LPA심층탐구 통합 슬라이드 (1

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<title>잠재프로파일분석(LPA) 전문가 가이드</title>
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<div class="slide-container">
<div class="icon-grid"></div>
<div class="decorative-element deco-1"></div>
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<div class="content-wrapper">
<div class="mb-8">
<h1 class="main-title">잠재프로파일분석</h1>
<h2 class="subtitle">Latent Profile Analysis</h2>
<p class="description">
                    이론적 기초부터 고급분석까지: LPA 설계·추정·해석·보고까지 연구 전 과정을 한눈에!
                </p>
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<div class="features">
<div class="feature-item">
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<span>이론적 기초</span>
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<div class="feature-item">
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<span>실무적 분석</span>
</div>
<div class="feature-item">
<i class="fas fa-cogs"></i>
<span>고급기법</span>
</div>
<div class="feature-item">
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<span>보고 가이드</span>
</div>
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</head>
<body>
<div class="slide-container">

<header class="header">
<h1 class="main-title">혼합모형(Mixture Models) 이론</h1>
<p class="sub-title">잠재프로파일분석의 통계적 기반</p>
</header>

<div class="equation-container">
<div class="equation-text">
                f(y) = <span style="font-style: normal;">Σ</span><sub>k=1</sub><sup>K</sup> π<sub>k</sub> · f<sub>k</sub>(y; θ<sub>k</sub>)
            </div>
<p class="equation-desc">
                관측된 분포 f(y)는 K개 하위집단 분포의 가중 합으로 표현됨
            </p>
</div>

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<div class="info-card">
<div class="card-header">
<div class="card-icon"><i class="fas fa-layer-group"></i></div>
<h2 class="card-title">혼합분포의 성질</h2>
</div>
<ul class="card-list">
<li>이질적인 하위집단들의 결합</li>
<li>각 집단은 고유한 분포(정규분포)</li>
<li>개체 i가 집단 k에 속할 확률 모델링</li>
</ul>
</div>

<div class="info-card" style="border-top-color: #10b981;">
<div class="card-header">
<div class="card-icon" style="color: #059669; background-color: #ecfdf5;"><i class="fas fa-sliders-h"></i></div>
<h2 class="card-title">주요 파라미터</h2>
</div>
<ul class="card-list">
<li><span class="math-inline">π<sub>k</sub></span> : 잠재집단 비율 (Sum = 1)</li>
<li><span class="math-inline">μ<sub>k</sub></span> : 각 집단별 평균 벡터</li>
<li><span class="math-inline">Σ<sub>k</sub></span> : 각 집단별 공분산 행렬</li>
</ul>
</div>

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<div class="card-header">
<div class="card-icon" style="color: #d97706; background-color: #fffbeb;"><i class="fas fa-fingerprint"></i></div>
<h2 class="card-title">식별 문제</h2>
</div>
<ul class="card-list">
<li>동일 우도를 갖는 여러 해 존재 가능</li>
<li><strong>Label Switching</strong>: 집단 명칭의 임의성</li>
<li>국소 해(Local Maxima) 주의 필요</li>
</ul>
</div>
</div>
</div>

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</head>
<body>
<div class="slide-container">
<h1 class="section-title">LPA vs LCA(잠재계층분석) 비교</h1>
<table class="comparison-table">
<thead>
<tr>
<th>비교 요소</th>
<th>LPA (Latent Profile Analysis)</th>
<th>LCA (Latent Class Analysis)</th>
</tr>
</thead>
<tbody>
<tr>
<td>
<div class="method-header">
<div class="icon-box"><i class="fas fa-chart-bar"></i></div>
                            지표 유형
                        </div>
</td>
<td>
<div class="tag-container">
<span class="concept-tag">연속형 (Continuous)</span>
<span class="concept-tag">정규분포 가정</span>
</div>
</td>
<td>
<div class="tag-container">
<span class="concept-tag lca">범주형 (Categorical)</span>
<span class="concept-tag lca">이항/다항분포</span>
</div>
</td>
</tr>
<tr>
<td>
<div class="method-header">
<div class="icon-box"><i class="fas fa-wave-square"></i></div>
                            분포 가정
                        </div>
</td>
<td>
<div class="tag-container">
<span class="concept-tag">다변량 정규분포</span>
<span class="concept-tag">평균·공분산 추정</span>
</div>
</td>
<td>
<div class="tag-container">
<span class="concept-tag lca">범주확률 모델</span>
<span class="concept-tag lca">응답확률 추정</span>
</div>
</td>
</tr>
<tr>
<td>
<div class="method-header">
<div class="icon-box"><i class="fas fa-search"></i></div>
                            해석 방식
                        </div>
</td>
<td>
<div class="tag-container">
<span class="concept-tag">평균 패턴(높낮이) 중심</span>
<span class="concept-tag">수준 비교</span>
</div>
</td>
<td>
<div class="tag-container">
<span class="concept-tag lca">응답 패턴(유무) 중심</span>
<span class="concept-tag lca">형태 분류</span>
</div>
</td>
</tr>
<tr>
<td>
<div class="method-header">
<div class="icon-box"><i class="fas fa-database"></i></div>
                            적용 사례
                        </div>
</td>
<td>
<div class="tag-container">
<span class="concept-tag">심리척도 (자존감 등)</span>
<span class="concept-tag">성취도 점수</span>
</div>
</td>
<td>
<div class="tag-container">
<span class="concept-tag lca">증상 유무 (우울 등)</span>
<span class="concept-tag lca">진단 카테고리</span>
</div>
</td>
</tr>
</tbody>
</table>
<div class="highlight-box">
<div class="highlight-icon">
<i class="fas fa-lightbulb"></i>
</div>
<div class="highlight-content">
<h3>핵심 차이점 요약</h3>
<p>LPA는 <strong>연속형 지표의 평균 패턴</strong>을, LCA는 <strong>범주형 지표의 응답 확률 패턴</strong>을 중심으로 잠재집단을 식별합니다. 연구 데이터의 척도 특성에 따라 적절한 방법론을 선택해야 합니다.</p>
</div>
</div>
</div>

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</head>
<body>
<div class="slide-container">
<h1 class="section-title">모형 식별(Model Identification)</h1>
<div class="grid-container">

