Livestock Research for Rural Development 25 (9) 2013 Guide for preparation of papers LRRD Newsletter

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Statistical tool for measuring the impact of milk production on the local development of a province in Cuba

V Torres, R Cobo, L Sanchez and N Raez

Instituto de Ciencia Animal, Carretera Central Km 47.5,
San José de las Lajas, Mayabeque, Cuba   ;


The impact of milk production in bovines on the local development of Las Tunas province was assessed through the Statistical Model of Impact Measuring (SMIM), with eight stages. It is an excellent combination of multivariate methods for the double purpose of identifying variables-indicators and typifying the performance of the productive units in this territory.  The assessments of the local development in the milk production of bovines were conducted during 2006-2010 in the cattle enterprise “Cuenca lechera Las Tunas”. In all the studies conducted, the statistical model allowed identifying the limiting factors in the productive processes, as well as characterizing properly the best two periods and those of worst productive results influencing on the production results.  This allowed orienting the researchers and directives when taking decisions in the cattle enterprise “Cuenca Lechera Las Tunas”.

Key words: local development, milk production, Statistical Model of Impact Measuring (SMIM)


Today’s Cuban cattle rearing is characterized by its low cow productivity per hectare. Cattle recovery would imply taking it to relevant stages inside the national economy, due to the interest of the Cuban state to achieve this problem, and to the high milk prices in the world market, apart from the real necessity imposed by the social pressure of the lack of fresh products and milk derivatives in amounts and prices adjusted to the acquisitive capacity of the population mean.  

Since 1959, the main objective of the Cuban cattle production has been to create the feeding basis supported mainly on pastures and forages. Pasture is the main feeding source of cattle and, knowing precisely the amount of pasture available and expected in each season is an important task in the process of cattle feeding (Senra 2000, Zamora et al 2000, Peters et al 2010). 

In spite of the results of the variety improvement programs developed during the 70’s and 80’s, the percentage of improved species of best productivity has decreased drastically in the grassland ecosystems (MINAGRI 1999). Such is that, in the 142 thousands hectares of agricultural land of cattle rearing, 60% is constituted by natural pastures of poor yield and low quality.  

Nowadays, new varieties are still under assessment and new biomass models arebeing eveloped for improving the feed quality and satisfy the animal requirement, allowing the necessary and wished productive values (Martínez et al 2010, Gómez et al 2010, Sardiñas et al 2011). 

The introduction of these and other research results is a very important step, so, since 2003, a technology transfer program was developed (Díaz et al 2010), on the basis of collaboration with research centers, universities, non-state organization (ONG), the Ministry of Science Technology and Environment (CITMA) and the Ministry of Agriculture (MINAGRI), to adequate and introduce technologies in different cattle enterprises, creating an interaction between the knowledge management and the enterprise sector. The sustainable of the investigation results in the extension or introduction process should be analyzed in a systematic way to know the increment of the productivity of the agricultural activities and the local development of the evaluated productive rubles. 

The impacts, defined as the changes achieved in time with the introduction of technologies, are determined by the technological or productive, economical, social and environmental aspects, and their interrelations. Their determination is achieved through a liable information system, allowing the counting of the highest amount of variables to be measured.


Methods and materials

The Statistical Model of Impact Measuring (SMIM) is a combination of multivariate methods and statistical inference (Torres et al 2008, 2010 and 2011) based on the following steps: 

  1. Application of a systemic diagnosis, surveys, and digitalization of the information.

  2. Organization and revision of the original data matrix.

  3. Verification of the necessary premises and adequate sample size on the correlation matrix.

    4.    Identification of the importance of the order of the variables in the explanation of the system variability.

    5.    Determination of the factorial punctuations

    6.    Impact assessment

    7.   Classification of the producers, farms or enterprises in function of the principal components

There are variants of analysis to achieve the necessary premises for the correct application of this model.  

This tool was used for assessing the impact of bovine milk production on the local development of Las Tunas province. The information on the records of the cattle enterprise “Cuenca Lechera Las Tunas”, during 2006-2010 was gathered. The variables included in the analysis were: milk production (liters), number of milking cows, yield/cow (liters), sales to the state (liters), number of total deaths, number of females in reproduction, number of births, cultivated surface of pastures and forages (ha), total surface (ha) and milk/ha. 

Start from the multivariate model for identifying the important order of the indicators

Theoretical value = w1Y1+ w2Y2 + w3Y3 + ....+ wqYq


Yi: new variables, called factors, linear combinations of the original variables xij

 and that have the following properties:

Yi  is not correlated with Yi´   (i ≠ i´)

Var (Y1 ) > Var (Y2 ) > …. > Var (Yq)

wi: way showing the importance of the original variables in each defined factor. 

