# 英国作业代写_多元数据分析方法在物流业中的应用 ## 多元数据分析方法在物流业中的应用

### Literature Review

Under this section the scholarly journals on the application of Multivariate Data Analysis Methods in logistics industry will be reviewed. Particularly the main aim of the Multivariate Data Analysis Methods was exploration, classification, and value forecasting. There are different multivariate data analysis methods in literature.

This paper only concentrates on those methods applicable to the applied marketing research in logistic industry. Therefore the review will not be exhaustive on the multivariate data analysis methods. The most popular methods in the applied marketing research are factor analysis and cluster analysis which will be used i the reviewed journals articles.

### Factor Analysis

Among the multivariate techniques molded here for review, factor analysis is most widely known and used by marketing practitioners and researchers.
Factor analysis is basically a method for reducing a set of data into a more compact form while throwing certain properties of the data into bold relief” (Anderson, T. W. 1958). More technically, it is a set of methods in which the observable or manifest responses of individuals on a set of variables are represented as functions of a small number of latent variables called factors.

It is, therefore, an attempt to descry those hidden underlying factors which have generated the dependence or variation in the responses. Such functions can be both linear and nonlinear although everyone generally limits himself to a linear functional relationship between the factors and the manifest responses (McDonald, 1962). A factor, then, is a linear combination of the variables in a data matrix. In other

### 译文：因子分析  英国作业代写 ### words,

Linear combinations are derived by using several judgmental criteria or the analytical criterion of least squares principle. The latter suggests a close resemblance to regression. However, the peculiarity of factor analysis lies in the fact that a number of linear combinations each giving one factor is more common. In short, it is not at all unusual to obtain a small number of factors in any data analysis. Thus, we can more generally stat, as follows:

### 译文：字， In factor analyzing a data matrix, two sets of values are obtained which are known as factor scores and factor loadings.4 A factor score is individual’s score as a result of linear combination of his manifest scores. Thus, Since there are as many scores per individual i as there are linear combinations (factors), we may generalize (Banks, S. 1968) to this:

### A factor loading is the correlation between factor scores and the manifest scores of the individuals in the sample.

These correlations may be high or low, positive or negative, depending on the dependence of manifest variables and the particular method of factor analysis. We may describe a factor loading as

### 译文：因子载荷是因子得分与样本中个体的明显得分之间的相关性。 英国作业代写 Factor analysis is more appropriately a set of data reduction techniques rather than a single unique method. Much of the confusion in marketing literature stems from not appreciating this fact. The set is created as a result of a variety of options available to the researcher for analyzing data. These options can be grouped as with regard to (Anderson, T. W. 1958) nature of data matrix to be factored,

Attneave, F. (1950) weights or coefficients to be specified in making the linear combinations, and (Banks, S. 1968) derivation of new (rotated) factors by transformation of original factors.

The option related to data matrix is with regard to factoring either a correlation matrix, a covariance matrix, or a cross—products matrix. Any multivariate analysis begins with a data matrix X consisting of n rows representing variables and N columns representing individuals. .n some cases, it is advantageous to redefine rows and columns by transposing the data matrix.

Attneave, F. (1950) 在进行线性组合时要指定权重或系数，以及 (Banks, S. 1968) 通过转换原始因子来推导新的（旋转的）因子。

### The cell xji refers to i individual’s response on jth variable.

This data matrix contains three types of information: level, dispersion and shape of variables or individuals. In some analyses, ail the three types of information are relevant. In that case, we obtain a cross—products matrix XX by post—multiplying the data matrix with its transpose. Each cell element contains sums of squares or cross products.

If only dispersion and shape are important, we may at first set levels of all variables equal, preferably at zero level, aid obtain transformed coil values which are deviation scores. A cross—products matrix of deviation scores becomes a covariance matrix when each cell is divided by the number of variables. Finally, if both levels aid dispersion are not relevant to the analysis we may equate both of these across the variables.

