# Articles by Aaron Schlegel

### Factor Analysis with the Principal Factor Method and R

February 23, 2017 |

As discussed in a previous post on the principal component method of factor analysis, the term in the estimated covariance matrix , , was excluded and we proceeded directly to factoring and . The principal factor method of factor analysis (also called the principal axis method) finds an initial estimate... The post Factor ... [Read more...]

### Factor Analysis with the Principal Component Method Part Two

February 16, 2017 |

In the first post on factor analysis, we examined computing the estimated covariance matrix of the rootstock data and proceeded to find two factors that fit most of the variance of the data using the principal component method. However, the variables in the data are not on the same scale... ... [Read more...]

### Factor Analysis Introduction with the Principal Component Method and R

February 9, 2017 |

Factor analysis is a controversial technique that represents the variables of a dataset as linearly related to random, unobservable variables called factors, denoted where . The factors are representative of ‘latent variables’ underlying the original variables. The existence of the factors is hypothetical as they cannot be measured or observed.... The ...

### Image Compression with Principal Component Analysis

January 26, 2017 |

Image compression with principal component analysis is a frequently occurring application of the dimension reduction technique. Recall from a previous post that employed singular value decomposition to compress an image, that an image is a matrix of pixels represented by RGB color values. Thus, principal component analysis can be used... ...

### Principal Component Analysis

January 19, 2017 |

Often, it is not helpful or informative to only look at all the variables in a dataset for correlations or covariances. A preferable approach is to derive new variables from the original variables that preserve most of the information given by their variances. Principal component analysis is a widely used... ...

### Quadratic Discriminant Analysis of Several Groups

January 12, 2017 |

Quadratic discriminant analysis for classification is a modification of linear discriminant analysis that does not assume equal covariance matrices amongst the groups . Similar to LDA for several groups, quadratic discriminant analysis of several groups classification seeks to find the group that maximizes the quadratic classification function and assign the... The ... [Read more...]

### LDA for Classification into Several Groups

January 5, 2017 |

Similar to the two-group linear discriminant analysis for classification case, LDA for classification into several groups seeks to find the mean vector that the new observation is closest to and assign accordingly using a distance function. The several group case also assumes equal covariance matrices amongst the groups . LDA... The ... [Read more...]

### Quadratic Discriminant Analysis of Two Groups

December 29, 2016 |

As mentioned in the post on classification with linear discriminant analysis, LDA assumes the groups in question have equal covariance matrices . Therefore, often when the groups do not have equal covariance matrices, observations are frequently assigned to groups with large variances on the diagonal of its corresponding covariance matrix... The ... [Read more...]

### Classification with Linear Discriminant Analysis

December 23, 2016 |

Classification with linear discriminant analysis is a common approach to predicting class membership of observations. A previous post explored the descriptive aspect of linear discriminant analysis with data collected on two groups of beetles. In this post, we will use the discriminant functions found in the first post to classify... ... [Read more...]

### Discriminant Analysis of Several Groups

December 15, 2016 |

Discriminant analysis is also applicable in the case of more than two groups. In the first post on discriminant analysis, there was only one linear discriminant function as the number of linear discriminant functions is , where is the number of dependent variables and is the number of groups. In... The ... [Read more...]

### MANOVA Test Statistics with R

December 8, 2016 |

Multiple tests of significance can be employed when performing MANOVA. The most well known and widely used MANOVA test statistics are Wilk’s , Pillai, Lawley-Hotelling, and Roy’s test. Unlike ANOVA in which only one dependent variable is examined, several tests are often utilized in MANOVA due to its multidimensional ... [Read more...]

### Multiple Analysis of Variance (MANOVA)

December 1, 2016 |

MANOVA, or Multiple Analysis of Variance, is an extension of Analysis of Variance (ANOVA) to several dependent variables. The approach to MANOVA is similar to ANOVA in many regards and requires the same assumptions (normally distributed dependent variables with equal covariance matrices). This post will explore how MANOVA is performed... ... [Read more...]

### Discriminant Analysis for Group Separation in R

November 17, 2016 |

The term ‘discriminant analysis’ is often used interchangeably to represent two different objectives. These objectives of discriminant analysis are: Description of group separation. Linear combinations of variables, known as discriminant functions, of the dependent variables that maximize the separation between the groups are used to identify the relative contribution of... ...