian model. The Bayesian model including a nonuniform postural prior well explained individual participants' biases in arm posture matching.

Factor-Analytic Variance-Covariance Structures for Prediction Into a Target Population of Environments.

Finlay-Wilkinson regression is a popular method for modeling genotype-environment interaction in plant breeding and crop variety testing. When environment is a random factor, this model may be cast as a factor-analytic variance-covariance structure, implying a regression on random latent environmental variables. This paper reviews such models with a focus on their use in the analysis of multi-environment trials for the purpose of making predictions in a target population of environments. We investigate the implication of random versus fixed effects assumptions, starting from basic analysis-of-variance models, then moving on to factor-analytic models and considering the transition to models involving observable environmental covariates, which promise to provide more accurate and targeted predictions than models with latent environmental variables.

Accuracy of prediction from multi-environment trials for new locations using pedigree information and environmental covariates: the case of sorghum (Sorghum bicolor (L.) Moench) breeding

Key messagesWe investigate a method of extracting and fitting synthetic environmental covariates and pedigree information in multilocation trial data analysis to predict genotype performances in untested locations.Plant breeding trials are usually conducted across multiple testing locations to predict genotype performances in the targeted population of environments. The predictive accuracy can be increased by the use of adequate statistical models. We compared linear mixed models with and without synthetic covariates (SCs) and pedigree information under the identity, the diagonal and the factor-analytic variance-covariance structures of the genotype-by-location interactions. A comparison was made to evaluate the accuracy of different models in predicting genotype performances in untested locations using the mean squared error of predicted differences (MSEPD) and the Spearman rank correlation between predicted and adjusted means. A multi-environmental trial (MET) dataset evaluated for yield performance in the dry lowland sorghum (Sorghum bicolor (L.) Moench) breeding program of Ethiopia was used. For validating our models, we followed a leave-one-location-out cross-validation strategy. A total of 65 environmental covariates (ECs) obtained from the sorghum test locations were considered. The SCs were extracted from the ECs using multivariate partial least squares analysis and subsequently fitted in the linear mixed model. Then, the model was extended accounting for pedigree information. According to the MSEPD, models accounting for SC improve predictive accuracy of genotype performances in the three of the variance-covariance structures compared to others without SC. The rank correlation was also higher for the model with the SC. When the SC was fitted, the rank correlation was 0.58 for the factor analytic, 0.51 for the diagonal and 0.46 for the identity variance-covariance structures. Our approach indicates improvement in predictive accuracy with SC in the context of genotype-by-location interactions of a sorghum breeding in Ethiopia.

Linear modeling of zonal level crop production in Ethiopia

Accounting for zonal-level variations and identifying factors that have linear effects on crop production help to make better decisions and plan new policies for effective crop production and food security. The main objective of this study is to identify potential subsets of covariates and estimate their linear effects on crop production. A linear mixed effects model (random--intercept) is used on agricultural sample survey data for Meher seasons from 2012/13 to 2019/20 to explore and identify the best variance-covariance structure for the longitudinal data on 90 zones with eight repeated observations and different sampling weights. The minimum, mean, and maximum crop production by farmers across the country are 1.616, 8.693, and 147.843 quintals, respectively, and about 98 % of farmers produced less than 25 quintals. There is a small rate of increase in mean and median crop production by farmers across the years, and the variability between zones is highest in the year 2019/20 and in the Somali region. The histogram, kernel density, and P–P plots suggested a common logarithm transformation on the crop production variable. Results from the data exploration and variance-covariance structure selection methods suggested a heterogeneous compound symmetry (CSH) structure. Covariates region, year, proportion of farmers who practice pure-agriculture and other-agriculture types, proportion of farmers who use any type of fertilizer, farmer's age, area used, farmer association crop production, indigenous seed used, improved seed used, UREA fertilizer used, other fertilizers used, and percentage of crop damaged are significant in linearly explaining/affecting log crop production, and among these area used, farmers association crop production, UREA fertilizer used, and indigenous seed used have relatively highest effect on log crop production. Zones Wolayita, North-Shewa (Am), West-Arsi, West-Welega, Dawro, and Guji are top/good performers while zones Southwest-Shewa, Waghimra, Guraghe, South-Omo, Keffa, North-Wello, South-Wello, and Eastern Tigray are bottom/poor performers in crop production. Model assumptions and influence diagnostics results suggested the linearity of the model and normality of random effects and residuals are not violated, even though some zones have influences on either model parameters, precisions of estimates of these parameters, and predicted values.