<div class="card card-1">
<div class="card-header">
<div class="icon-wrapper">
<i class="fas fa-key"></i>
</div>
<h2 class="card-title">필요조건<br/><span style="font-size: 0.9em; color: #64748b; font-weight: 500;">Necessary Conditions</span></h2>
</div>
<div class="card-content">
<ul class="bullet-list">
<li><p>정보량 > 추정모수 수 (자유도 ≥ 0 확보)</p></li>
<li><p>관측변수 수 ≥ 3 (최소 식별 조건)</p></li>
<li><p>프로파일 수 상한: K < n / 지표수 (충분한 표본)</p></li>
</ul>
</div>
</div>

<div class="card card-2">
<div class="card-header">
<div class="icon-wrapper">
<i class="fas fa-cogs"></i>
</div>
<h2 class="card-title">공분산 제약<br/><span style="font-size: 0.9em; color: #64748b; font-weight: 500;">Covariance Constraints</span></h2>
</div>
<div class="card-content">
<ul class="bullet-list">
<li><p>대각구조(Diagonal): 지표 간 독립 가정 (단순성)</p></li>
<li><p>동일분산(Equal): 프로파일 간 분산 동일 (식별 용이)</p></li>
<li><p>완전/가변(Full/Varying): 유연하지만 과적합 위험</p></li>
</ul>
</div>
</div>

<div class="card card-3">
<div class="card-header">
<div class="icon-wrapper">
<i class="fas fa-random"></i>
</div>
<h2 class="card-title">초기값 설정<br/><span style="font-size: 0.9em; color: #64748b; font-weight: 500;">Initial Values</span></h2>
</div>
<div class="card-content">
<ul class="bullet-list">
<li><p>국소극값(Local Maxima) 문제 방지 필수</p></li>
<li><p>다중 시작값(Random Starts): 50~500회 이상 반복</p></li>
<li><p>최종 최우도(Max Likelihood) 해의 재현성 확인</p></li>
</ul>
</div>
</div>

<div class="card card-4">
<div class="card-header">
<div class="icon-wrapper">
<i class="fas fa-exchange-alt"></i>
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<h2 class="card-title">라벨 스위칭<br/><span style="font-size: 0.9em; color: #64748b; font-weight: 500;">Label Switching</span></h2>
</div>
<div class="card-content">
<ul class="bullet-list">
<li><p>프로파일 순서가 바뀌어도 우도(Likelihood)는 동일</p></li>
<li><p>문제: 해석 및 베이지안 추정 시 혼란 유발</p></li>
<li><p>해결: 사전 제약(Constraints) 또는 사후 정렬(Relabeling)</p></li>
</ul>
</div>
</div>
</div>
</div>

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<div class="slide-container">

<div class="header">
<h1 class="section-title">정규분포 가정과 위반</h1>
<p class="section-subtitle">프로파일 내 다변량 정규성(Within-class Normality) 가정의 이해</p>
</div>

<div class="top-section">
<div class="equation-wrapper">
<i class="fas fa-bell" style="margin-right: 15px; color: #60a5fa;"></i>
                y | class = k  ~  N( μ<sub>k</sub>, Σ<sub>k</sub> )
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<i class="fas fa-exclamation-triangle"></i>
                위반 시: 수렴 실패, 왜곡된 해, 표준오차 편향
            </div>
</div>

<div class="content-grid">

<div class="card">
<div class="card-header">
<div class="icon-box remedy-icon">
<i class="fas fa-tools"></i>
</div>
<h2 class="card-title">데이터 및 추정 대처 (Remedies)</h2>
</div>
<div class="list-group">
<div class="list-item">
<i class="fas fa-check-circle check-icon"></i>
<div class="item-content">
<span class="item-title">변수 변환 (Transformation)</span>
<span class="item-desc">로그(Log), 제곱근(Sqrt), Box-Cox 변환으로 분포 개선</span>
</div>
</div>
<div class="list-item">
<i class="fas fa-check-circle check-icon"></i>
<div class="item-content">
<span class="item-title">이상치 처리 (Outliers)</span>
<span class="item-desc">Mahalanobis $D^2$ 기준 제거 또는 Winsorization(5% 절사)</span>
</div>
</div>
<div class="list-item">
<i class="fas fa-check-circle check-icon"></i>
<div class="item-content">
<span class="item-title">강건 추정 (Robust Estimation)</span>
<span class="item-desc">MLR 추정기(Huber-White SE) 사용하여 비정규성에 강건</span>
</div>
</div>
</div>
</div>

<div class="card">
<div class="card-header">
<div class="icon-box alt-icon">
<i class="fas fa-bezier-curve"></i>
</div>
<h2 class="card-title">대안 모형 (Alternative Models)</h2>
</div>
<div class="list-group">
<div class="list-item">
<i class="fas fa-arrow-right check-icon" style="color: #d97706;"></i>
<div class="item-content">
<span class="item-title">t-분포 혼합 (t-Mixture)</span>
<span class="item-desc">꼬리가 두꺼운 분포를 허용하여 이상치 영향 감소</span>
</div>
</div>
<div class="list-item">
<i class="fas fa-arrow-right check-icon" style="color: #d97706;"></i>
<div class="item-content">
<span class="item-title">왜도-정규 혼합 (Skew-Normal)</span>
<span class="item-desc">비대칭 분포(Skewness) 파라미터를 직접 모델링</span>
</div>
</div>
<div class="list-item">
<i class="fas fa-arrow-right check-icon" style="color: #d97706;"></i>
<div class="item-content">
<span class="item-title">비모수적 접근 (Non-parametric)</span>
<span class="item-desc">분포 가정을 최소화한 모형 고려 (단, 해석 복잡성 증가)</span>
</div>
</div>
</div>
</div>
</div>
</div>

/* Cards Layout */
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        display: grid;
        grid-template-columns: repeat(3, 1fr);
        gap: 2rem;
        flex: 1;
        min-height: 0; /* Important for flex container */
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        background-color: white;
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        border-radius: 12px;
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        flex-direction: column;
        justify-content: flex-start;
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        display: flex;
        align-items: center;
        margin-bottom: 1rem;
        gap: 0.75rem;
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        margin: 0;
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        font-size: 1.1rem; /* ~18pt */
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        margin-bottom: 0.6rem;
        padding-left: 1.25rem;
        position: relative;
        line-height: 1.4;
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        content: "•";
        color: #3b82f6;
        font-weight: bold;
        position: absolute;
        left: 0;
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        font-family: 'Times New Roman', serif;
        font-style: italic;
        font-weight: 600;
        color: #0f172a;
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</style>
</head>
<body>
<div class="slide-container">

