Alternative Regression Research Articles

A new alternative quantile regression model for the bounded response with educational measurements applications of OECD countries

This article introduces a new distribution with two tuning parameters specified on the unit interval. It follows from a ‘hyperbolic secant transformation’ of a random variable following the Weibull distribution. The lack of research on the prospect of hyperbolic transformations providing flexible distributions over the unit interval is a motivation for the study. The main distributional structural properties of the new distribution are established. The different estimation methods and two simulation works have been derived for model parameters. Subsequently, we develop a related quantile regression model for further statistical perspectives. We consider two real data applications based on the educational measurements of both OECD and some non-members of OECD countries. Our regression model aims to relate the desire to get top grades on certain young students in the OECD countries with some of their Education and School Life Index such as reading performance, work environment at home, and paid work experience. It is shown that the elaborated quantile regression model has a better fitting power than famous regression models when the unit response variable possesses skewed distribution as well as two independent variables are significant in the statistical sense at any standard significance level for the median response.

Logistic Knowledge Tracing: A Constrained Framework for Learner Modeling

Adaptive learning technology solutions often use a learner model to trace learning and make pedagogical decisions. The present research introduces a formalized methodology for specifying learner models, logistic knowledge tracing (LKT), that consolidates many extant learner modeling methods. The strength of LKT is the specification of a symbolic notation system for alternative logistic regression models that is powerful enough to specify many extant models in the literature and many new models. To demonstrate the generality of LKT, we fit 12 models, some variants of well-known models and some newly devised, to six learning technology datasets. The results indicated that no single learner model was best in all cases, further justifying a broad approach that considers multiple learner model features and the learning context. We introduce features to stand in for student-level intercepts and argue that to be maximally applicable, a learner model needs to adapt to student differences. The results of our comparisons show the general importance of modeling recent learning for all datasets, with special importance for terms that model memory in datasets involving fact learning.

Comparison between Deep Learning and Tree-Based Machine Learning Approaches for Landslide Susceptibility Mapping

The efficiency of deep learning and tree-based machine learning approaches has gained immense popularity in various fields. One deep learning model viz. convolution neural network (CNN), artificial neural network (ANN) and four tree-based machine learning models, namely, alternative decision tree (ADTree), classification and regression tree (CART), functional tree and logistic model tree (LMT), were used for landslide susceptibility mapping in the East Sikkim Himalaya region of India, and the results were compared. Landslide areas were delimited and mapped as landslide inventory (LIM) after gathering information from historical records and periodic field investigations. In LIM, 91 landslides were plotted and classified into training (64 landslides) and testing (27 landslides) subsets randomly to train and validate the models. A total of 21 landslides conditioning factors (LCFs) were considered as model inputs, and the results of each model were categorised under five susceptibility classes. The receiver operating characteristics curve and 21 statistical measures were used to evaluate and prioritise the models. The CNN deep learning model achieved the priority rank 1 with area under the curve of 0.918 and 0.933 by using the training and testing data, quantifying 23.02% and 14.40% area as very high and highly susceptible followed by ANN, ADtree, CART, FTree and LMT models. This research might be useful in landslide studies, especially in locations with comparable geophysical and climatological characteristics, to aid in decision making for land use planning.

MYTH OR REALITY? UNVEILING THE EFFECTIVENESS OF HIERARCHICAL CEO SUCCESSION ON FIRM PERFORMANCE AND CASH HOLDINGS

The objective of the study is to contemplate the effectiveness of hierarchical CEO succession and hierarchical CEO succession intensity on SOEs & Non-SOEs performance separately. Meanwhile, the impact of hierarchical CEO succession on cash holdings has also been analysed. The authenticated data has been accumulated from CSMAR for the years 2012-2016 contemplating the listed companies (SOE and Non-SOEs separately for performance while overall companies for cash holdings) on Shenzhen and Shanghai stock exchanges. Through categorization of hierarchical CEO succession, it has been signified that middle-level hierarchical CEO succession elevates the SOEs performance. In contrast, middle and high-level hierarchical CEO succession mitigate the cash holdings. Conclusively, earning management as a moderator has been analysed while deducing that hierarchical CEO succession reduces cash holdings despite firms involving earning management activity which is ultimately beneficial for firms’ growth. The empirical results are robust to alternate technique 2SLS instrumental regression that controls for endogeneity.

