Loss of smell (anosmia) is a frequently
found symptom in Parkinson's disease. Moreover, numerous studies have
highlighted a significant incidence of cerebrovascular disease in patients with
Parkinson’s disease. The smell disorder has been framed as an indicator of a
sensory pathological process consistent with the hypothesis of the origin of
the disease from the peripheral and visceral nervous system, according to Braak
theory. In this study, we sought a correlation between vascular damage, a
possible contributing factor for 'central' type neurodegeneration, and anosmia
in a cohort of 118 patients with Parkinson’s disease of the outpatients’ clinic
for Movement Disorders. In this investigation we calculated the absolute and
relative percentages of the two considered parameters for the total population
and the subpopulations respectively; thereafter we performed the statistical
analysis for cerebrovascular disease and anosmia with the chi-square test,
which showed no correlation. This finding corroborates the idea of different
and independent mechanisms of pathogenic processes and compromises the symptom
anosmia as a unique marker or predictor of the disease.
Abstract
Introduction
Scale construction is a technique used in social
science research. It is a systematic approach to understanding a particular
component or problem, prevailing in the community and quantifying it
scientifically. Measurement is an integral part of science and helps to
identify and quantify a particular problem, object, or process [1]. According
to De Vellis [2], measurement scales are found to be important in attributing
scores, numbers, factors, in some numerical dimensions, which cannot be
measured directly. In the process of developing the scale, principal factor
analysis plays a very vital role. Large data are statistically very difficult
to manage and interpret. In literature, there are different methods to reduce
the dimensions of the large data set and make it more interpretable without
losing the efficacy of the data [3]. Principal factor analysis also called
principal component analysis is one of the oldest methods for reducing data,
finding the correlation between variables, and helping to get the most
comprehensive and combined variables also called items without compromising on
variability [4]. It is generally used to lower the items of the scale and to
check the psychometric property of the newly developed tool, without
compromising on the statistical importance of the scale. Mooi and Sarstedt [5]
proposed a few points to conduct principal factor analysis.
Pre-requisite for conducting PFA
In the process of conducting PFA, there are certain pre-requisite that need to be taken care of by the researcher. These pre-requisites are as follows
Suitability
of measurement scale: To carry PFA, the data
must be measured on an interval or ratio scale level. In an interval scale, the
items and responses are measured based on numerical values, and each of the
numerical values is at the same interval, with others [6].
Large
sample size: To carry PFA, the sample size
should be adequately large, with an item-to response ratio of 1:4 to 1:10 [7]
which means the number of valid observations should be at least 4 to 10 times,
the number of items used in the analysis.
Independent
Observation: It meant that the responses
collected from the sample, should be independent, which means, totally
uncorrelated. If dependent observation is used, it will give birth to
"artificial correlation”, which can alter the result.
Sufficiently
correlation on the variables: As discussed earlier,
PFA is based on the correlation between items. So, to perform PFA the item must
be correlated sufficiently. To check the adequacy of correlation, researchers
generally used The Kaiser-Meyer-Olkin (KMO) criteria proposed by Kaiser [8].
The
Kaiser-Meyer-Olkin (KMO) by Kaiser (1974): To
measure the adequacy of a sample, Kaiser (1974) proposed criteria known as
"Kaiser Criterion". According to this criterion, the KMO values need
to be 0.6 to and close to 1.0.
The
Bartlett's Test of Sphericity [9]: Bartlett's (1951)
test of sphericity tests whether "a matrix (of correlations) is
significantly different from an identity matrix." The test indicates that
the correlation matrix must fall at a significance level with the variable in
the data set.
Extraction of the Factor
The researcher generally uses PFA, when data reduction is the primary objective. In other words, it can be said that PFA, is widely used because it extracts "a minimum number of factors that account of a maximum proportion of the variables total variance". In the process of factor extraction, principal factor analysis, it self develops a new set of factors, which are the 'Linear Composite' of the original factor in the data set. These linear composites are also called Eigen factors. This process of generating factors continues until a significant share of factors is explained.
The mathematical equation for eigenvalue:
AX = ?X
Where,
A is an arbitrary matrix,
? are eigenvalues, and
X is an eigenvector corresponding to each eigenvalue
Communality- Communality may be defined as the "proportion of common variance found in a particular variable" and is denoted by h2. [11] The communality indicates how much variance of each variable factor extraction can produce. Generally, the extracted factor should account for at least 50% of the variance of a variable. Thus, the commonality should be above 0.50. A variable with a variance that is completely unexplained by any other variables will have a commonality of zero. [12] Since the objective is to reduce the number of factor variables through factor extraction, the researcher should extract only a few factors that account for a high degree of the overall variance. Communality in PFA [13],
Where,
cj
= commonality of the jth variable (h2)
sij
= loading (or correlation) between the ith component and the jth variable.
Determining the number of factors
After the factors are extracted, the major task is to identify and determine the extracted factors and their adequacy. In this process, the researcher generally makes use of two methods – (i) the Kaiser Criteria and (ii) The Scree Plot. The purpose behind using these two methods simultaneously is because if a different method suggests the same number of factors, it leads to great confidence in the result.
The
Kaiser criterion [8]: The most common way to
determine the number of factors is to select all the factors with an eigenvalue
greater than 1. The reason for choosing an eigenvalue greater than 1 is that it
accounts for more variances than a single variance. Extracting all the factors
with an eigenvalue greater than 1 is frequently called the Kaiser criteria or
latent root criterion.