<header class="header">
<h1 class="main-title">EM 알고리즘 수학적 원리</h1>
<p class="sub-title">Expectation-Maximization의 핵심 메커니즘</p>
</header>

<div class="equation-container">
<div class="equation-text">
                Q(θ|θ<sub>t</sub>) = E<sub>Z|Y,θ<sub>t</sub></sub>[log L<sub>c</sub>(θ;Y,Z)]
            </div>
<p class="equation-desc">
                관측되지 않은 잠재변수 Z에 대한 완전데이터 로그우도의 조건부 기대값
            </p>
</div>

<div class="cards-wrapper">

<div class="info-card">
<div class="card-header">
<div class="card-icon"><i class="fas fa-search"></i></div>
<h2 class="card-title">Maximization (M-Step)</h2>
</div>
<ul class="card-list">
<li>Q함수를 최대화하는 파라미터 탐색</li>
<li><span class="math-inline">θ<sub>t+1</sub> = argmax<sub>θ</sub> Q(θ|θ<sub>t</sub>)</span></li>
<li>반복적 갱신을 통한 최적화</li>
</ul>
</div>

<div class="info-card" style="border-top-color: #10b981;">
<div class="card-header">
<div class="card-icon" style="color: #059669; background-color: #ecfdf5;"><i class="fas fa-chart-line"></i></div>
<h2 class="card-title">수렴성 (Monotonicity)</h2>
</div>
<ul class="card-list">
<li>각 반복마다 우도가 감소하지 않음</li>
<li><span class="math-inline">log L(θ<sub>t+1</sub>) ≥ log L(θ<sub>t</sub>)</span></li>
<li>Jensen 부등식에 의해 보장됨</li>
</ul>
</div>

<div class="info-card" style="border-top-color: #f59e0b;">
<div class="card-header">
<div class="card-icon" style="color: #d97706; background-color: #fffbeb;"><i class="fas fa-stop-circle"></i></div>
<h2 class="card-title">정지 규칙 (Stopping Rule)</h2>
</div>
<ul class="card-list">
<li>파라미터 변화량 < ε (10<sup>-6</sup>)</li>
<li>로그우도 변화량 < ε</li>
<li>Gradient 크기 < ε (수렴 판정)</li>
</ul>
</div>
</div>
</div>

/* Cards Layout */
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        display: grid;
        grid-template-columns: repeat(2, 1fr);
        gap: 2rem;
        flex: 1;
        align-items: stretch;
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    .info-card {
        background-color: white;
        border: 1px solid #e2e8f0;
        border-radius: 12px;
        padding: 1.5rem;
        box-shadow: 0 4px 6px -1px rgba(0, 0, 0, 0.05);
        display: flex;
        flex-direction: column;
        justify-content: flex-start;
        border-top: 6px solid #3b82f6;
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        display: flex;
        align-items: center;
        margin-bottom: 1rem;
        gap: 0.75rem;
        border-bottom: 1px solid #f1f5f9;
        padding-bottom: 0.75rem;
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        width: 44px;
        height: 44px;
        background-color: #eff6ff;
        border-radius: 50%;
        display: flex;
        align-items: center;
        justify-content: center;
        color: #2563eb;
        font-size: 1.25rem;
        flex-shrink: 0;
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        font-size: 1.4rem;
        font-weight: 700;
        color: #1e293b;
        margin: 0;
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    .card-list {
        list-style: none;
        padding: 0;
        margin: 0;
        display: flex;
        flex-direction: column;
        gap: 0.85rem;
    }
    .card-list li {
        font-size: 1.15rem; /* ~18pt */
        color: #475569;
        padding-left: 1.5rem;
        position: relative;
        line-height: 1.4;
    }
    .card-list li::before {
        content: "\f00c";
        font-family: "Font Awesome 6 Free";
        font-weight: 900;
        color: #3b82f6;
        position: absolute;
        left: 0;
        top: 0.2em;
        font-size: 0.8em;
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        font-family: 'Times New Roman', serif;
        font-style: italic;
        font-weight: 600;
        color: #0f172a;
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        display: inline-block;
        background-color: #fef3c7;
        color: #d97706;
        font-weight: 600;
        padding: 0.2em 0.6em;
        border-radius: 4px;
        font-size: 0.9em;
        margin-right: 0.3em;
    }
</style>
</head>
<body>
<div class="slide-container">

<header class="header">
<h1 class="main-title">우도함수 (Likelihood Function)</h1>
<p class="sub-title">모형 적합도의 핵심 척도와 최적화</p>
</header>

<div class="equation-container">
<div class="equation-text">
                log L(θ) = Σ<sub>i=1</sub><sup>N</sup> log [ Σ<sub>k=1</sub><sup>K</sup> π<sub>k</sub> · φ(y<sub>i</sub> | μ<sub>k</sub>, Σ<sub>k</sub>) ]
            </div>
<p class="equation-desc">
                관측 데이터의 로그 우도 합: 모수 벡터 θ = (π, μ, Σ)에 대해 최대화
            </p>
</div>

<div class="cards-wrapper">

<div class="info-card">
<div class="card-header">
<div class="card-icon"><i class="fas fa-calculator"></i></div>
<h2 class="card-title">수치적 최적화 (Optimization)</h2>
</div>
<ul class="card-list">
<li>
<p><strong>닫힌 해(Closed Form) 부재:</strong> 미분값 0인 해를 직접 구할 수 없음</p>
</li>
<li>
<p><strong>반복적 방법 사용:</strong> EM 알고리즘, Newton-Raphson 활용</p>
</li>
<li>
<p><strong>구배(Gradient)와 헤시안(Hessian):</strong> <span class="math-inline">∇log L</span>(기울기)과 <span class="math-inline">∇²log L</span>(곡률)로 극대값 탐색</p>
</li>
<li>
<p><span class="highlight-badge">알고리즘</span> BFGS, L-BFGS-B 등 준-뉴턴(Quasi-Newton) 기법 적용</p>
</li>
</ul>
</div>