Does early-life war exposure of a CEO enhance corporate information transparency?

This study investigates the relationship between a CEO’s war experience and corporate information transparency. Using the Korean War as an exogenous shock, we find that firms managed by war-exposed CEOs have greater information transparency than firms managed by CEOs who are not war-exposed. Specifically, war-exposed CEOs tend to mitigate information in an asymmetrical fashion as they are more concerned about the potential downside risks. This observation is more pronounced during the global financial crisis. Additionally, war-exposed CEOs who have lived close to the regions where large-scale massacres have occurred seek more information transparency than the CEOs who have lived at a distance from such inhumane experiences. Lastly, we employ regression discontinuity design, propensity score matching, CEO change analysis, and alternative sample regressions to show that the results are not driven by endogeneity concerns.

The influence of board independence on dividend policy in controlling agency problems in family firms

PurposeThis study aims to investigate the impact of board independence on the cash dividend payments of family firms listed on the Borsa Istanbul (BIST) in balancing controlling families’ power to mitigate agency problems between family and minority shareholders in the post-2012 period. The authors focus on this period because Turkish authorities implemented mandatory regulations on the employment of independent directors on boards from fiscal year 2012.Design/methodology/approachThe research model uses a panel dataset of 153 BIST-listed family firms over the period 2012–2017, employs alternative dependent variables and regression techniques and is applied to various sub-groups to improve robustness.FindingsThe empirical results show a strong positive effect of board independence on dividend decisions. The authors further detect that family directorship exhibits a negative effect, whereas both board size and audit committees have positive influences but chief executive officer (CEO)/duality has had no significant impact on the dividend policies of Turkish family firms since the new compulsory legal requirements in the Turkish market.Research limitations/implicationsThe findings suggest that independent directorship and dividend policy are complementary governance mechanisms to reduce agency conflicts between families and minority shareholders in Turkey, which is a civil law-based emerging country characterized by high family ownership concentration.Practical implicationsThe authors present evidence that Turkish family firms’ corporate boards have evolved, to some extent, from being managerial rubber stamps to more independent boards that raise opposing voices in family decision-making. However, independent directors’ preference for dividend-induced capital market monitoring implies that their direct monitoring is less effective than it is supposed to be. This suggests a need to revise the Turkish Corporate Governance Principles to enhance independent directors’ monitoring and supervisory power.Originality/valueThis is thought to be the first study to provide insights on how board independence influences dividend policy in controlling agency problems in Turkish family firms since Turkish authorities introduced compulsory rules on the employment of independent directors on boards.

Association of prurigo nodularis and infectious disease hospitalizations: a national cross-sectional study.

Prurigo nodularis (PN) is associated with a variety of systemic comorbidities, including infectious diseases such as HIV and viral hepatitis. There are limited data on other infectious disease comorbidities in patients with PN. To characterize infectious disease hospitalizations among patients with PN and the associated cost burden. We searched the 2016-2017 National Inpatient Sample, a cross-sectional sample of 20% of all US hospitalizations, for infectious disease hospitalizations among patients with PN. Associations of PN with infections and related costs were determined using multivariable logistic and linear regression, adjusting for age, race, sex and insurance type. PN was associated with any infection overall (OR=2.98, 95% CI 2.49-3.56), and with HIV, cutaneous, hepatobiliary, central nervous system, bacterial, viral and fungal/parasitic infections and for sepsis. Patients with PN had a higher mean cost of care (US$11667 vs. US$8893, P<0.001) and length of stay (5.5 vs. 4.2days, P<0.001) for any infection overall and for 7 of 13 other infections. Adjusting for age, race, sex and insurance coverage, PN was associated with higher cost (+30%, 95% CI +17 to +44%) and higher length of stay (+30%, 95% CI +18 to +44%) for any infection overall, and for several specific infections. These associations remained with alternate regression models adjusting for severity of illness. There is a high infectious disease burden among patients with PN, corresponding to higher healthcare utilization and spending. Clinicians must be aware of these associations when treating these patients with immunomodulatory drugs.

