The principal component (PC) can be expressed as in Eq. (5): z_{ij} = a_{i1} x_{1j} + a_{i2} x_{2j} + a_{i3} x_{3j} + cdots + a_{im} x_{mj}, (5 where a is the component loading, z the component score, x the measured value of a variable, I the component number, j the sample number and m the total number of variables.
Invalid responses included >100% in the calculation of component number 4 of the PSQI (i.e., percent of time spent sleeping while in bed).
where z is the component score, a is the component loading, x is the measured value of a variable, i is the component number, j is the sample number, and m is the total number of variables.
The principal component (PC) can be expressed as: z_{ij} = a_{i 1} x_{ 1j} + a_{i 2} x_{ 2j} + a_{i 3} x_{ 3j} + cdots + a_{im} x_{mj}, where z is the component score, a is the component loading, x the measured value of variable, i is the component number, j the sample number and m the total number of variables.
PCA can be expressed as: Z_{ij} = a_{i1} x_{1j} + a_{i2} x_{2j} + a_{i3} x_{3j} + cdots + a_{im} x_{mj} (1 where Z is the component score, a is the component loading, x is the measured value of variable, i is the component number, j is the sample number and m is the total number of variables.
PCA can be expressed mathematically as presented in Eq. (2): Z_{ij} = pc_{i1} x_{1j} + pc_{i2} x_{2j} + cdots pc_{im} x_{mj} (2 where z is the component score, pc is the component loading, x is the measured value of the variable, i is the component number, j is the sample number, and m is the total number of variables.
lambda_{i} = sumlimits_{j in i} {lambda_{j} } (7) r_{i} = sumlimits_{j in i} {frac{{left( {lambda_{j} r_{j} } right)}}{{lambda_{i} }}} (8 where i is section number; j is component number; and (lambda) is failure rate.
where c i is the mixture weight, μ i is the mean vector, Σ i is the covariance matrix, and M is the component number.
For the multidimensional case, the component number rule generalizes in a straightforward way to m_{i} = Sigma_{[i,i]} + 1. (40).