<div class="info-card" style="border-top-color: #ef4444;">
<div class="card-header">
<div class="card-icon" style="color: #dc2626; background-color: #fef2f2;"><i class="fas fa-exclamation-triangle"></i></div>
<h2 class="card-title">비정규 경계 문제 (Boundary Problem)</h2>
</div>
<ul class="card-list">
<li>
<p><strong>모형 비교의 난점:</strong> K개를 K+1개와 비교 시 일반적 <span class="math-inline">χ²</span> 검정 불가</p>
</li>
<li>
<p><strong>이유:</strong> 귀무가설 하에서 파라미터가 경계값(비율=0)에 위치함</p>
</li>
<li>
<p><strong>결과:</strong> -2LL 차이가 카이제곱 분포를 따르지 않음</p>
</li>
<li>
<p><span class="highlight-badge">해결책</span> 표준 LRT 대신 <strong>LMR-LRT</strong> 또는 <strong>BLRT</strong> 사용 필수</p>
</li>
</ul>
</div>
</div>
</div>

/* Top Section: MAP Classification */
    .top-section {
        background-color: #f0f9ff;
        border-left: 6px solid #3b82f6;
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        padding: 1.25rem;
        margin-bottom: 1.5rem;
        display: flex;
        align-items: center;
        gap: 1.5rem;
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        background-color: #3b82f6;
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        height: 60px;
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        font-size: 1.4rem;
        font-weight: 700;
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        font-size: 1.15rem;
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        margin: 0;
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        background-color: #eff6ff;
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        font-size: 2rem;
        font-weight: 700;
        color: #1d4ed8;
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        font-size: 1rem;
        color: #64748b;
        margin-top: 0.5rem;
        font-weight: 500;
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        font-size: 1.35rem;
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/* Correction Box */
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        background-color: #fef3c7;
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        border-radius: 9999px;
        font-size: 0.9rem;
        font-weight: 600;
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</style>
</head>
<body>
<div class="slide-container">

<header class="header">
<h1 class="main-title">사후확률과 분류 (Classification)</h1>
<p class="sub-title">개체를 잠재 프로파일에 할당하는 방법론</p>
</header>

<div class="top-section">
<div class="map-icon-box">
<i class="fas fa-crosshairs"></i>
</div>
<div class="map-content">
<h3>MAP 분류 (Maximum A Posteriori)</h3>
<p>각 개체(i)를 사후확률이 가장 높은 잠재 프로파일(k)에 할당하는 결정론적 방식</p>
</div>
</div>

<div class="equation-section">
<div class="equation-text">
            class<sub>i</sub> = argmax<sub>k</sub> P(z<sub>i</sub> = k | y<sub>i</sub>)
        </div>
<div class="equation-label">
            개별 관측치 y<sub>i</sub>에 대해 조건부 확률이 최대가 되는 클래스 k 선택
        </div>
</div>

<div class="bottom-grid">

<div class="info-card">
<div class="card-header">
<i class="fas fa-chart-line text-green-600"></i>
<h2 class="card-title">분류 정확도 지표</h2>
</div>
<div class="accuracy-item">
<span class="acc-label">Entropy (엔트로피)</span>
<p class="acc-desc">0~1 범위, 1에 가까울수록 명확한 분류 (권장 ≥ 0.80)</p>
</div>
<div class="accuracy-item">
<span class="acc-label">AVEPP (Average Posterior Probability)</span>
<p class="acc-desc">할당된 클래스에 대한 평균 사후확률 (권장 ≥ 0.70)</p>
</div>
</div>

<div class="info-card">
<div class="card-header">
<i class="fas fa-tools text-amber-600"></i>
<h2 class="card-title">오분류 보정 (3-Step)</h2>
</div>
<div class="correction-item">
<span class="corr-label">3-Step Approach</span>
<span class="corr-tag">표준 방법</span>
</div>
<div class="correction-item">
<span class="corr-label">BCH Method</span>
<span class="corr-tag">연속형 결과</span>
</div>
<div class="correction-item">
<span class="corr-label">DCAT Method</span>
<span class="corr-tag">범주형 결과</span>
</div>
</div>
</div>
</div>

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        display: flex;
        flex-direction: column;
        align-items: center;
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</style>
</head>
<body>
<div class="slide-container">
<h1 class="section-title">적용 사례 1: 교육심리 (학업동기 프로파일)</h1>
<div class="grid-container">

<div class="card">
<div class="card-header">
<div class="icon-box icon-data"><i class="fas fa-database"></i></div>
<div class="card-title">1. 데이터 (Data)</div>
</div>
<div class="card-content">
<p class="mb-2"><strong>표본:</strong> 대학생 <span class="highlight-stat">n=1,000명</span></p>
<p><strong>지표:</strong> 학업동기 6개 하위요인<br/>(자기효능감, 내재동기 등, 7점 리커트)</p>
</div>
</div>

<div class="card">
<div class="card-header">
<div class="icon-box icon-proc"><i class="fas fa-cogs"></i></div>
<div class="card-title">2. 분석 절차 (Procedure)</div>
</div>
<div class="card-content">
<p class="mb-2"><strong>모형 추정:</strong> 1~6개 프로파일 순차 비교</p>
<p><strong>결정 기준:</strong> <span class="highlight-stat">BIC 최저값</span>, LMR/BLRT 유의성(p<.05) 및 이론적 해석 가능성 종합 고려</p>
</div>
</div>

<div class="card">
<div class="card-header">
<div class="icon-box icon-res"><i class="fas fa-chart-pie"></i></div>
<div class="card-title">3. 결과 (Results)</div>
</div>
<div class="card-content">
<div class="result-row">
<div class="result-item">
<span class="result-val text-blue-600">4개</span>
<span class="result-label">최적 프로파일</span>
</div>
<div class="result-item">
<span class="result-val text-green-600">0.84</span>
<span class="result-label">Entropy</span>
</div>
<div class="result-item">
<span class="result-val text-purple-600">25.3%</span>
<span class="result-label">최소집단</span>
</div>
</div>
</div>
</div>

<div class="card">
<div class="card-header">
<div class="icon-box icon-int"><i class="fas fa-lightbulb"></i></div>
<div class="card-title">4. 해석 & 원위결과</div>
</div>
<div class="card-content">
<p class="mb-2"><strong>프로파일 명명:</strong> 고동기형, 무동기형, 회피형, 불균형형</p>
<p><strong>성취도 비교(BCH):</strong> <span class="highlight-stat">F=12.34***</span><br/>고동기형 > 불균형형 > 회피형 > 무동기형 순으로 학업성취도 유의한 차이 확인</p>
</div>
</div>
</div>
</div>

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</head>
<body>
<div class="slide-container">
<h1 class="section-title">적용 사례 2: 건강행동 (Health Behavior)</h1>
<div class="grid-container">