Facies Architecture and Sedimentary Structures in the drill cores of Uranium Bearing Sediments of Banganapalle Formation of Palnad Sub-basin, Guntur District, Andhra Pradesh

The Banganapalle Formation, the lowest member of the Neoproterozoic Kurnool Group of rocks, resting over the basement granites, has been identified as the host rock for uranium in Koppunuru area in the western part of Palnad sub-basin. The uppermost arenite facies of the Banganapalle Formation is exposed on surface and shows only few bedform indicators like ripple marks, planer laminations etc. Down-hole lithological examinations on course of core drilling in Koppunuru and adjoining areas identified five recognizable lithofacies of Banganapalle Formation, viz. basal conglomerate unit, quartzite-shale intercalated facies, and two quartz arenite facies separated by a grey shale dominated argillaceous facies.&#x0D; The polymictic conglomerate, with unsorted grit to pebble size clasts of granite, shale, quartzite, vein quartz and dolerite indicate short distance transportation and derivation from nearby granitoids traversed by quartz reef/dolerite dykes. Cyclic repetitions of arenaceous and argillaceous sediments in Banganapalle lithocolumn above the basal conglomerates point to alternate rhythmic marine transgression and regression regimes. These units can also be discriminated based on their sedimentary texture, bedforms and several soft-sedimentary penecontemporaneous deformational structures (PCD) like load structure, convolute bedding/laminations, and slump structures such as micro-slips, gravity faults and folds. These syn-sedimentary structures clearly indicate perturbation and submergence of the basin contemporaneous to deposition. Cross-beds suggests change in current direction/intensity while bi-directional symmetrical ripples in outcrops of upper arenite facies suggests that the Banganapalle sediments are derived from the basement granitoids exposed to the north as well as upper Cuddapah sediments to its west. Overall, the sedimentary structures, textural and composition variation of the lithounits suggest deposition of these sediments in marginal marine, inter- to supra-tidal flat environment. The porous and permeable nature of the quartz arenite and the basal conglomerates and the presence of available reductants in the form of sulphides and carbonaceous matter make them the best suited loci for fluid movement and precipitation of uranium.

COVID-19 pneumonia in Galicia (Spain): Impact of prognostic factors and therapies on mortality and need for mechanical ventilation.

IntroductionThis study was aimed to identify risk factors associated with unfavorable outcomes (composite outcome variable: mortality and need for mechanical ventilation) in patients hospitalized in Galicia with COVID-19 pneumonia.MethodsRetrospective, multicenter, observational study carried out in the 8 Galician tertiary hospitals. All Patients admitted with confirmed COVID-19 pneumonia from 1st of March to April 24th, 2020 were included. A multivariable logistic regression analysis was performed in order to identify the relationship between risk factors, therapeutic interventions and the composite outcome variable.ResultsA total of 1292 patients (56.1% male) were included. Two hundred and twenty-five (17.4%) died and 327 (25.3%) reached the main outcome variable. Age [odds ratio (OR) = 1.03 (95% confidence interval (CI): 1.01–1.04)], CRP quartiles 3 and 4 [OR = 2.24 (95% CI: 1.39–3.63)] and [OR = 3.04 (95% CI: 1.88–4.92)], respectively, Charlson index [OR = 1.16 (95%CI: 1.06–1.26)], SaO2 upon admission [OR = 0.93 (95% CI: 0.91–0.95)], hydroxychloroquine prescription [OR = 0.22 (95%CI: 0.12–0.37)], systemic corticosteroids prescription [OR = 1.99 (95%CI: 1.45–2.75)], and tocilizumab prescription [OR = 3.39 (95%CI: 2.15–5.36)], significantly impacted the outcome. Sensitivity analysis using different alternative logistic regression models identified consistently the ratio admissions/hospital beds as a predictor of the outcome [OR = 1.06 (95% CI: 1.02–1.11)].ConclusionThese findings may help to identify patients at hospital admission with a higher risk of death and may urge healthcare authorities to implement policies aimed at reducing deaths by increasing the availability of hospital beds.