A cautionary tale on the effects of different covariance structures in linear mixed effects modeling of fMRI data.

With the steadily increasing abundance of longitudinal neuroimaging studies with large sample sizes and multiple repeated measures, questions arise regarding the appropriate modeling of variance and covariance. The current study examined the influence of standard classes of variance-covariance structures in linear mixed effects (LME) modeling of fMRI data from patients with pediatric mild traumatic brain injury (pmTBI; N = 181) and healthy controls (N = 162). During two visits, participants performed a cognitive control fMRI paradigm that compared congruent and incongruent stimuli. The hemodynamic response function was parsed into peak and late peak phases. Data were analyzed with a 4-way (GROUP×VISIT×CONGRUENCY×PHASE) LME using AFNI's 3dLME and compound symmetry (CS), autoregressive process of order 1 (AR1), and unstructured (UN) variance-covariance matrices. Voxel-wise results dramatically varied both within the cognitive control network (UN>CS for CONGRUENCY effect) and broader brain regions (CS>UN for GROUP:VISIT) depending on the variance-covariance matrix that was selected. Additional testing indicated that both model fit and estimated standard error were superior for the UN matrix, likely as a result of the modeling of individual terms. In summary, current findings suggest that the interpretation of results from complex designs is highly dependent on the selection of the variance-covariance structure using LME modeling.

A framework to study and predict functional trait syndromes using phylogenetic and environmental data

Abstract Traits do not evolve in isolation but often as part of integrated trait syndromes, yet the relative contributions of environmental effects and evolutionary history on traits and their correlations are not easily resolved. In the present study, we develop a methodological framework to elucidate eco‐evolutionary patterns in functional trait syndromes. We do so by separating the amount of variance and covariance related to phylogenetic heritage and environmental variables (environmental phylogenetic conservatism), only phylogenetic heritage (non‐attributed phylogenetic conservatism) and only to environmental variables (evolutionarily labile environmental effects). Variance–covariance structures of trait syndromes are displayed as networks. We then use this framework to guide a newly derived imputation method based on machine learning models that predict trait values for unsampled taxa, considering environmental and phylogenetic information as well as trait covariation. TrEvol is presented as an R package providing a unified set of methodologies to study and predict multivariate trait patterns and improve our capacity to impute trait values. To illustrate its use, we leverage both simulated data and species‐level traits related to hydraulics and the leaf economics spectrum, in relation to an aridity index, demonstrating that most trait correlations can be attributed to environmental phylogenetic conservatism. This conceptual framework can be employed to examine issues ranging from the evolution of trait adaptation at different phylogenetic depths to intraspecific trait variation.

Modeling basal area yield using simultaneous equation systems incorporating uncertainty estimators

Abstract Over the last three decades, many growth and yield systems developed for the southeast USA have incorporated methods to create a compatible basal area (BA) prediction and projection equation. This technique allows practitioners to calibrate BA models using both measurements at a given arbitrary age, as well as the increment in BA when time series panel data are available. As a result, model parameters for either prediction or projection alternatives are compatible. One caveat of this methodology is that pairs of observations used to project forward have the same weight as observations from a single measurement age, regardless of the projection time interval. To address this problem, we introduce a variance–covariance structure giving different weights to predictions with variable intervals. To test this approach, prediction and projection equations were fitted simultaneously using an ad hoc matrix structure. We tested three different error structures in fitting models with (i) homoscedastic errors described by a single parameter (Method 1); (ii) heteroscedastic errors described with a weighting factor ${w}_t$ (Method 2); and (iii) errors including both prediction ($\overset{\smile }{\varepsilon }$) and projection errors ($\tilde{\varepsilon}$) in the weighting factor ${w}_t$ (Method 3). A rotation-age dataset covering nine sites, each including four blocks with four silvicultural treatments per block, was used for model calibration and validation, including explicit terms for each treatment. Fitting using an error structure which incorporated the combined error term ($\overset{\smile }{\varepsilon }$ and $\tilde{\varepsilon}$) into the weighting factor ${w}_t$ (Method 3), generated better results according to the root mean square error with respect to the other two methods evaluated. Also, the system of equations that incorporated silvicultural treatments as dummy variables generated lower root mean square error (RMSE) and Akaike’s index values (AIC) in all methods. Our results show a substantial improvement over the current prediction-projection approach, resulting in consistent estimators for BA.

