Study On Multicollinearity Of Sow Reproductive Performance Indicators For Different Types Of Data

The use of big data analytics to analyse key factors affecting sows reproductive performance and develop targeted solutions is of great significance for improving production and economic efficiency on pig farms.Indicators of sow reproductive performance can be divided into numerical variables（such as total litter size and individual birth weight）and categorical variables（such as conception rate and farrowing rate）.When establishing statistical models to analyze the key factors affecting these performance indicators,linear regression models are usually established for numerical variables and logistic regression models for categorical variables.However,both of these statistical models require independent variables（i.e.no multicollinearity）to avoid inconsistencies between the results of model fitting and that of actual conditions.In addition,there are also indicators in sow production that need to consider the impact of data from two or more breeding stages on reproductive performance,such as the impact of gilt breeding during estrus and mating stages（age,weight and backfat thickness）on lifetime productivity.Due to the mutual influence among these indicators,so suitable statistical models need to be established to clarify the key factors affecting sow lifetime productivity based on different breeding qualities in different stages.This is of great significance for establishing the best breeding program for gilts.In summary,this study aimed to use principal component analysis,Lasso-logistic regression and structural equation models to study statistical methods that can effectively deal with multicollinearity problems for different data types.Through this study,we aimed to reveal the key factors that influence the total litter size and farrowing rate of sows,and to determine the crucial parameters for gilt breeding.The main results are as follows:Part I.Study of the effect of backfat thickness on total born piglets of sows at various stages of gestation using principal component analysisThis section of the study was based on 3562 sow records from a large-scale pig breeding enterprise in Southwest China.The impact of backfat thickness at mating(BF_G0),as well as at 30 days(BF_G30),60 days(BF_G60),90 days(BF_G90),and 108 days(BF_G108)of gestation on total born piglets was estimated using principal component analysis.The main findings are outlined below:1.Total born piglets and backfat thickness at different gestation stages:total born piglets,BF_G0,BF_G30,BF_G60,BF_G90,and BF_G108 were 14.13±2.53,14.35±3.76 mm,14.71±3.65 mm,15.17±3.70 mm,15.41±3.77 mm and 15.32±3.87 mm,respectively.2.Diagnosis of multicollinearity in backfat thickness at different gestation stages:The results of the multicollinearity diagnosis showed that VIF of BF_G0,BF_G30,BF_G60,BF_G90 and BF_G108 were greater than 4,which indicated serious multicollinearity in backfat thickness at different gestation stages of sows.3.Results of linear regression analysis without elimination multicollinearity:without elimination multicollinearity of sow backfat thickness at different gestation stages,the regression equation between total born piglets and sow backfat thickness at different gestation stages was Y _{total litter size}=14.1390-0.0081BF_G0+0.0656BF_G30-0.0446BF_G60+0.0892BF_G90-0.1014BF_G108（R²=0.0053,P<0.01）.This result was not consistent with the actual production pattern.4.The principal component analysis was used to eliminate the effect of multicollinearity in backfat thickness at different gestation stages,and the cumulative variance contribution of principal component 1（PC1,86.42%）and principal component 2（PC2,7.81%）was 94.23%.The regression equation between the two principal components and total born piglets was Y_{total litter size}=14.1319+0.0001PC1-0.0408PC2（R²=0.0014,P=0.078）.The regression equation for total born piglets and backfat thickness at different gestation stages of the sow was transformed from PC1 and PC2 to Y_{total litter size}=14.1319+0.0284BF_G0+0.0133BF_G30-0.0031BF_G60-0.0146BF_G90-0.0216BF_G108.The results indicate that backfat thickness at G0 and G30 were positively correlated with total born piglets,while the backfat thickness at G90 and G108 were negatively correlated with total born piglets.Part II.Development of a Lasso-logistic regression model to analyze the key factors affecting sow farrowing rateThe data for this part was collected from 61,843 farrowing records of sows from a large pig farming enterprise in Southwest China.Focusing on the farrowing rate as the representative variable,the study explored solutions for multicollinearity in the analysis of factors affecting categorical variables.Factors including region（A and B）,source（Canadian line and American line）,herd type（GGP,GP,and PS）,breed/combination（Duroc,Yorkshire,Landrace,Landrace×Yorkshire,and Yorkshire×Landrace）,year（2017,2018,and 2019）,mating parity（0-8）,and pre-mating status（replacement gilts,empty sows,re-serve sows,aborted sows,and normal weaned sows）were included in the analysis.A Lasso-logistic regression model was established to identify the key factors affecting the sow farrowing rate.The main results are as follows.1.The average farrowing rate of sows was 86.35%.Results of multicollinearity diagnosis showed the VIF of farm type,year,breed/combination,sow parity and pre-mating status were<4,which means these factors were independent of each other.However,the VIF of regional and source factors were 4.374 and 4.588 respectively,which means there was significant multicollinearity between them.Therefore,logistic regression models could not be built directly for the analysis.2.Variable selection using Lasso regression:To