Revisiting linear regression to test agreement in continuous predicted-observed datasets

CONTEXTIn agricultural research and related disciplines, using a scatter plot and a regression line to visually and quantitatively assess agreement between model predictions and observed values is an extensively adopted approach, even more within the simulation modeling community. However, linear model fit, use, and interpretation are still controversial in the literature. OBJECTIVEThe overall goal of this research is to evaluate the usefulness of a symmetric regression line to test agreement on predicted-observed datasets. The specific aims of this study are to: i) discuss the selection of a regression model to fit a line to the predicted-observed scatter, and ii) provide a geometric interpretation of the regression line, decomposing the prediction error into lack of accuracy and lack of precision components, via utilization of illustrative field crop datasets. METHODSThis study tested and contrasted three alternative linear regression models (Ordinary Least Squares -OLS-, Major Axis -MA-, and Standardized Major Axis -SMA-) in terms of assumptions, loss functions, parameters estimates, and model interpretation for the predicted-observed case. RESULTS AND CONCLUSIONSWhen the uncertainty of predictions and observations are unknown, the SMA represents the most appropriate approach to fit a symmetric-line describing the bivariate predicted-observed scatter. The SMA-line serves as a reference to estimate a weighed difference between predictions and observations. Moreover, this symmetric regression can assist in the decomposition of the square error into additive components related to both lack of accuracy and precision. In summary, the SMA regression tackles the axis orientation problem of the traditional OLS (y vs. x or x or y) and allows to identify error sources that are meaningful to the user. SIGNIFICANCEThis work offers a novel and simple perspective about the use of linear regression to assess simulation models performance. In order to assist potential users, we also provide a tutorial to compute the proposed assessment of agreement using R-software.

Non-asymptotic Confidence Regions for the Transfer Functions of Errors-in-Variables Systems

Finite-sample system identification (FSID) methods provide guaranteed confidence regions for the unknown model parameter of dynamical systems under <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mild statistical assumptions</i> for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a finite number of data points</i> . In this article, two FSID methods, the leave-out sign-dominant correlation region (LSCR) and sign-perturbed sums (SPS) methods are extended to errors-in-variables (EIV) systems. In EIV systems, both the measured input and the measured output are corrupted by noise, and they are not noise invertible in the sense that the noise signals cannot be recovered from the measured signals given the true system. Hence, standard FSID methods are not applicable. The present article deals with FSID of EIV systems where the input and noise on input are i.i.d. Gaussian processes and the signal-to-noise ratio is known. By utilizing an alternative regression model and swapping the role of the input and the prediction error in the FSID methods, new LSCR and SPS confidence regions are constructed, which include the true model parameter with a guaranteed user-chosen probability. It is shown that the confidence regions are asymptotically included in an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula> -neighborhood of the true parameter. An ellipsoidal approximation which can be computed at low computational cost is proposed for the SPS confidence region. The methods and their properties are illustrated in numerical experiments.

Lowering post‐construction yield assessment uncertainty through better wind plant power curves

AbstractMany operational analyses of wind power plants require a statistical relationship, which can be called the wind plant power curve, to be developed between wind plant energy production and concurrent atmospheric variables. Currently, a univariate linear regression at monthly resolution is the industry standard for post‐construction yield assessments. Here, we evaluate the benefits in augmenting this conventional approach by testing alternative regressions performed with multiple inputs, at a finer time resolution, and using nonlinear machine‐learning algorithms. We utilize the National Renewable Energy Laboratory's open‐source software package OpenOA to assess wind plant power curves for 10 wind plants. When a univariate generalized additive model at daily or hourly resolution is used, regression uncertainty is reduced, in absolute terms, by up to 1.0% and 1.2% (corresponding to a −59% and −80% relative change), respectively, compared to a univariate linear regression at monthly resolution; also, a more accurate assessment of the mean long‐term wind plant production is achieved. Additional input variables also reduce the regression uncertainty: when temperature is added as an input to the conventional monthly linear regression, the operational analysis uncertainty connected to regression is reduced, in absolute terms, by up to 0.5% (−43% relative change) for wind power plants with strong seasonal variability. Adding input variables to the machine‐learning model at daily resolution can further reduce regression uncertainty, with up to a −10% relative change. Based on these results, we conclude that a multivariate nonlinear regression at daily or hourly resolution should be recommended for assessing wind plant power curves.

Firm life cycle and trade credit

AbstractThis study investigates the relation between firm life cycle and trade credit. We find evidence that firms in the introduction, growth, and decline stages use significantly more trade credit, whereas firms in the mature stage use significantly less trade credit. Firm life cycle works as a separate channel to affect trade credit independently from other channels proposed in the literature. These results are robust to alternative regression specifications, alternative measures of life cycle and trade credit, and the endogeneity concern. Firms in the introduction and decline stages adjust trade credit to the target level quickly compared to others.