One way is to obtain standard scores where, means are equal to zero and variances are ail equal to unity. The cross—products of a matrix of standard scores then results in the well-known and common correlation matrix.

Obviously, covariance and correlation matrices are one specific way of removing the effects of level and dispersion on the data. They are commonly used because of their mathematical relationships to known distributions such as normal distribution. However, any other method of equalizing level aid dispersion would be relevant as data input for factor analysis.

### Of course, there are some situations where a particular type of data matrix is almost mandatory.

For example, when the units of measurement of variables are quite diverse so as to lack common dimensionality, it is desired that data be standardized. On the other hand, if the researcher believes, based on his theory, that he should expect individual differences in the sample on level aid dispersion, it is better to use the cross—products matrix (Ross, 1964).

Finally, there are six separate ways that data can be correlated with the use of cross—products, covariance or correlation procedures because, in general, we have three kinds of information:

variables, people, and separate time periods. Holding one dimension Constant, and using the second dimension as replications, a cross— products, covariance or correlation matrix can be obtained on the various elements of the third dimension. For example, we may get a variable—by-variable correlation matrix, or people—by-people correlation matrix or time-by-time correlation matrix.

Cattell (1952) has given various labels to the six types out of which factoring a variable by variable at a point in time correlation matrix is called K—type factor analysis, and that of a person—by—person correlation matrix at a point in time is called Q—type factor analysis.

### 译文：当然，在某些情况下，特定类型的数据矩阵几乎是强制性的。

Cattell (1952) 对六种类型给出了不同的标签，其中在某个时间点相关矩阵逐个变量分解的因子分析称为 K 型因子分析，而一个人与一个人在某个时间点的相关矩阵的因子分析称为 K 型因子分析。时间称为Q型因子分析。

### The second option is the choice of weights for making linear combinations.

This option is two—fold; judgmental methods and analytical methods. As the name implies, judgmental procedures only approximate some exact solutions and there is no statistical rationale for their choice. The best known of these procedures are centroid method, factor method and multiple group method. Among the analytical procedures which use the basic structure theorems of matrix algebra, the most widely known is the principal components analysis. Finally, both the judgmental awl analytical procedures give further options (particularly in a correlation matrix input) s to the diagonal values.

The third option is regarding the derivation of new (rotated) factors by linear transformation procedures. Once again, there are two broad types: judgmental or analytical. The judgmental procedures all date back to Thurstone’s simple structure principle whereby a factor is rotated to an extent that any one variable is highly loaded on one and only one factor.

The analytical procedures use a number of variations of this simple structure principle. The two most common analytical procedures are quartimax and varimax rotations. The third option is resorted to by researchers for better interpretation of the results, and has no statistical significance per so. It is also the most controversial aspect of factor analysis.

It is obvious that possible combinations of the three types of options and further sub options in each type generate hundreds of separate factor analyses.

### Profile and Cluster Analysis

A second major multivariate technique is profile or cluster analysis. Profile analysis is a generic term for all methods concerning grouping of individuals. Cluster analysis is a generic term for all methods concerning grouping of variables. The procedures for both cluster and profile analysis are very similar, and hence we will refer to both of them as profile analysis.

Profile analysis involves at least two separate steps. The first is the, measurement of similarity between two persons or variables. The second is classification of persons or variables based on the similarity measures.

A series of cut—and-try methods have been proposed to perform profile analysis (Attneave, F. (1950), Cronbach, (1955)) Most of these calculate distance between two persons by putting them in some sort of space. In general, a person with his scores cm n variables is considered a point in n-dimensional space.

### The distance between two points gives a measure of similarity:

the greater the distance the less similar the two points. Then several arbitrary methods are available which specify the cut-off point for the marginal person to be included in a group.

The two most common distance measures are calculation of absolute differences and distances based on Pythagorean Theorem. Mathematically, they can be stated as:

### 译文：两点之间的距离给出了相似性的度量：  英国作业代写 -where i and j are two persons or points in n-dimensional space constructed from measurement on k scales.
The similarity measured. in the above methods contains all the three types of information: level, dispersion and shape. By removing one or more of these, several other distance measures are possible.