address the issue of multicollinearity,Lasso regression was used for variable selection to retain variables that have a greater impact on the farrowing rate and mitigate the effects of multicollinearity.Cross-validation results showed that the minimumλvalue corresponded to a Logistic regression model in which some variables did not pass the significance test,while the optimalλvalue corresponded to a Logistic regression model in which all variables passed the significance test（P<0.01）.3.Analysis of factors affecting farrowing rate using Lasso-logistic regression model:Results of the Lasso-logistic regression model corresponding to the optimalλvalue showed in addition to regional factors,herd type,year,breed/combination,source,sow parity and pre-mating status all had a significant impact on farrowing rate（P<0.01）.Specifically,the farrowing rate in PS farms（81.45%）was significantly lower than that in GGP farms（87.66%）and GP farms（89.02%）（P<0.001）.the farrowing rate in 2017（93.31%）was significantly higher than that in 2018（88.99%）and 2019（76.83%）（P<0.001）.Yorkshire sows（90.38%）had a greater farrowing rate than other breed/combination sows（P<0.001）.The farrowing rate of Canadian-line sows（83.47%）was significantly lower than that of American-line sows（87.04%）（P<0.01）.Compared with sows with parities≥3,the farrowing rate of sows with 1-3 parities（84.00%）was significantly lower（P<0.001）.Compared with the farrowing rate of gilts（84.47%）,that of empty sows（67.72%）and re-service sows（79.09%）and aborted sows（69.83%）were significantly lower（P<0.001）,while normal weaned sows（86.67%）was significantly higher（P<0.001）.Part III.Analysis of the key parameters of gilt breeding using structural equation modelA total of 1984 gilt records at puberty and first mating and total born piglets in the first two parities of gilts from a large pig breeding enterprise in South China were collected and a structural equation model was established to explore the impact of parameters at puberty and first mating of gilts on total born piglets in the first two parities of sows in this part.The main results are as follows:1.Parameters of gilt breeding and total born piglets in the first two parities of sows:the age,body weight,and backfat thickness of gilts at puberty were 215.07±26.56 d,133.84±19.18 kg and 13.32±2.12 mm,respectively.And those at first mating were 247.59±24.89 d,152.95±14.34 kg and 15.17±2.34 mm,respectively.In addition,the total born piglets in the first two parities of sows were 26.56±7.27.2.Collinearity diagnosis of gilt breeding parameters and establishment of structural equation model:Although the VIF of backfat thickness at puberty and first mating were both less than 4,the VIF of age at puberty（3.828）and first mating（3.721）and body weight and at puberty（>4）and first mating（3.595）were all close to 4.These results indicated there is multicollinearity among the various parameters of gilt breeding.The overall fit results of the structural equation model show that the standardized root mean square residual（0.202）,comparative fit index（0.862）,and incremental fit index（0.709）were all close to or reach the ideal level.3.Study of the key parameters affecting gilt breeding using a structural equation model.The latent variable of pubertal factor（reflecting the breeding quality of gilts at puberty）had both direct and indirect effects on the total born piglets in the first two parities of sows,with effect values of 0.096 and 0.014,respectively,and a total effect of 0.110.The latent variable of first mating factor（reflecting breeding quality of gilts at first mating）only had a direct effect on the total born piglets in the first two parities of sows only had a direct effect on the total number of piglets born in the first two parities of sows,with a total effect of 0.032,indicating that the pubertal factor had a greater impact on the first two parities of sows.In addition,among the three gilt breeding parameters of weight,age and backfat thickness,weight has the greatest impact on both pubertal and mating factors,with total effects of 0.789 and 0.732,respectively.The second important parameter was backfat thickness at puberty and mating,with total effects of 0.690 and 0.649 respectively.And the last was age at puberty and mating,with total effects of 0.608 and 0.474 respectively.The conclusions of this study are as follows:1.The influence of multicollinearity in backfat thickness at different gestation stages can be eliminated by using principal component analysis,and it improves to obtain a regression equation that can reasonably explain the impact of backfat thickness at gestation stages on the total born piglets.The results reveal that the backfat thickness at mating and30 days of gestation is positively correlated with the total born piglets,while that at 108days of gestation is negatively correlated with total born piglets.It provides data support for establishing a reasonable precision feeding plan for sows during gestation.2.The Lasso-logistic regression model can solve the influence of multicollinearity on the analysis of factors affecting sow farrowing rate.Factors of sows from PS farm,with low parity,and with empty,re-service,and abortion decreases the farrowing rate,while Yorkshire×Landrace sows has a better farrowing rate than other breed/combination.3.Structural equation modeling can solve the multicollinearity problem of gilt breeding data at puberty and first mating.Compared with the first mating factor,pubertal factor has a more significant impact on the total born piglets in the first two parities of sows.Appropriate weight at puberty and first mating are the most critical indicators for gilt breeding,and it is the key to improving the lifetime reproductive performance of sows.