Prema-chandra Athukorala Comment on Rethinking “Economic Fundamentals” in an Era of Global Physical Shocks: Insights from the Philippines Experience with COVID-19

Prema-chandra Athukorala Comment on Rethinking “Economic Fundamentals” in an Era of Global Physical Shocks: Insights from the Philippines Experience with COVID-19

Alternative Regression Model Structure for the HCM-6 Equal-Capacity Passenger Car Equivalency Methodology

In the current version of the Highway Capacity Manual (HCM-6), equal-capacity passenger car equivalencies (EC-PCEs) are used to account for the effect of trucks for capacity analyses. The EC-PCEs for freeway segments were estimated using a microsimulation-based methodology where the capacities of the mixed-traffic and car-only flow scenarios were modeled. A nonlinear regression (NLR) model was used to develop capacity adjustment factor (CAF) models using the microsimulation data as input. The NLR model has a complex model structure and includes 15 model parameters. It is argued in this paper that simpler regression models could provide comparable results. This would allow CAF and EC-PCE equations to be used directly in the HCM-6 rather than tables. It would also allow for the development of new regression models for exploring new technologies such as connected and automated vehicles (CAVs). The objective of this paper was to develop alternative and simpler regression models of CAFs needed to derive the EC-PCE values in the HCM-6 methodology for freeway and multilane highway segments. It was found that simpler regression models provided similar results as those obtained with the current NLR model. Additionally, it was found that the current NLR model may not be adequate for analyzing CAV traffic conditions. If the HCM-6 EC-PCE methodology is expected to be used to analyze traffic conditions beyond the scope of the HCM-6, it is important to perform a deeper assessment of the form and error of the regression models used in fitting the simulated and estimated data.

Improving contrast between gray and white matter of Logan graphical analysis’ parametric images in positron emission tomography through least-squares cubic regression and principal component analysis

Logan graphical analysis (LGA) is a method for in vivo quantification of tracer kinetics in positron emission tomography (PET). The shortcoming of LGA is the presence of a negative bias in the estimated parameters for noisy data. Various approaches have been proposed to address this issue. We recently applied an alternative regression method called least-squares cubic (LSC), which considers the errors in both the predictor and response variables to estimate the LGA slope. LSC reduced the bias in non-displaceable binding potential estimates while causing slight increases in the variance. In this study, we combined LSC with a principal component analysis (PCA) denoising technique to counteract the effects of variance on parametric image quality, which was assessed in terms of the contrast between gray and white matter. Tissue time–activity curves were denoised through PCA, prior to estimating the regression parameters using LSC. We refer to this approach as LSC–PCA. LSC–PCA was assessed against OLS–PCA (PCA with ordinary least-squares (OLS)), LSC, and conventional OLS-based LGA. Comparisons were made for simulated 11 C-carfentanil and 11C Pittsburgh compound B (11C-PiB) data, and clinical 11 C-PiB PET images. PCA-based methods were compared over a range of principal components, varied by the percentage variance they account for in the data. The results showed reduced variances in distribution volume ratio estimates in the simulations for LSC–PCA compared to LSC, and lower bias compared to OLS–PCA and OLS. Contrasts were not significantly improved in clinical data, but they showed a significant improvement in simulation data —indicating a potential advantage of LSC–PCA over OLS–PCA. The effects of bias reintroduction when many principal components are used were also observed in OLS–PCA clinical images. We therefore encourage the use of LSC–PCA. LSC–PCA can allow the use of many principal components with minimal risk of bias, thereby strengthening the interpretation of PET parametric images.

Heterogeneous treatment effects and bias in the analysis of the stepped wedge design

The effect of an intervention in a stepped wedge design can vary across clusters or with time since exposure to treatment, but consequences of such heterogeneous treatment effects for the analysis of stepped wedge designs are not well recognized. In this article, we advance the idea that the stepped wedge design can be framed as a special case of a difference-in-differences design with staggered treatment exposure. Using this perspective, we show that the standard difference-in-differences regression approach estimates the average treatment effect of the treatment period with bias when treatment effects vary by cluster or time since exposure. We then use Monte-Carlo simulations of stepped wedge designs to examine the performance of the standard regression approach as well as alternative approaches that estimate treatment effects relative to intervention exposure. Simulation results confirm that estimates from the standard approach are biased when treatment effects are heterogeneous. Alternative regression approaches may perform better, but only if the research design allows estimation of the full treatment effect across all clusters. We conclude by offering recommendations for the design and analysis of stepped wedge trials.