The Scree Plot [14]: This is again a method to determine the factors. In the scree plot, several factors to be extracted with eigenvalue (y-axis) is a plot against the factor with which it is associated (x-factor). The result is the output of the scree plot where there is a typical distinct break in it, showing the correct number of factors. This distinct break is known as "elbow". It is recommended to retain all the factors which are above the elbow break because it contributes most to the explanation of the variance in the database. In the figure, shown below 2 to 3 factors could be retained.
Figure
1:
Scree
Plot (Eigenvalues of Full Correlation Matrix).
Figure 1: Scree Plot (Eigenvalues of Full Correlation Matrix).
|
KMO Value |
Adequacy
of the Correlation |
|
Below 0.50 |
Unacceptable |
|
0.50-0.59 |
Miserable |
|
0.60-0.69 |
Mediocre |
|
0.70-0.79 |
Middling |
|
0.80-0.89 |
Meritorious |
|
0.90 and
higher |
Marvelous |
After the factors are identified and determined,
Interpretation of the factor solution takes place. It follows two methods:
Rotation
of the Factor- To interpret the solution, the
researcher has to determine which variables relate to each of the factors
extracted. The researcher does this by examining the factor loadings, which
represent the correlations between the factors and the variables (range -1 to
+1). A high factor loading indicates that a certain factor represents a
variable well. Subsequently, the researcher looks for high absolute values,
because the correlation between a variable and a factor can also be negative.
Studies conducted in the past have suggested that in the rotation of the factor
‘Promax rotation’ is widely used [15,16].
Promax
Rotation- It is an oblique rotation, which allows
factors to be correlated. This rotation can be calculated more quickly than a
direct oblimin rotation, so it is useful for large datasets [17]. In oblique
rotations the new axes are free to acquire any angle in the factor space, here,
the degree of correlation is generally seen as small because two highly
correlated factors are understood as one factor. Oblique rotations, therefore,
relax the orthogonality constraint to gain simplicity in the interpretation and
hence are widely followed.
Final Item Reduction
A pattern coefficient ("loading") of 0.4 and
higher (that is, a factor explaining at least 16% of an item's variance) were
retained. For a factor to be considered, a minimum three-item should have a
loading of more than 0.40. It is to be noted that the interpretation of the
factors is entirely based on the pattern matrix coefficients.
Factor
Loading: Factor loading is a sort of “indices” or
“scale” that shows the “relative importance” or “magnitude” of some collection
of items (characteristics, features) that collectively form a whole [18].
Pattern Matrix Coefficients: It is defined as the “unique loads or investments of the given factor into variables” [19]. It gives an overview of the number of factors developed with factor loading (more than 0.4), and the overview of the final items retained. For example: If 10 factors were developed and the factor loading of 20 (for say) items was below 0.40, hence they will be discarded. So, it is necessary to develop at least twice as many items in the question pool.
Internal Consistency Assessment of the new tool (PIC)
Internal consistency is a statistical measurement for the reliability of a particular scale. It is defined as the extent to which items within a scale or construct, measure various aspects of the same characteristics of the scale [20]. A scale is considered to be having good internal consistency reliability if the items of the scales measure the same construct. It can be calculated by two methods (i) Cronbach’s Alpha Co-efficiency (ii) Composite Reliability.
Cronbach’s
Alpha Co-efficiency: Cronbach’s alpha, ? (or
coefficient alpha), developed by Cronbach [21] measures the reliability or
internal consistency of a particular construct. It assesses reliability in the
Likert-type scale. It helps in identifying, how closely a set of items is
grouped.
The formula for Cronbach’s is,
Where
- N
= the number of items.
- c?
= average covariance between item pairs.
- v?
= average variance.
Mathematical expression for calculating Composite Reliability (CR),
?i = completely standardized loading for the ith indicator,
V
(?i) = variance of the error term for the ith indicator,
p
= number of indicators
Construct validity is one of the types to measure the validity of a constructor scale, to see how well the scale is constructed, and how well it is measuring the component or variable, it is supposed to measure [23]. The most common way to see the construct validity of a particular scale is by comparing the scale, with other pre-existing tools of the same construct. If the outcome is significant, then it can be said that construct validity is established. There are two types of construct validity (i) Convergent Validity (ii) Divergent Validity.
Convergent Validity: In convergent validity, it is seen that, to what level the newly construct converges with the pre-existing tools. The scores of the new construct tool are correlated with the scores of the pre-existing tool, and a level of significance is seen (Strauss & Smith, 2009). For convergent validity, the expected average variance (AV) should be greater than 0.5, though, Fornell & Larcker [24] have suggested that if average variance (AV) falls below the cut off of 0.5 but Composite Reliability (CR) falls above 0.6, therefore the convergent validity of a specific construct stands adequate [25].
Average Variance Extraction (AVE): It is a measure to assess convergent validity. AVE is the average amount of variance in indicator variables that a construct is measuring [26].
AVE =
K=is the number of items, 
The factor
loading of an item, and
The variance of the
error of item.
Discriminant Validity: It is the other type of construct validity that is the opposite of convergent validity. In discriminant validity, the newly formed measure should not be highly correlated with the other pre-existing measures. Discriminant validity coefficients should be noticeably smaller in magnitude than convergent validity coefficients [27].
Conclusion
The construction of a psychosocial scale is undeniably effortful. Prompt theoretical understanding of psychosocial construct along with needful statistical knowledge can be a boon. The intention of writing this review paper was to offer a comprehensive overview of PFA so that, its intimidating nature can be debunked. This simplified understanding of the steps of PFA may encourage young researchers to construct psychosocial scales in the Indian context.
Financial Support and sponsorship
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Conflicts of Interest
There are no conflicts of interest.