<div class="card card-data">
<div class="card-header">
<div class="card-icon"><i class="fas fa-database"></i></div>
<h2 class="card-title">연구 데이터</h2>
</div>
<div class="card-content">
<p class="mb-2"><span class="highlight-text">표본:</span> 성인 남녀 1,200명</p>
<p class="mb-2"><span class="highlight-text">지표:</span> 신체활동, 식습관, 수면, 스트레스 (4요인)</p>
<p><span class="highlight-text">척도:</span> 모든 지표를 Z-score로 표준화하여 패턴 비교</p>
<span class="badge badge-blue">연속형 지표 활용</span>
</div>
</div>

<div class="card card-extract">
<div class="card-header">
<div class="card-icon"><i class="fas fa-filter"></i></div>
<h2 class="card-title">프로파일 추출</h2>
</div>
<div class="card-content">
<ul class="check-list">
<li>K=3~5 모형 비교 → <strong>4개 프로파일</strong> 최적 선정</li>
<li>적합도: SABIC 최저, Entropy 0.79 (양호)</li>
<li>최소 집단 비율: 18.7%로 안정적 구조 확보</li>
</ul>
<span class="badge badge-purple">4-Profile Model 채택</span>
</div>
</div>

<div class="card card-target">
<div class="card-header">
<div class="card-icon"><i class="fas fa-bullseye"></i></div>
<h2 class="card-title">개입 타겟팅</h2>
</div>
<div class="card-content">
<p class="mb-2"><strong>'고스트레스-저활동'</strong> 집단을 위험군으로 식별</p>
<p>맞춤형 건강 증진 프로그램의 우선 대상자로 선정하여 효율적 자원 배분 가능</p>
<span class="badge badge-green">고위험군 조기 선별</span>
</div>
</div>

<div class="card card-group">
<div class="card-header">
<div class="card-icon"><i class="fas fa-users"></i></div>
<h2 class="card-title">성별 다집단 분석</h2>
</div>
<div class="card-content">
<p class="mb-2"><span class="highlight-text">남성:</span> '고활동-저스트레스' 비율 높음 (32.1%)</p>
<p class="mb-2"><span class="highlight-text">여성:</span> '평균 균형형' 비율 높음 (28.4%)</p>
<p>성별에 따른 프로파일 분포의 유의한 차이 확인</p>
<span class="badge badge-yellow">인구통계학적 특성 반영</span>
</div>
</div>
</div>
</div>

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        font-weight: 700;
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</style>
</head>
<body>
<div class="slide-container">
<h1 class="section-title">이론적 기초 요약</h1>
<div class="content-wrapper">

<div class="card card-blue blue-theme">
<div class="card-header">
<div class="icon-circle"><i class="fas fa-brain"></i></div>
<div class="card-title">LPA<br/>핵심 개념</div>
</div>
<ul class="check-list">
<li class="check-item">
<i class="fas fa-check-circle check-mark"></i>
<p>정규 혼합 기반의 <strong>사람중심(Person-centered)</strong> 접근법</p>
</li>
<li class="check-item">
<i class="fas fa-check-circle check-mark"></i>
<p><strong>연속형 지표</strong>를 활용하여 이질적인 잠재프로파일 식별</p>
</li>
<li class="check-item">
<i class="fas fa-check-circle check-mark"></i>
<p>각 프로파일 내 <strong>다변량 정규분포</strong> 가정 (독립성)</p>
</li>
<li class="check-item">
<i class="fas fa-check-circle check-mark"></i>
<p>주요 모수: <strong>사전확률(π), 평균(μ), 공분산(Σ)</strong></p>
</li>
</ul>
</div>

<div class="card card-indigo indigo-theme">
<div class="card-header">
<div class="icon-circle"><i class="fas fa-cogs"></i></div>
<div class="card-title">추정 및<br/>알고리즘</div>
</div>
<ul class="check-list">
<li class="check-item">
<i class="fas fa-sync-alt check-mark"></i>
<p><strong>EM 알고리즘</strong>: E-step(확률 추정)과 M-step(모수 갱신) 반복</p>
</li>
<li class="check-item">
<i class="fas fa-exclamation-triangle check-mark"></i>
<p><strong>국소극값(Local Maxima)</strong> 문제 발생 가능성 주의</p>
</li>
<li class="check-item">
<i class="fas fa-key check-mark"></i>
<p>해결책: 충분한 수의 <strong>Random Starts</strong> 설정 필수</p>
</li>
<li class="check-item">
<i class="fas fa-search check-mark"></i>
<p>모형 식별성(Identification) 확보를 위한 공분산 제약</p>
</li>
</ul>
</div>

<div class="card card-slate slate-theme">
<div class="card-header">
<div class="icon-circle"><i class="fas fa-balance-scale"></i></div>
<div class="card-title">LPA vs LCA<br/>핵심 차이</div>
</div>
<ul class="check-list">
<li class="check-item">
<i class="fas fa-ruler-horizontal check-mark"></i>
<p><strong>지표 유형</strong>: LPA는 연속형(Continuous), LCA는 범주형</p>
</li>
<li class="check-item">
<i class="fas fa-chart-area check-mark"></i>
<p><strong>모델링 대상</strong>: 평균/분산 패턴(LPA) vs 응답 확률(LCA)</p>
</li>
<li class="check-item">
<i class="fas fa-file-medical-alt check-mark"></i>
<p><strong>적용 예시</strong>: 심리 척도 프로파일(LPA) vs 증상 유무(LCA)</p>
</li>
</ul>
<div class="footer-note">
<i class="fas fa-lightbulb"></i>
<p>연구 데이터의 척도에 따라 선택</p>
</div>
</div>
</div>
</div>

</style>
</head>
<body>
<div class="slide-container">
<h1 class="section-title">데이터 준비와 전처리</h1>
<div class="grid-container">

<div class="card card-1">
<div class="card-header">
<div class="icon-wrapper">
<i class="fas fa-database"></i>
</div>
<h2 class="card-title">결측 처리<br/><span style="font-size: 0.8em; color: #64748b; font-weight: 500;">Missing Data</span></h2>
</div>
<div class="card-content">
<ul class="bullet-list">
<li><p>FIML: 모든 관측치 정보 활용 (편향 최소화)</p></li>
<li><p>MLR: 로버스트 표준오차로 비정규성 보정</p></li>
<li><p>MAR(Missing at Random) 가정 필수</p></li>
</ul>
<div class="tip-box">
<i class="fas fa-check-circle mt-1"></i>
<p>단순 제거(Listwise Deletion)보다 FIML 사용 권장 (Mplus 기본값)</p>
</div>
</div>
</div>