Tekrarlanan ölçümlerde farklı kovaryans yapılarının Bayes yöntemi ile modellenmesi

Objective: The objective of this study was to obtain solutions by modeling different covariance structures with Bayesian analysis methods in repeated measurement and to show its applicability to data in animal science. 
 Materials and Methods: This article focused on the analysis of the body weight data of 4154 weaned 8-month-old lambs. Repeated measurement analyses based on the mixed effect model were evaluated with Bayesian methods. Models were created for 12 different covariance structures. As the model comparison criterion, Deviation Information Criteria based on the relationship between the fit of the data to the model and the complexity of the model were used. 
 Result: Among 12 different covariance structures, the unstructured covariance structure was determined as a suitable structure for the data of this study.
 Conclusions: It was concluded that various variance-covariance structures, such as body weight, can be easily modeled in repeated measurement data. Instead of PROC MCMC methods that require complex and computational difficulties and profound coding knowledge, it was presented a relatively user-friendly and fast procedure with its theoretical structure and demonstrated its feasibility. As a result of the literature review, this is the first study in which Bayesian methods solved a wide variety of variance-covariance structure models.

Comparison between multiple-trait and random regression models for genetic evaluation of weight traits in Australian meat sheep.

Random regression (RR) models are recommended as an alternative to multiple-trait (MT) models for better capturing the variance-covariance structure over a trajectory and hence more accurate genetic evaluation of traits that are repeatedly measured and genetically change gradually over time. However, a limited number of studies have been done to empirically compare RR over a MT model to determine how much extra benefit could be achieved from one method over another. We compared the prediction accuracy of RR and MT models for growth traits of Australian meat sheep measured from 60 to 525d, using 102,579 weight records from 24,872 animals. Variance components and estimated breeding values (EBVs) estimated at specific ages were compared and validated with forward prediction. The accuracy of EBVs obtained from the MT model was 0.58, 0.51, 0.54, and 0.56 for weaning, postweaning, yearling, and hogget weight stages, respectively. RR model produced accuracy estimates of 0.56, 0.51, 0.54, and 0.54 for equivalent weight stages. Regression of adjusted phenotype on EBVs was very similar between the MT and the RR models (P > 0.05). Although the RR model did not significantly increase the accuracy of predicting future progeny performance, there are other benefits of the model such as no limit to the number of records per animal, estimation of EBVs for early and late growth, no need for age correction. Therefore, RR can be considered a more flexible method for the genetic evaluation of Australian sheep for early and late growth, and no need for age correction.

PSIX-16 Observational Canine Aging Study: a Diet Enriched in Antioxidants Reduces Cognitive and Physical Decline