Do Minimum Wages Increase Female Employment? Evidence from Vietnamese Manufacturing Firms

ABSTRACT In this article, I empirically examine the employment effect of minimum wages using firm-level data on Vietnamese manufacturing and find that minimum wages have a positive association with a firm’s female employment. This effect is the highest in automotive and engineering manufactures, and the lowest in textile, garment, and footwear manufactures. Alternative regressions provide evidence that the higher the total factor productivity, the increased female labor share, and the higher pay to their employees, the stronger the female employment effect. The female employment impact is positive, but this impact weakened after the uniform minimum wage rate was applied in 2012.

Evolution of observed and modelled temperatures in Finland in 1901–2018 and potential dynamical reasons for the differences

AbstractObserved monthly and annual mean temperatures in Finland in 1901–2018 were compared with simulations performed with 28 global climate models (GCMs), and dynamical factors behind the emerging differences were studied by regression analysis. Observational temperatures were extracted from high‐quality kriging analyses specifically tailored for Finland. Considering the entire time interval, the increase in the annual multi‐GCM mean temperature agrees well with the observed warming, even though observations exhibit substantial inter‐decadal fluctuations. After 2000, the mean temperatures have been higher than during any period in the 20th century. In the baseline regression model, the 10 leading EOFs of the European—Northeast Atlantic sea‐level pressure (SLP) field were used to explain differences between the GCM‐mean and observed evolution of temperature. The regression model is able to reduce the mean squared difference of the temporally‐smoothed temperature by 58%. The performance is highest in winter and summer and lowest in April. For a sensitivity assessment, multiple alternative regression models were tested, for example, one using the local SLP, geostrophic wind and vorticity as predictors. These models mostly showed somewhat inferior performance. We specifically explored the trends of monthly temperatures during 1961–2018, a period considerably affected by anthropogenic emissions. Compared with the multi‐GCM mean, warming proved to be negligible in June, fairly slow in October and quite rapid in December. All these features were explained rather nicely by dynamical factors. Accordingly, the deviations of the observed regional temperature trends from the multi‐GCM mean largely appear to be related to internal variability.

English

This study aimed to estimate the genetic parameters and breeding values of milk yield traits of Holstein cows in Shandong Province using the best model identified by a comparison between a numbers of alternative random regression test day models (RRMs). The data included 585,702 test day records of milk yield in the first lactation of 88,215 Holstein cows, covering 219 cattle farms in Shandong Province during the period from 2005 to 2016. Different models were investigated, which differed in the number of knots of Spline functions to improve the fitting of population lactation curve and in orders (2, 3, or 4) of Legendre polynomials to fit additive genetic effect and permanent environmental effect. The optimal test day model was screened out by Akaike information criterion (AIC) and Bayesian information criterion (BIC) criteria. Detailed analysis of genetic parameters and accuracy of estimation of breeding values were performed using the optimal model. In the results, the optimal model (Sp15-La4-Lp3) for analyzing the milk yield data was the one with 15 knots of Splines, 4 orders of Legendre polynomials for additive genetic effect and 3 orders of Legendre polynomials for permanent environmental effect. Using the optimal model, estimates of additive genetic variances of milk yield at different days in milk (DIM) during the whole lactation ranged from 8.54 to 15.39, the permanent environmental variance ranged from 17.65 to 31.42. Correspondingly, the heritability ranged from 0.20 to 0.30, and repeatability ranged from 0.43 to 0.54. Rank correlations between EBV of bull with different number of daughters and the bull’s parent average ranged from 0.79 to 0.94, and the correlations between EBV of bulls and the sire-maternal grandsire index ranged from 0.48 to 0.86. In conclusion, Sp15-La4-Lp3 could be the optimal model for estimation of genetic parameters and prediction of breeding values of milk in Shandong Holstein population. The amount of progeny information is critical to the conventional genetic evaluation of bulls. © 2021 Friends Science Publishers