Common Method Variance Pdf UPDATED Free

Factor analysis is a technique that is used to reduce a large number of variables into fewer numbers of factors. This technique extracts maximum common variance from all variables and puts them into a common score. As an index of all variables, we can use this score for further analysis. Factor analysis is part of general linear model (GLM) and this method also assumes several assumptions: there is linear relationship, there is no multicollinearity, it includes relevant variables into analysis, and there is true correlation between variables and factors. Several methods are available, but principal component analysis is used most commonly.

1. Principal component analysis: This is the most common method used by researchers. PCA starts extracting the maximum variance and puts them into the first factor. After that, it removes that variance explained by the first factors and then starts extracting maximum variance for the second factor. This process goes to the last factor.

2. Common factor analysis: The second most preferred method by researchers, it extracts the common variance and puts them into factors. This method does not include the unique variance of all variables. This method is used in SEM.

Factor loading:Factor loading is basically the correlation coefficient for the variable and factor. Factor loading shows the variance explained by the variable on that particular factor. In the SEM approach, as a rule of thumb, 0.7 or higher factor loading represents that the factor extracts sufficient variance from that variable.Eigenvalues: Eigenvalues is also called characteristic roots. Eigenvalues shows variance explained by that particular factor out of the total variance. From the commonality column, we can know how much variance is explained by the first factor out of the total variance. For example, if our first factor explains 68% variance out of the total, this means that 32% variance will be explained by the other factor.Factor score: The factor score is also called the component score. This score is of all row and columns, which can be used as an index of all variables and can be used for further analysis. We can standardize this score by multiplying a common term. With this factor score, whatever analysis we will do, we will assume that all variables will behave as factor scores and will move.

Rotation method: Rotation method makes it more reliable to understand the output. Eigenvalues do not affect the rotation method, but the rotation method affects the Eigenvalues or percentage of variance extracted. There are a number of rotation methods available: (1) No rotation method, (2) Varimax rotation method, (3) Quartimax rotation method, (4) Direct oblimin rotation method, and (5) Promax rotation method. Each of these can be easily selected in SPSS, and we can compare our variance explained by those particular methods.

In this article we use simple and elementary inequalities and approximations in order to estimate the mean and the variance for such trials. Our estimation is distribution-free, i.e., it makes no assumption on the distribution of the underlying data.

To perform meta-analysis of continuous data, the meta-analysts need the mean value and the variance (or standard deviation) in order to pool data. However, sometimes, the published reports of clinical trials only report the median, range and the size of the trial. In this article we use simple and elementary inequalities in order to estimate the mean and the variance for such trials. Our estimation is distribution-free, i.e., it makes no assumption on the distribution of the underlying data. In fact, the value of our approximation(s) is in giving a method for estimating the mean and the variance exactly when there is no indication of the underlying distribution of the data. In current practice, the median is often substituted for the mean, and the Range/4 or Range/6 for the standard deviation. However, it has not been shown that median can indeed be used to replace mean values, nor when the range-formulas are appropriate.

We drew samples from five different distributions, Normal, Log-normal, Beta, Exponential and Weibull. The size of the sample ranged from 8 to about 100. In the first subsection we present the results of our estimation for a normal distribution, which is what meta-analysts would commonly assume. We also show the results of simulations where the data were selected from a skewed distributions. In each case we compared the relative error made by estimating the sample mean with the approximation given by formulas (4) and (5), as well as by the median, and the relative error made by estimating the sample variance by the formulas (12) and (16), as well as the well-known standard deviation estimators Range/4 and Range/6.

To determine whether our estimates make a huge difference when compared to the actual mean difference and variance, we drew two samples of the same size from a same distribution. We applied our methods to the Log-Normal [4, 0.3] distribution since this skewed distribution is frequently encountered in biology and medicine.

This example outlines how our method can be potentially useful for meta-analysts. It is important to realize that this example is provided only to illustrate our method. Our goal here is not to challenge the Cochrane review or ASH/ASCO guidelines. Nevertheless, we believe that this example is a good illustration of the potential of our method. While it is common practice that the investigators simply pool what is available to them it is actually not known how often studies are excluded because of reporting a different summary statistic. In future we will attempt to systematically address this issue and evaluate, for example, how often the Cochrane reviews did not pool data from the available median values when they pooled data on continuous outcomes. We hope that availability of our methods to the wider meta-analytic audience may further improve the inclusiveness of all relevant studies for the Cochrane and other meta-analyses.

Using questionnaires is not without problems. The most frequent is the common method variance bias (i.e., the variance attributable to the measurement method rather than to the constructs the measures represent). Research has illustrated a variety of ways in which data obtained using questionnaires may be compromised in this way (7). Such bias must be carefully considered in interpreting research data.

Historically, factor analysis is used to answer the question, how much common variance is shared among the items. This variance-covariance matrix can be described using the model-implied covariance matrix $\Sigma(\Theta)$. Note that this is in contrast to the observed population covariance matrix $\Sigma$ which comes only from the data. The formula for the model-implied covariance matrix is:

The most fundamental model in CFA is the one factor model, which will assume that the covariance among items is due to a single common factor. Suppose the Principal Investigator is interested in testing the assumption that the first items in the SAQ-8 is a reliable estimate measure of SPSS Anxiety. The eight items are observed indicators of the latent or unobserved construct which the PI calls SPSS Anxiety. The items are the fundamental elements in a CFA and the covariances between the items forms the the fundamental component in CFA. The observed population covariance matrix $\Sigma$ is a matrix of bivariate covariances that determines how many total parameters can be estimated in the model. The model implied matrix $\Sigma(\theta)$ has the same dimensions as $\Sigma$. Recall that the model implied covariance matrix is defined as

The concept of a fixed or free parameter is essential in CFA. The total number of parameters in a CFA model is determined by the number of known values in your population variance-covariance matrix $\Sigma$, given by the formula $p(p+1)/2$ where $p$ is the number of items in your survey. Suppose the principal investigator thinks that the third, fourth and fifth items of the SAQ are the observed indicators of SPSS Anxiety. To obtain the sample covariance matrix $S=\hat{\Sigma}$, which is an estimate of the population covariance matrix $\Sigma$, use the column index [,3:5], and the command cov. The function round with the option 2 specifies that we want to round the numbers to the second digit.

The example above is unrealistic because it would be pointless to have all the parameters be fixed. Instead, many models are just-identified or saturated with zero degrees of freedom. This means that the number of free parameters takes up all known values in $\Sigma$. This is commonly seen in linear regression models, and the main drawback is that we cannot assess its model fit because it supposedly is the best we can do. An under-identified model means that the number of known values is less than the number of free parameters, which is undesirable. In CFA, what we really want is an over-identified model where the number of known values is greater than the number of free parameters. Over-identified models allow us to assess model fit (to be discussed later). To summarize

Answer: We start with 10 total parameters in the model-implied covariance matrix. Since we fix one loading, and 3 unique residual covariances, the number of free parameters is $10-(1+3)=6$. Since we have 6 known values, our degrees of freedom is $6-6=0$, which is defined to be saturated. This is known as the marker method.

Identification for the one factor CFA with three items is necessary due to the fact that we have seven total parameters from the model-implied covariance matrix $\Sigma(\theta)$ but only six known values from the observed population covariance matrix $\Sigma$ to work with. The total parameters include three factor loadings, three residual variances and one factor variance. The extra parameter comes from the fact that we do not observe the factor but are estimating its variance. In order to identify a factor in a CFA model with three or more items, there are two options known respectively as the marker method and the variance standardization method. The 2b1af7f3a8