Abstract Older pets often exhibit changes in behaviors and/or mental health such as altered sleeping habits, activity level, social orientation, cognitive ability and overall vitality. Nutrition has been shown in animal models to impact senescence progression. However, symptoms associated with aging often are insidious and unobserved. As a result, nutritional adjustments may be delayed or in some cases never implemented as some pets age. This study was conducted to measure observed behavioral responses of aging dogs being fed an investigational food, enriched with antioxidants, fatty acids and an experimental nutrient blend specific for aging dogs. A secondary objective was to determine behaviors dog owners use to infer their aging pet’s quality of life (QoL). Two-arm, controlled, multicenter, blinded study was conducted in adult dogs living with varying aging stages. Healthy dogs enrolled were categorized as small (15 to 25 lbs.) and medium (26 to 50 lbs.) breeds ≥7 years old, and large (51+ lbs.) breeds were ≥ 5 years old. The dogs were transitioned onto the experimental diet over 28 days and were fed the study food for a minimum of 84 days. Evaluations included physical examination, body weight, triaxial accelerometry, daily and monthly surveys assessing overall aging health, QoL, food, and daily activity with aging questionnaires on days 0, 28, 56, 84. Data from the aging questionnaire were analyzed using a linear mixed-model with Diet, Day, and Diet x Day as fixed-effects. An appropriate variance-covariance structure was selected to model the correlation between the repeated measurements. Single degree-of-freedom estimate statements were used to compare the two diets at each time point, and to compare all test period time points to baseline within each diet. A simulation-based multiplicity adjustment was used to control the Type I error rate. Population: A total of 140 dogs were enrolled, with 98 completing the study. Of the 98 completed participants, 76 dogs met completion criteria and were utilized for the statistical analysis. The dogs transitioned smoothly and accepted the test diet well throughout the study. Statistically significant findings from the monthly owner assessments showed an increase (d 28 P = 0.0032, d 56 P = 0.0081, and d 84 P = 0.0023) in affection from their pets. There was also a perceived increase in stamina (P = 0.0032) within 28 days. By day 56 dogs showed an increase in mental ability (P = 0.0426). The investigational study food was well-accepted and efficacious in supporting aging dogs. Notably, observed markers of social orientation, bonding and affection that often decline in aging dogs and those with canine cognitive dysfunction.

Theoretical Study for Adjusting ANOVA Procedures For The One-Way Random Effects Model Under Correlated Errors Within Class And Across Classes

In this study, a method was developed to adjust the procedures of analysis of variance for the one-way balanced random effects model when error limits across classes are not independent, while the assumption of independence between the error terms among the different classes is essential in the analysis of variance. The variance-covariance structure and the correlation coefficients for the error limits were defined. The was assumed as the correlation coefficient of error terms within the class and the is the correlation coefficient for error terms in different classes. The work performed by deriving correction factor and calculating the expectation of the mean sum of squares of errors and treatments as well as correcting the f-statistic.

Task sequencing does not systematically affect the factor structure of cognitive abilities.

Latent variable analyses of cognitive abilities are among the major means by which cognitive psychologists test theories regarding the structure of human cognition. Models are fit to observed variance-covariance structures, and the fit of those models are compared to assess the merits of competing theories. However, an often unconsidered and potentially important methodological issue is the precise sequence in which tasks are delivered to participants. Here we empirically tested whether differences in task sequences systematically affect the observed factor structure. A large sample (N = 587) completed a battery of 12 cognitive tasks measuring four constructs: working memory, long-term memory, attention control, and fluid intelligence. Participants were assigned to complete the assessment in one of three sequences: fixed and grouped by construct vs. fixed and interleaved across constructs vs. random by participant. We generated and tested two hypotheses: grouping task sequences by construct (i.e., administering clusters of tasks measuring a cognitive construct consecutively) would (1) systematically increase factor loadings and (2) systematically decrease interfactor correlations. Neither hypothesis was supported. The measurement models were largely invariant across the three conditions, suggesting that latent variable analyses are robust to such subtle methodological differences as task sequencing.

A non-linear mixed model approach for detecting outlying profiles

In parametric non-linear profile modeling, it is crucial to map the impact of model parameters to a single metric. According to the profile monitoring literature, using multivariate T statistic to monitor the stability of the parameters simultaneously is a common approach. However, this approach only focuses on the estimated parameters of the non-linear model and treats them as separate but correlated quality characteristics of the process. Consequently, they do not take full advantage of the model structure. To address this limitation, we propose a procedure to monitor profiles based on a non-linear mixed model that considers the proper variance-covariance structure. Our proposed method is based on the concept of externally studentized residuals to test whether a given profile significantly deviates from the other profiles in the non-linear mixed model. The results show that our control chart is effective and appears to perform better than the T chart.