<div class="card card-2">
<div class="card-header">
<div class="icon-wrapper">
<i class="fas fa-ruler-combined"></i>
</div>
<h2 class="card-title">표준화<br/><span style="font-size: 0.8em; color: #64748b; font-weight: 500;">Standardization</span></h2>
</div>
<div class="card-content">
<ul class="bullet-list">
<li><p>Z-score 변환: 평균 0, 표준편차 1로 통일</p></li>
<li><p>서로 다른 척도(Scale) 간 비교 가능성 확보</p></li>
<li><p>프로파일 패턴의 직관적 해석 지원</p></li>
</ul>
<div class="tip-box">
<i class="fas fa-info-circle mt-1"></i>
<p>분석 전 표준화는 수렴성(Convergence) 향상에도 기여함</p>
</div>
</div>
</div>

<div class="card card-3">
<div class="card-header">
<div class="icon-wrapper">
<i class="fas fa-search-minus"></i>
</div>
<h2 class="card-title">이상치 탐지<br/><span style="font-size: 0.8em; color: #64748b; font-weight: 500;">Outlier Detection</span></h2>
</div>
<div class="card-content">
<ul class="bullet-list">
<li><p>마할라노비스 거리(Mahalanobis) 활용</p></li>
<li><p>다변량 이상치: χ² 분포 기준 상위 1% 검토</p></li>
<li><p>극단치는 별도 집단일 수 있으므로 신중 처리</p></li>
</ul>
<div class="tip-box">
<i class="fas fa-exclamation-triangle mt-1"></i>
<p>무조건 제거하기보다 민감도 분석(Sensitivity Analysis) 수행 권장</p>
</div>
</div>
</div>
</div>
</div>

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</head>
<body>
<div class="slide-container">
<h1 class="section-title">모형 설정: 분산-공분산 구조</h1>
<table class="comparison-table">
<thead>
<tr>
<th>구조 옵션</th>
<th>제약 조건</th>
<th>장점 (Pros)</th>
<th>단점 (Cons)</th>
</tr>
</thead>
<tbody>
<tr>
<td>
<div class="method-header">
<div class="icon-box"><i class="fas fa-grip-lines"></i></div>
                            공통 대각<br/>(Invariant Diag)
                        </div>
</td>
<td>
<span class="constraint-tag">Σ_k = diag(σ²)</span>
</td>
<td class="pros-cell">
<ul class="pros-list">
<li>가장 단순, 추정 안정적</li>
<li>소표본에 적합</li>
</ul>
</td>
<td class="cons-cell">
<ul class="cons-list">
<li>비현실적 가정(동일분산)</li>
<li>모형 오지정 위험 큼</li>
</ul>
</td>
</tr>
<tr>
<td>
<div class="method-header">
<div class="icon-box"><i class="fas fa-grip-vertical"></i></div>
                            군집별 대각<br/>(Varying Diag)
                        </div>
</td>
<td>
<span class="constraint-tag">Σ_k = diag(σ²_k)</span>
</td>
<td class="pros-cell">
<ul class="pros-list">
<li><strong>일반적 권장 옵션</strong></li>
<li>분산 차이 반영, 현실적</li>
</ul>
</td>
<td class="cons-cell">
<ul class="cons-list">
<li>모수 증가로 추정 부담</li>
<li>더 큰 표본 크기 요구</li>
</ul>
</td>
</tr>
<tr>
<td>
<div class="method-header">
<div class="icon-box"><i class="fas fa-square"></i></div>
                            공통 완전<br/>(Invariant Full)
                        </div>
</td>
<td>
<span class="constraint-tag">Σ_k = Σ</span>
</td>
<td class="pros-cell">
<ul class="pros-list">
<li>공분산(변수 간 관계) 반영</li>
<li>이론적 타당성 확보 가능</li>
</ul>
</td>
<td class="cons-cell">
<ul class="cons-list">
<li>계산 복잡도 증가</li>
<li>식별 문제 발생 가능성</li>
</ul>
</td>
</tr>
<tr>
<td>
<div class="method-header">
<div class="icon-box"><i class="fas fa-th-large"></i></div>
                            군집별 완전<br/>(Varying Full)
                        </div>
</td>
<td>
<span class="constraint-tag">Σ_k 자유 추정</span>
</td>
<td class="pros-cell">
<ul class="pros-list">
<li>최대 유연성, 최적 적합도</li>
<li>클래스별 고유 패턴 반영</li>
</ul>
</td>
<td class="cons-cell">
<ul class="cons-list">
<li>모수 과다(Over-parameterized)</li>
<li>수렴 실패 빈번, 해석 난해</li>
</ul>
</td>
</tr>
</tbody>
</table>
<div class="highlight-box">
<div class="highlight-icon">
<i class="fas fa-check-circle"></i>
</div>
<div class="highlight-content">
<h3>실무 권장사항</h3>
<p>대부분의 연구에서는 <strong>'군집별 대각(Class-varying diagonal)'</strong> 구조가 균형 잡힌 선택입니다. 분산의 이질성을 허용하면서도 공분산 제약으로 모형의 복잡도를 관리할 수 있어 안정적인 해를 제공합니다.</p>
</div>
</div>
</div>

</style>
</head>
<body>
<div class="slide-container">
<h1 class="section-title">프로파일 수 결정 전략</h1>
<div class="grid-container">

<div class="card card-1">
<div class="card-header">
<div class="icon-wrapper">
<i class="fas fa-chart-line"></i>
</div>
<h2 class="card-title">정보기준 지표<br/><span style="font-size: 0.7em; color: #64748b; font-weight: 500;">Information Criteria</span></h2>
</div>
<div class="card-content">
<ul class="bullet-list">
<li><p><strong>AIC & BIC</strong>: 낮을수록 모델 적합도 우수</p></li>
<li><p><strong>SABIC</strong>: 표본크기 보정, 중간 규모에 적합</p></li>
<li><p><strong>Entropy</strong>: 분류 정확도 0.80 이상 권장</p></li>
<li><p><strong>Tip</strong>: BIC 최저점과 엘보우(Elbow) 확인</p></li>
</ul>
</div>
</div>