This corresponds with the mathematical model of an Analysis of Principal Components (APC).  

With values of KOM near to the unit and significant Bartlett’s test of sphericity from the correlation matrix of the original variables and with the application of the criterion of eigen value higher than or equal to the unit, the main components explaining higher variability were selected. 

For the principal components selected, the factorial punctuations are calculated. They are estimated through e regression method and it is guaranteed their cero mean and variance equal to the square of the multiple correlations between the estimated factorial punctuations and the true factorial values. These factorial punctuations, obtained for each unit, may be used as an absolute measurement of the impact or performance positive or negative) of the variables with greater importance in each unit and permit the classification of the units applying the Analysis of Clusters. 

Once the groups of similar units with the use of the coefficient of dissimilarity and the inferential statistics was used for facilitating the analysis and interpretation of the results.

All the processing was conducted with the statistical system SPSS+ (2006).


The general statigraphs of the variables included in the analysis of “Cuenca Lechera Las Tunas” are shown in Table 1.  

The matrix of Person’s regression coefficients showed that 49% of the correlation coefficients between the variables analyzed are superior to 0.30, besides, the statistical criterion KMO = 0,70 it is good to be near to the unit and  significant Bartlett’s test of sphericity (P<0,001), indicating that the correlation matrix is not of identity and that the selected data are adequate for the analysis. 

Table 1: Statigraphs of the analyzed variables for all  years and months considered






Milk production, liters





Milking cows





Yield per cow, liters





Sales to the State, liters





Total deaths





Females in reproduction










Pastures and forages cultivated surface





Surface, ha










Table 2 presents the results related with the principal components extracted. The first three explain 82.6% of the total variability of the milk production system of such enterprise. The principal component 1, has an eigen value of 5.30 and explains  53.0% of the variance, being this component the one offering higher explanation. The second, with an eigen value of 1.88, explains 18.8% of variance and the third, with an eigen value of 1.09, explain 10.9%.  

The variables with higher weights in the first component have superior weight values for milk production, milking cows, sales to the state, cultivated surfaces of pastures and forages and milk/ha. These variables are related with milk production and indicate that this is the most important and variable factor inside the system. This principal component was identified as milk production-cows-pastures and forages surface. 

Table 2. Matrix of rotated components, eigenvalue,  variance accounted % and  Cumulative of the variance % by each component







Milk production




Milking cows




Yield per cow




Sales to the state




Total deaths




Females in reproduction








Pastures and forages cultivated surface




Total surface, ha








Eigen value




% of the variance




% accumulated variance




The highest weights in the second component corresponded to yield per cow and total deaths. The latter with a minus sign indicating the inverse relation between them. Finally, the principal component 3 has high weight value in births.  

With these values, the impact indexes of each component were determined. That of component 1, identified as milk production-cow-pastures and forages surface, is shown in Figure 1, from January 2006 to June 2007, the contributions were not satisfactory, the impact of milk production in the enterprise was negative, corresponding to the decreases occurring since 1993 and that was of 70% in milk production (records of the Enterprise) in 2006. Due to this situation, eight Basic Units of Cooperative Production (BUCP) were dissolved, as they were decapitalized for objective, sub-objective and economical reasons and became part of the State System of Enterprise. 

From this time on, the impact index varied and from July 2007 to December 2010, a tendency to increase is observed, highlighting some periods when the impact decreased due to the dry seasons presented regularly in the country and particularly in this Enterprise, where the irrigation conditions are not created for guaranteeing the enough water and feed availability for animals. Another cause of this performance is the low availability of forage areas to cover the needs of the stock during these stages.

Figure 1. Impact indexes for the principal component: milk production-cows-surface.

 Figure 2 shows the performance of the impact indexes for the principal component 2, identified as milk yield-mortality. It is very complicated to explain the performance of these variables and their relationship. Higher values of mortality indicate losses of animals in the herd and high and positive values of this index are not favorable for this activity. Further studies to assess this variable according to the index instead of the heads could be convenient. On the other hand, the milk yield is an indicator of productive efficiency and it is shown in the indexes obtained that there are periods when the maximum values tend to stabilizing and the negative impacts tend to diminishing.

Figure 2. Impact indexes for the principal component: milk yield-mortality

The results of the SMIM explained up to here, allow analyzing, identifying and showing the factors influencing on the productive and performance results of the enterprise during the period analyzed.  