Statistical analysis of wastewater treatment plant data

In this paper, we propose to apply the linear mixed effects model (LMEM) for the first time in this discipline to evaluate wastewater treatment plant (WWTP) data. Because the most widely used statistical analyses cannot handle data dependency, as well as fixed and random factors, a new approach was essential. We used the LMEM method to analyze three groups of 19 pharmaceuticals and personal care products (PPCPs) from a California municipal WWTP. We studied the relationships between five treatments, seasons, and three groups of PPCPs. The main contributions of this paper are to investigate three-way and two-way factor interactions and propose that the autoregressive lag 1, AR (1), is a suitable variance-covariance structure for data dependency. While the seasons did not affect the mean concentration levels for the treatments and groups (p=0.2540), the mean concentration levels for the seasons differed by groups (p<0.0001) and the treatments (p=0.0027).

Principal Component Analysis of Hierarchical and Multivariate Data

Principal component analysis concerned with explaining the variance-covariance structure of a set of variables through a few linear combinations of these variables. To determine how many principal components should be considered, the eigenvalues should first be examined. Investigating whether the processing of numbers depend on the way the numbers were presented, i.e. whether the data could be reduced. Four variables (WordDiff, WordSame, ArabicDiff and ArabicSame) were used. Both covariate and correlation matrix were used to obtain the principal components and compare the results between them. In addition, canonical correlation was used to examine the correlation between the set of Word variables and the set of Arabic variables. To see the correlation between the Word variables and Arabic variables, observing the canonical correlation between the first Word canonical variable and the first Arabic variable is enough. Data was reduced into a single principal component (PC1) as more than 80% of the total variability was explained by this principal component.

Understanding the relationship between weather variables and intake in beef steers.

The relationship between weather variables and dry matter intake (DMI) in beef steers was examined using daily intake data from 790 beef steers collected through a computer-controlled feeding system in nonsummer months. Daily data were condensed into weekly averages (N = 13,895 steer-weeks). The variables considered to predict DMI (2.50 to 23.60 kg/d) were body weight (197 to 796 kg), dietary net energy for maintenance (NEm; 0.79 to 2.97 Mcal/kg), ambient temperature (-23.73 °C to 21.40 °C), range of temperature (2.79 °C to 19.43 °C), dew point (-27.84 °C to 14.34 °C), wind speed (2.08 to 6.49 m/s), solar radiation (30.8 to 297.1 W/m2), and 2-wk lag (average of previous 2 wk's values) and monthly lag (average of previous 4 wk's values) of each weather variable. Toeplitz variance-covariance structure for repeated measures was used to determine the model to predict DMI, while accounting for the effects of body weight, dietary NEm, and other variables in the model. Two-week lag of ambient temperature interacted (P ≤ 0.005) with 2-wk lag of range of temperature, monthly lag of wind speed, 2-wk lag of solar radiation, and dew point to predict DMI. Interactions (P = 0.0001) between 2-wk lag of range of temperature vs. dew point and monthly lag of wind speed vs. 2-wk lag of solar radiation were also detected. This study reports important weather variables associated with differences in DMI of growing and finishing steers and will help improve the accuracy of DMI prediction equations for beef cattle. Improvements in the accuracy of predicting DMI should give producers better tools to plan and execute efficient feeding management programs. The R2 of the overall model was 0.8891.

Estimation of Combining Ability for Yield Traits in Groundnut using Genetic Variance-covariance among Relatives

Background: In standard mating designs, the suitability of a line as a parent is generally assessed by examining its overall genetic effects. However, if the given attributes of a line are due to gene interaction (epistasis), this approach becomes less reliable. As the performance of the line will exceed the sum of alleles, thereby inflating its breeding potential. The current study aimed to partition these genetic effects into additive and non-additive effects and their interaction with the environment for authentic selection of parental line(s) having high additive effects. Methods: In this study, genetic effects of 40 advanced breeding lines (ABLs) of groundnut developed through pedigree method were partitioned into additive and non-additive effects by incorporating the pedigree information into analysis. These effects and their interactions were further modelled by incorporating variance-covariance structures constructed as Kronecker product across sites. Result: The merit of 40 ABLs of groundnut was demarcated based on their breeding values. The differential ranking based on both genetic values and additive effects led to conclude that selection for parents should be preferred on breeding values for high genetic gains.