<div class="card card-2">
<div class="card-header">
<div class="icon-wrapper">
<i class="fas fa-calculator"></i>
</div>
<h2 class="card-title">검정 통계량<br/><span style="font-size: 0.7em; color: #64748b; font-weight: 500;">Likelihood Ratio Tests</span></h2>
</div>
<div class="card-content">
<ul class="bullet-list">
<li><p><strong>LMR-LRT</strong>: K-1 vs K 모델 비교 (p < .05)</p></li>
<li><p><strong>BLRT</strong>: 부트스트랩 기반, 검정력 가장 우수</p></li>
<li><p><strong>비유의(ns)</strong>: p > .05 시 더 적은 K 선택</p></li>
<li><p><strong>주의</strong>: 단순 p값 의존보다 종합 판단 필요</p></li>
</ul>
</div>
</div>

<div class="card card-3">
<div class="card-header">
<div class="icon-wrapper">
<i class="fas fa-balance-scale"></i>
</div>
<h2 class="card-title">실무 고려사항<br/><span style="font-size: 0.7em; color: #64748b; font-weight: 500;">Practical Considerations</span></h2>
</div>
<div class="card-content">
<ul class="bullet-list">
<li><p><strong>이론적 해석</strong>: 프로파일 패턴의 타당성</p></li>
<li><p><strong>집단 크기</strong>: 최소 5% 이상 (너무 작으면 제외)</p></li>
<li><p><strong>활용성</strong>: 개입 및 정책 적용 가능 여부</p></li>
<li><p><strong>결론</strong>: 통계적 지표 + 해석 가능성 종합</p></li>
</ul>
</div>
</div>
</div>
</div>

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<body>
<div class="slide-container">

<header class="header">
<h1 class="main-title">LMR-LRT(Lo-Mendell-Rubin) 검정</h1>
<p class="sub-title">모형 간 적합도 비교를 위한 통계적 검정 절차</p>
</header>
<div class="content-wrapper">

<div class="hypothesis-container">
<div class="hypothesis-card h0">
<div class="hypo-label">
<i class="fas fa-minus-circle"></i> 귀무가설 (H₀)
                </div>
<p class="hypo-text">
                    K-1개 프로파일 모형이 데이터 설명에 충분함
                </p>
</div>
<div class="hypothesis-card h1">
<div class="hypo-label">
<i class="fas fa-plus-circle"></i> 대립가설 (H₁)
                </div>
<p class="hypo-text">
                    K개 프로파일 모형이 유의한 설명력을 추가함 (채택 목표)
                </p>
</div>
</div>

<div class="procedure-container">
<div class="proc-text">
<div class="proc-title">
<i class="fas fa-calculator mr-2"></i>적률기반 근사 (Moment-based Approximation)
                </div>
<p class="proc-desc">
                    K-1 모형의 파라미터 분포를 이용해 K 모형의 우도비 통계량 분포를 근사 추정.<br/>
<strong>p < .05</strong> 시 K-1 모형 기각 → <strong>K 모형이 더 우수함</strong>을 시사.
                </p>
</div>
<div class="equation-box">
<div class="equation-text">
                    Δ(-2 log L) ~ χ²(df)
                </div>
</div>
</div>

<div class="caution-grid">

<div class="info-card" style="border-top: 5px solid #f59e0b;">
<div class="card-header">
<div class="card-icon" style="background-color: #fffbeb; color: #d97706;">
<i class="fas fa-exclamation-triangle"></i>
</div>
<h2 class="card-title">해석 주의사항 (민감도)</h2>
</div>
<p class="card-content">
                    • <strong>표본 크기</strong>: 소표본(n<200)에서 정확도 저하<br/>
                    • <strong>초기값</strong>: 국소 해(Local Maxima)에 매우 민감<br/>
                    • 충분한 Random Starts (최소 500회) 설정 필수
                </p>
</div>

<div class="info-card" style="border-top: 5px solid #10b981;">
<div class="card-header">
<div class="card-icon" style="background-color: #ecfdf5; color: #059669;">
<i class="fas fa-check-circle"></i>
</div>
<h2 class="card-title">실무 적용 가이드</h2>
</div>
<p class="card-content">
                    • 단독 지표로 사용하지 말고 <strong>BIC, Entropy와 종합 판단</strong><br/>
                    • 유의하더라도 <span class="highlight">최소 집단 크기(<5%)</span>나 해석 가능성이 낮으면 기각<br/>
                    • 최근 연구에서는 <strong>BLRT</strong>와 병행 보고를 권장함
                </p>
</div>
</div>
</div>
</div>

/* Equation Section */
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    border: 2px solid #bfdbfe;
    border-radius: 16px;
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    margin-bottom: 2.5rem;
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    font-family: 'Times New Roman', serif;
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</style>
</head>
<body>
<div class="slide-container">

<header class="header">
<h1 class="main-title">BLRT (Bootstrap Likelihood Ratio Test)</h1>
<p class="sub-title">모형 비교를 위한 부트스트랩 우도비 검정</p>
</header>

<div class="equation-container">
<div class="equation-text">
            H₀: K-1 모형 충분 vs H₁: K 모형 필요
        </div>
</div>

<div class="cards-wrapper">

<div class="info-card">
<div class="card-header">
<div class="card-icon"><i class="fas fa-random"></i></div>
<h2 class="card-title">부트스트랩 아이디어</h2>
</div>
<ul class="card-list">
<li>K-1 모형 기반으로 부트스트랩 표본 생성</li>
<li>우도차 분포(-2LL diff)를 경험적으로 추정</li>
<li>표본 크기가 작거나 정규분포 위반 시 강건함</li>
</ul>
</div>

<div class="info-card" style="border-top-color: #10b981;">
<div class="card-header">
<div class="card-icon" style="color: #059669; background-color: #ecfdf5;"><i class="fas fa-check-circle"></i></div>
<h2 class="card-title">장점 및 비용</h2>
</div>
<ul class="card-list">
<li>LMR-LRT보다 검정력(Power)이 우수함</li>
<li>경계값 문제(Boundary Issue)에 덜 민감</li>
<li>계산 비용 큼 (예: 500회 이상 반복 추정 필요)</li>
</ul>
</div>
</div>
</div>

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</head>
<body>
<div class="slide-container">
<h1 class="section-title">적합도 지수 비교표 예시 (K=1~6)</h1>
<div class="content-wrapper">