The typification of the variables was conducted using the impact indexes of the three principal components selected and classifying the values obtained in homogenous groups. Two different groups showing the periods of best and worst results were identified, using a dissimilarity coefficient of 8.25. 

As shown in Figure 3, the values of the total milk production and sold corresponding to the group of best performance are over 60,000 liters from July 2007 to December 2010. The results of worst performance for these same variables do not surpass 10,000 liters from January 2006 to June 2007. 

In Figure 4, the variables yield/cow and milk/ha show that in the first period, from January 2006 to June 2007, the average of milk liters/ha was higher than the second one, from July 2007 to December 2010. It is important to highlight that, in the first period, some conditions were considered, including the irrigation, the pastures and forages that increased the efficiency values and, in the second,  with the new units from the BUCP and their production problems, the milk efficency decreased.

Figure 3. Classification of the milk production results in the groups of best and worst performance.

Figure 4. Classification of the results of yield per cows, milk/ha in the groups of best and worst performance.

Figure 5 shows the mean values of milking cows, births and mortality in the two groups of best and worst performance. Likewise, inferior results in the three variables were presented from January 2006 to June 2007. In the other period, although births and mortality are not so high, they show a better performance. In the case of milking cows, a superior performance is noticed.

Figure 5. Classification of the results of milking cows, births, mortality in the groups of best and worst performance.

Table 3, presents the average values of each variable analyzed in both groups identified. The results of the variables of best and worst performance are also indentified. This propitiates the directives an efficient tool when taking decisions. The performance of milk production from the statistical information of the units is understood and the actions and recommendations to the productive system are scientific.

Table 3. Typified values in the two groups of best and worst performance.


January 2006 to June 2007

July 2007 to Dec 2010






Milk production





Milking cows










Sales to the state





Total deaths





Females in reproduction










Pastures and forages cultivated surface
















The value of the statigraphs of the variables included in the analysis are within the ranges established for milk production under the conditions of Las Tunas province (Raez 2012). The first component and its impact index (Figure 1), show that even during 2006 and part of 2007, cattle rearing in this province is still affected by the falling of the socialist system, due to the drastic reduction of raw materials used for feeding and other incomes in general, as milk production technologies were basically supported by their use. Another important factor is the organization system of the Cuban dairy enterprises that influences on the decrease of milk production in the country of up to 50% (Bulletin Hist. Productive MINAGRI).

From the middle of 2007, impacts increase because of the introduction of new varieties capable of producing higher amounts of grasses under drought and salinity conditions of the soils of middle and low fertility (Herrera et al 2003). The adquisition of animals of improved breeds such as Siboney de Cuba, influenced on the increase of the productive results. 

The component 2 and its impact (Figure 2), highlights because milk yield and mortality are two important factors of the results of the enterprise. Besides, the affection of the dry periods is also included, increased all years and extending from the beginning of the dry season up to the end of May or beginning of June. The average rainfall does not surpass 1080 mm per year, versus a historical mean of 1200 mm, concentrating rainfall in three out of the six months of the rainy season. Anon (2009), states that drought is normal component of the climatic variability, is a phenomenon of gradual development, the higher presentation frequency is in the months when the Winter finishes, mainly on March, April and May, when temperaature increases and the summer rain does not appear. In this sense, the Eastern provinces go, since 1997, towards a new climatic stage with more prolonged droughts, reduction of the day temperature range and increase of the air superficial temperature (Brito et al 1998). Vélez (2007) proved that a cow consumes 35% less of feed when the temperature is of 35 ºC, compared with that when it is of 25 ºC. 

The difference between the two periods classified (January 2006 to June 2007 vs July 2007 to December 2010), is of 50000 L of milk (Figure 3), because in the second period, the biomass supplies increased through the use of forages such as Cuba CT-169,  king grass (Pennisetum purpureum) and Cuba OM -22 (Pennisetum hybrid) (Martínez et al 2010)),  sugar cane and other feeds recommended by authors as Ray et al (2000),  guaranteeing the increase of production and sales to the state. The milk production/cow was also superior in 2,2 l (Figure 4), and guaranteed the consumption increase of the population. The milk production/ha decreased in the second period as consequence of increasing the milking cows of improved breeds in the grasslands (Figure 5). 


The Statistical Model for Impact Measurement (SMIM) is validated as an efficient tool when studying the performance of the main production indexes in the cattle enterprise “Cuenca Lechera de las Tunas”. The necessity of a reliable and of quality information is evidenced. This aspect shows the best results when applying this tool.  


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Received 14 December 2012; Accepted 3 August 2013; Published 4 September 2013

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