A pseudo principal component analysis method for multi-dimensional open-high-low-close data in candlestick chart

As the most widely-used data form in the field of finance, the open-high-low-close (OHLC) data is being collected by all kinds of financial trading systems all the time. This paper puts forward a pseudo-principal component analysis (PCA) for multi-dimensional OHLC data, which can extract their useful information in a comprehensible way for visualization and easy interpretation. Firstly, a novel feature-based representation for OHLC data is proposed, which contains fruitful and explicit economic implications. Next, we define a full set of numerical characteristics and variance-covariance structures for the feature-based OHLC data. Then, the pseudo-PCA procedure for OHLC data is deduced based on the proposed algebraic operators. Finally, the effectiveness and interpretability of the proposed pseudo-PCA method are verified through finite simulations and three typical empirical experiments. This paper enriches the application scenarios of classical PCA and contributes to the multivariate statistical modeling of symbolic data. The proposed applications can serve as models for related studies.

Parsimonious genotype by environment interaction covariance models for cassava (Manihot esculenta).

The assessment of cassava clones across multiple environments is often carried out at the uniform yield trial, a late evaluation stage, before variety release. This is to assess the differential response of the varieties across the testing environments, a phenomenon referred to as genotype-by-environment interaction (GEI). This phenomenon is considered a critical challenge confronted by plant breeders in developing crop varieties. This study used the data from variety trials established as randomized complete block design (RCBD) in three replicates across 11 locations in different agro-ecological zones in Nigeria over four cropping seasons (2016–2017, 2017–2018, 2018–2019, and 2019–2020). We evaluated a total of 96 varieties, including five checks, across 48 trials. We exploited the intricate pattern of GEI by fitting variance–covariance structure models on fresh root yield. The goodness-of-fit statistics revealed that the factor analytic model of order 3 (FA3) is the most parsimonious model based on Akaike Information Criterion (AIC). The three-factor loadings from the FA3 model explained, on average across the 27 environments, 53.5% [FA (1)], 14.0% [FA (2)], and 11.5% [FA (3)] of the genetic effect, and altogether accounted for 79.0% of total genetic variability. The association of factor loadings with weather covariates using partial least squares regression (PLSR) revealed that minimum temperature, precipitation and relative humidity are weather conditions influencing the genotypic response across the testing environments in the southern region and maximum temperature, wind speed, and temperature range for those in the northern region of Nigeria. We conclude that the FA3 model identified the common latent factors to dissect and account for complex interaction in multi-environment field trials, and the PLSR is an effective approach for describing GEI variability in the context of multi-environment trials where external environmental covariables are included in modeling.

Solar radiation and temperature as predictor variables for dry matter intake in beef steers

Solar radiation may be an important weather variable that has not been included in previous dry matter intake (DMI) prediction models. Solar radiation affects the overall effective ambient temperature, which in turn contributes to the net gain of heat in an animal’s body. This experiment examined ambient temperature and solar radiation with DMI in beef steers. Data from 790 beef steers collected between 2011 and 2018 using an Insentec feeding system was used. Daily data was condensed into weekly averages (n = 13,895 steer-weeks). The variables considered for this study were DMI (2.50 to 23.60 kg/d), body weight (197 to 796 kg), calculated dietary energy density (NEm; 0.79 to 2.97 Mcal/kg), ambient temperature (-23.73 to 21.40°C), two-week lag of ambient temperature (-20.73 to 23.56°C), monthly lag of ambient temperature (-17.95 to 22.74°C), solar radiation (30.8 to 297.1 W/m2), two-week lag of solar radiation (34.6 to 272 W/m2) and monthly lag of solar radiation (43.7 to 256.6 W/m2). Residuals of DMI fitting week of the year (fixed) and experiment (random) were used to generate scatter plots with other explanatory variables to identify if non-linear relationships existed. Body weight and NEm had both linear and quadratic relationships with DMI, while the relationship with DMI for other variables was linear. The MIXED procedure of SAS with Toeplitz variance-covariance structure was used to determine the final model of DMI. After accounting for body weight and NEm in the model, two-week lag of ambient temperature and monthly lag of solar radiation interacted together (P = 0.0001), and this accounted for 0.7790 (R2) variation in DMI and improved the model fit. Therefore, these two variables and their interactions should be considered in DMI prediction equations of beef steers.