In data science, we often want to measure variables such as social-economic status (SES). Some variables have a lot of parameters (or items), for example, SES can be measured based on income, education, etc. Then, to proceed with the analysis, it is common to reduce the number of parameters to fewer components through Principal Components Analysis (PCA). However, we will see why some variables cannot be reduced by PCA and we will learn how to use Exploratory Factor Analysis in our favor.

Differences Between EFA and PCA

Model difference

Both of them are used to reduce the number of parameters to fewer variables. Also, both methods assume that the variance of a parameter is divided into specific variance, common variance, and error variance. …

If you are familiar with research with human subjects, you may have seen some examples of group comparison. For example, if we want to test the efficacy of an antidepressant, we may want to compare sex differences (since depression may differ based on sex). However, are you sure the instrument you are using (e.g. Beck Depression Inventory) has the same structure for men or women?

Another example is in cross-cultural researches. We could measure differences in subjective well-being between countries and see if some countries are happier than others (e.g Jebb et al., 2020). …

In physics, we often have an instrument that exists physically and measures physical properties. For example, an instrument that measures length uses this property (i.e. length) to measure the length of another object. Therefore, there’s no need to prove that this property is congruent with the same property of the object being measure.

However, there are some cases that this is not that clear. For example, if we are measuring speed using the Doppler effect, where approximation/distance of spectral lines of galaxy lights is the instrument. In this case, we have the problem of the validity of an instrument, because we need to know if it’s true or not that the distance between spectral lines is related to speed. For this, we have to prove empirically. Validity is common in areas of knowledge that use indirect measures. The same that happens to the Doppler effect is very common in psychosocial sciences (e.g. Psychology, Education), especially if we are using the concept of latent trait (e.g. …

O R é uma ferramenta que nos permite realizar diversas análises, inclusive acerca de instrumentos psicológicos. Por meio do R podemos baixar o pacote psych, que nos ajudará nas análises deste tutorial. Neste texto o nosso foco será nas análises mais básicas de uma Análise Fatorial Exploratória.

Para saber mais acerca da Análise Fatorial Exploratória, pode dar uma olhada na nossa publicação anterior.

Para saber mais acerca do pacote psych, consulte a documentação em https://cran.r-project.org/web/packages/psych/psych.pdf

Nesse tutorial, vamos pegar um novo banco de dados, o da Escala de Afetos Positivos e Negativos. …

In this series of posts, I`ll be writing about some basics of Linear Algebra [LA] so we can learn together. The book I`ll be using as the material is:

Cabral, M. & Goldfeld, P. (2012). Curso de Álgebra Linear: Fundamentos e Aplicações. Third Edition.

Anton, H. & Rorres, C. (2012). Algebra Linear com Aplicações. Tenth edition.

You’ll have to be familiarized with the topics I wrote in this series before jumping into eigenvalues and eigenvectors, here are the links to it:

• Introduction to Linear Algebra [LA1]
• Linear Systems and Matrices [LA2]
• A Brief Summary of Linear Transformation [LA3]

The topics we’ll see in this post…

In this series of posts, I`ll be writing about some basics of Linear Algebra [LA] so we can learn together. The book I`ll be using as the material is:

Cabral, M. & Goldfeld, P. (2012). Curso de Álgebra Linear: Fundamentos e Aplicações. Third Edition.

Last time we talked about Linear Systems and Matrices. Now, it’s time to know more about linear transformation.

In the context of linear algebra, we use linear transformation as a synonym for a function.

Análise Fatorial Exploratória (AFE) é uma ferramenta estatística que serve para diversas propostas. Em ciências sociais (e.g. Psicologia, Educação) ela tem servido o propósito geral de diminuir o número de dimensões/fatores de uma escala ou instrumento. Isto é, a redução do número de parâmetros para o número de traços latentes/construtos psicológicos. Assim, podemos definir como objetivo da AFE:

Avaliar a dimensionalidade de uma série de indicadores de maneira a identificar o menor número de traços latentes que explica o padrão das correlações (Osborne, 2014).

De maneira mais formal, o modelo fatorial comum (Common Factor Model) vê a covariância entre variáveis observáveis como um reflexo da influência de um ou mais fatores e a variância não explicada. Os itens são considerados indicadores que variam de acordo com o nível de traço latente, ou seja, quanto maior seu nível de Depressão, maior seria sua concordância com o item “Tenho me sentido deprimido”. …

In this series of posts, I`ll be writing about some basics of Linear Algebra [LA] so we can learn together. The book I`ll be using as the material is:

Cabral, M. & Goldfeld, P. (2012). Curso de Álgebra Linear: Fundamentos e Aplicações. Third Edition.

Last time we talked about Vectors, Linear Combination, Span, Basis, and Dimensions. Now, it’s time to know more about linear systems and matrices.

We will talk about:

• Matrices and Vectors in ℝⁿ
• Linear Systems
• Matrices and operations in linear systems
• Operations with Matrices
• Solving Linear Systems
• Matrix-vector product and Dot Product

Linear systems are all around us. We use linear systems, for example, to determine a, b ∈ ℝ such that the line
y = ax + b that cross the plane closest to the dots (x, y), such…