Most of the profile analyses suffer from two problems.

First is the lack of invariance of similarity between two persons resulting from adding or dropping the dimensions on which they are measured. This becomes a serious issue when the dimensions for comparison are based on convenience and, at best, judgment instead of any theory. The second and related problem is the dimensions. If the dimensions are not orthogonal, the distances based on space become less meaningful.

### Applications in Marketing  英国作业代写

The first attempts relate to measurement of similarity between self—concept and some consumer behavior variable where attempt is made to show greater congruence between the two (Birdwell, A. E. 1964). However, classification of consumers in these studies is already known based on the particular consumer behavior under investigation.

The pioneering efforts to measure similarity and then classify objects or people from Green, Frank and Robinson (1967). They used the distances to obtain clusters of cities which are potential for test marketing.

### 译文：在市场营销中的应用  英国作业代写

Green, Frank 和 Robinson (1967) 开创性地测量相似性，然后对对象或人进行分类。 他们使用距离来获得具有试销潜力的城市群。

### Discriminatory Analysis

Discriminant analysis is useful in situations where total sample is divided into known groups based on some classificatory variable (sex), and the researcher is interested in understanding group differences or in predicting correct belonging to a group of a new sample based on the information on a set of predictor variables.

Discriminant analysis, therefore, can be considered either a type of profile analysis or a type of multiple regressions. As a profile analysis, its significance lies in the structure of weights obtained which discriminate various groups.

Then, it is sometimes referred to as structural analysis (King, 1967). As a multiple regression, its significance lies in providing predictive power to the researcher in terms of classifying individuals more accurately than by chance. In either case, the criterion variable is Single and classificatory.
Discriminant analysis entails transformation of scores of individuals on a set of predictor variables by using a set of linear weights.

The transformed value is called the discriminant score. This score is treated as projection of a point, on the discriminant axes and depending on whether it lies above or below the discriminant line, the individual is classified as belonging to one or the other group. The linear transformation of raw scores into discriminant scores can be represented as:

### This is analogous to one—may classification in analysis of variance.

It is possible to obtain more than one discriminant axis similar to factor analysis. However, the total number of axes does not exceed the number of groups minus one. In a two—group situation, therefore, only one discriminant axis and one discrirninant score for each individual are obtained.
Once the discriminant axis is obtained, the function could be tested for significance.

Then based on the discriminant scores, individuals in the sample void are classified in one of the groups. The proportion of correct classification then is compared against what could have been predicted by chance without any knowledge of the scores on the predictor variables. To this extent, it resembles the Bayesian approach.

### 译文：这类似于方差分析中的分类。 英国作业代写

It is, however, more appropriate to validate the analysis by using the discriminant weights on another sample of individuals because predicting on the same sample from which coefficients are derived is shown to result in biases (Frank et al, 1965).

## 译文：然而，通过对另一个个体样本使用判别权重来验证分析更合适，因为预测来自同一样本的系数会导致偏差（Frank 等，1965）。

### Applications in Marketing

A large number of research studies in marketing have recently applied discriminant analysis mostly for prediction purposes. Evans, F. B. (1959), for example, attempted to discriminate new Ford and Chevrolet buyers based on personality needs, socioeconomic variables, and a combination of both with little success.

Recently, however, Ito (1967) successfully discriminated loyal and switching Ford and Chevrolet buyers on the basis of nine attitude scales. However, he used intention measures for the second purchase as opposed to actual purchases.

A number of studies (Day, G. S. (1967), Frank, R. E., & Massy, W. F. (1961)) deal with prediction of innovators from non-adaptors or late adopters on a series of socioeconomic, personality, psychological and purchase characteristics.

