Inline mathmode goes out the page margin in LyX

Question

I'm using LyX for my document writing. Some of my inline mathmode formulas go out the page margin (see attached fig). I wonder how can I force these formulas to stay inside the page margin. Thanks in advance for your help and time.

Edit Code

where $vec\left(\mathbf{Y}\right)=vec\left(\begin{bmatrix}\mathbf{y}^{\left(1\right)} & \ldots & \mathbf{y}^{\left(j\right)} & \ldots & \mathbf{y}^{\left(t\right)}\end{bmatrix}\right)\equiv\mathbf{y}^{*}$;
$\mathbf{I}\otimes\mathbf{X}\equiv\mathbf{X}^{*}$; $vec\left(\mathbf{B}\right)=vec\left(\begin{bmatrix}\boldsymbol{\beta}^{\left(1\right)} & \ldots & \boldsymbol{\beta}^{\left(j\right)} & \ldots & \boldsymbol{\beta}^{\left(t\right)}\end{bmatrix}\right)\equiv\mathrm{\bm{\beta}}^{*}$;
$\mathbf{I}\otimes\mathbf{Z}\equiv\mathbf{Z}^{*}$; $vec\left(\mathbf{U}\right)=vec\left(\begin{bmatrix}\mathbf{u}^{\left(1\right)} & \ldots & \mathbf{u}^{\left(j\right)} & \ldots & \mathbf{u}^{\left(t\right)}\end{bmatrix}\right)\equiv\mathbf{u}^{*}$;
and $vec\left(\mathbf{E}\right)=vec\left(\begin{bmatrix}\mathbf{e}^{\left(1\right)} & \ldots & \mathbf{e}^{\left(j\right)} & \ldots & \mathbf{e}^{\left(t\right)}\end{bmatrix}\right)\equiv\mathbf{e}^{*}$.
Thus the univariate linear mixed model involving all variables can
be obtained from multivariate linear mixed model

Answer 1

The ; and and are really part of the sentence structure, not the mathematics,so TeX can do a better job if you code this as a sentence with multiple inline fragments. Also it still is hard so I have used \sloppy to tell LaTeX to allow white space to stretch more than usual. It still looks pretty hard to read and I would definitely consider setting this as a display using an AMS alignment, but to get it inline:

\documentclass{article}

\renewcommand\vec[1]{\mathop{\mathrm{vec}}(#1)}

\begin{document}
\large

where $
\vec{\mathbf{Y}} = 
\vec{[\mathbf{y}^{1} \ldots \mathbf{y}^{j} \ldots \mathbf{y}^{t}]}
\cong
\mathbf{y}^*;
\mathbf{I}\otimes\mathbf{X}\cong\mathbf{X}^*;
\vec{\mathbf{B}} = 
\vec{[\beta^{1} \ldots \beta^{j} \ldots \beta^{t}]}
\cong
\beta^*;
\mathbf{I}\otimes\mathbf{Z}\cong\mathbf{Z}^*;
\vec{\mathbf{U}} = 
\vec{[\mathbf{u}^{1} \ldots \mathbf{u}^{j} \ldots \mathbf{u}^{t}]}
\cong
\mathbf{u}^*;
\mbox{ and }
\vec{\mathbf{E}} = 
\vec{[\mathbf{e}^{1} \ldots \mathbf{e}^{j} \ldots \mathbf{e}^{t}]}
\cong
\mathbf{e}^*;$
Thus the invariate linear mixed model involving all variables
can be obtained from multivariate linear mixed

\bigskip

{\sloppy where 
$\vec{\mathbf{Y}} = 
\vec{[\mathbf{y}^{1} \ldots \mathbf{y}^{j} \ldots \mathbf{y}^{t}]}
\cong
\mathbf{y}^*$;
$\mathbf{I}\otimes\mathbf{X}\cong\mathbf{X}^*;
\vec{\mathbf{B}} = 
\vec{[\beta^{1} \ldots \beta^{j} \ldots \beta^{t}]}
\cong
\beta^*$;
$\mathbf{I}\otimes\mathbf{Z}\cong\mathbf{Z}^*$;
$\vec{\mathbf{U}} = 
\vec{[\mathbf{u}^{1} \ldots \mathbf{u}^{j} \ldots \mathbf{u}^{t}]}
\cong
\mathbf{u}^*$;
 and 
$\vec{\mathbf{E}} = 
\vec{[\mathbf{e}^{1} \ldots \mathbf{e}^{j} \ldots \mathbf{e}^{t}]}
\cong
\mathbf{e}^*;$
Thus the invariate linear mixed model involving all variables
can be obtained from multivariate linear mixed\par}

\end{document}