The success is only moderate. Other areas of applications include discriminating among listeners who sent f or a program guide from those who did not among various types of holders of savings accounts, among consumer decision types on personality variables (Brody, R. P. & Cunninghan, S. M. (1968), among social classes, among those who intend to buy,

### And to obtain scale values in an advertising study (Benson, P. H. (1967).

Perhaps the most extensive use of discriminant analysis in a single study comes from Sethi  who attempted to discriminate high and low buyers of brands of analgesic on socioeconomic purchase characteristics and a combination of both types of variables.

In using discriminant analysis for prediction purposes, there are two problems which a researcher generally encounters. First, the dependent classificatory variable is more often than not forced on the data by the researcher with the result that there exists an overlap between groups to an extent that separation of groups is not powerful.

A greater caution is needed among the users of discriminant analysis in their definition of classificatory dependent variable. The second problem concerns validation of the analysis pointed out earlier. If the same sample is used .it overe8timates the predictive power of the discriminant function. A pragmatic suggestion is to split the sample into half, using one half for analysis and the other half for validation.

The above-mentioned problems have led King (1967) to suggest that we may use discriminant analysis not so much for prediction as for relative importance of predictor variables based on structural analysis of discriminant coefficients.

### References

Anderson, T. W. (1958). An introduction to Multivariate Statistical Analysis, John & Sons, New York.

Attneave, F. (1950) “Dimentions of Similarity,” American journal of Psychology, Vol. 63, pp. 516-556.

Banks, S. (1968). “Why people buy particular brands,” in Ferber, R & Wales (eds), Motivation and behavior, pp. 361-381

Benson, P. H. (1967). “Individual Exposure to Advertising and Changes in Brands Bought,” Journal of Advertising Research, Vol 7.

Birdwell, A. E. (1964). “Influence of Image Congruence on Consumer Choice” in Smith, L. G (ed.), Reflecting on Progress in Marketing, American marketing Association, Chicago, 1964, pp. 317-303.

### Brody, R. P. & Cunninghan, S. M. (1968).  英国作业代写

“Personality Variables and the Consumer Decision Process,” Journal of Marketing Research, vol. 5, pp. 50-57

Cattel, R. B. (1952). “The Three Basic Factors Analytic Designs – Their interrelationships and Delivertives,” Psychological Bulletin, Vol. 49, pp. 499-520.

Cronbach, L. J. & Gleser, G. C. (1955). “Assessing Similariry between Profiles,” Psychological Bulletin, Vol. 52, pp. 281-302.

Day, G. S. (1967). Attributes and Brand Choice Behavior. Phd Dissertation, Columbia University.

Fisher, R. A. (1958). Statistical Methods for Research Works. Haftner Publishing Co. New York.

Evans, F. B. (1959) “Psychological and objective factors in the Pro-Business. Vol. 31, pp. 340-309

### Frank, R. E., & Green, P. E. (1968).

“Numerical Taxonomy of Marketing Analysis: A Review Article,” Journal of Marketing Resources, Vol. 5, pp. 83-93

Frank, R. E., & Massy, W. F. (1961) “Innovation and Brand Choices: The Folger’s Invasion,” In Greser, S. A.

Frank, R. E., Massy, W. F, & Morrison, D. G. (1965). “Bias in Multivariate Discriminant Analysis,” Journal of Marketing Research. Vol. 2, pp. 250-258

Gales, K (1957), “Discriminant Analysis for marketing Research: An Evaluation,” Applied Statistics. Vol. 6, pp. 123-132.

Green, B. F., Frank, R. E., & Robinson, P. J. (1967). “Cluster Analysis in the Test Market Selection,” Management Science, Vol. 13, pp. 387-400.

McDonald, R. P., “A General Approach to Non-linear Factors Analysis.” Psychometrika, Vol. 27, pp.397-415.

Ross, J. (1964) “Mean Performance and the Factor Analysis Learning Data,” Psychometrika. Vol. 29, pp. 67-73.

King, W. R. (1967) “On Methods: Structured Analysis and Descriptive Discriminant Function,” journal of Advertising Research. Vol. 7, pp. 39-43. 