<div class="table-section">
<table class="comparison-table">
<thead>
<tr>
<th style="width: 10%;">K</th>
<th style="width: 20%;">AIC</th>
<th style="width: 20%;">BIC</th>
<th style="width: 15%;">Entropy</th>
<th style="width: 15%;">BLRT<span class="sub-text">(p-value)</span></th>
<th style="width: 20%;">Min Class<span class="sub-text">(%)</span></th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>12456.3</td>
<td>12489.7</td>
<td>1.000</td>
<td>-</td>
<td>100.0</td>
</tr>
<tr>
<td>2</td>
<td>11892.1</td>
<td>11952.8</td>
<td>0.847</td>
<td>0.001</td>
<td>42.3</td>
</tr>
<tr>
<td>3</td>
<td>11745.6</td>
<td>11833.5</td>
<td>0.852</td>
<td>0.018</td>
<td>28.7</td>
</tr>

<tr class="highlight-best-row">
<td><span class="badge-k">4</span></td>
<td class="best-val">11682.4</td>
<td class="best-val">11797.5</td>
<td class="best-val">0.864</td>
<td class="best-val">0.009</td>
<td>19.4</td>
</tr>
<tr>
<td>5</td>
<td>11678.9</td>
<td>11821.2</td>
<td>0.858</td>
<td>0.142</td>
<td>12.8</td>
</tr>
<tr>
<td>6</td>
<td>11675.2</td>
<td>11844.7</td>
<td>0.841</td>
<td>0.254</td>
<td>8.3</td>
</tr>
</tbody>
</table>
</div>

<div class="summary-section">
<div class="info-card">
<div class="info-title">
<i class="fas fa-clipboard-check"></i>
                    의사결정 요약
                </div>
<div class="info-item">
<i class="fas fa-check-circle info-icon"></i>
<div class="info-text">
<p><strong>최적 모델 선택: K=4</strong></p>
<p class="text-sm text-gray-600 mt-1">BIC 최저, Entropy 양호(0.86), BLRT 유의(p<.01)</p>
</div>
</div>
<div class="info-item">
<i class="fas fa-exclamation-triangle info-icon text-yellow-500"></i>
<div class="info-text">
<p><strong>기각 사유 (K=5, 6)</strong></p>
<p class="text-sm text-gray-600 mt-1">LMR/BLRT 비유의(p>.05), 과적합(Overfitting) 가능성</p>
</div>
</div>
<div class="info-item">
<i class="fas fa-search info-icon"></i>
<div class="info-text">
<p><strong>참고 지표</strong></p>
<p class="text-sm text-gray-600 mt-1">SABIC, LMR-LRT 등 추가 지표는 부록 참조</p>
</div>
</div>
</div>
</div>
</div>
</div>

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</style>
</head>
<body>
<div class="slide-container">
<h1 class="section-title">모형 비교 의사결정 흐름도</h1>
<div class="main-content">

<div class="flow-column">
<div class="flow-step">
<div class="step-icon-wrapper step-1">
<i class="fas fa-play"></i>
</div>
<div class="step-text">
<div class="step-title">1. K=1부터 시작</div>
<div class="step-keywords">
<span class="keyword-tag">순차적 증가</span>
<span class="keyword-tag">기본 모형</span>
</div>
</div>
</div>
<div class="flow-step">
<div class="step-icon-wrapper step-2">
<i class="fas fa-chart-bar"></i>
</div>
<div class="step-text">
<div class="step-title">2. 적합도 수집</div>
<div class="step-keywords">
<span class="keyword-tag">정보기준(IC)</span>
<span class="keyword-tag">검정통계량</span>
</div>
</div>
</div>
<div class="flow-step">
<div class="step-icon-wrapper step-3">
<i class="fas fa-filter"></i>
</div>
<div class="step-text">
<div class="step-title">3. 비정상 해 제외</div>
<div class="step-keywords">
<span class="keyword-tag">수렴 실패</span>
<span class="keyword-tag">식별 불가</span>
</div>
</div>
</div>
<div class="flow-step">
<div class="step-icon-wrapper step-4">
<i class="fas fa-balance-scale"></i>
</div>
<div class="step-text">
<div class="step-title">4. 종합 판단</div>
<div class="step-keywords">
<span class="keyword-tag">지표 종합</span>
<span class="keyword-tag">해석 가능성</span>
</div>
</div>
</div>
<div class="flow-step">
<div class="step-icon-wrapper step-5">
<i class="fas fa-sync-alt"></i>
</div>
<div class="step-text">
<div class="step-title">5. 대안 검토</div>
<div class="step-keywords">
<span class="keyword-tag">구조 변경</span>
<span class="keyword-tag">변수 재설정</span>
</div>
</div>
</div>
</div>

<div class="detail-column">

<div class="info-card">
<div class="card-header">
<i class="fas fa-clipboard-check card-icon text-blue-600"></i>
<h3 class="card-title">주요 판단 기준 (Technical Criteria)</h3>
</div>
<div class="card-content">
<ul class="card-list">
<li><strong>정보기준:</strong> AIC, BIC, SABIC 값이 낮을수록 우수 (BIC 최우선)</li>
<li><strong>검정통계량:</strong> LMR-LRT, BLRT 유의확률(p < .05) 확인</li>
<li><strong>분류품질:</strong> Entropy 0.80 이상 권장 (절대 기준 아님)</li>
</ul>
</div>
</div>

<div class="info-card warning">
<div class="card-header">
<i class="fas fa-exclamation-triangle card-icon text-red-600"></i>
<h3 class="card-title">제외 및 주의 사항 (Constraints)</h3>
</div>
<div class="card-content">
<ul class="card-list">
<li><strong>비정상 해:</strong> 분산이 0이거나 극단적으로 작은 경우</li>
<li><strong>최소 집단:</strong> 전체 표본의 1~5% 미만인 소수 집단 존재 시 주의</li>
<li><strong>경계 문제:</strong> 국소 최적해(Local Maxima) 가능성 확인 (다중 시작값)</li>
</ul>
</div>
</div>

<div class="info-card success">
<div class="card-header">
<i class="fas fa-star card-icon text-green-600"></i>
<h3 class="card-title">최종 의사결정 (Final Decision)</h3>
</div>
<div class="card-content">
<p>단일 지표에 의존하지 않고 <strong>통계적 적합도</strong>와 <strong>이론적 해석 가능성</strong>을 종합하여 결정합니다. "가장 적합한 모형은 해석이 명확하고 실용적인 모형입니다."</p>
</div>
</div>
</div>
</div>
</div>

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        max-height: 520px; /* Constraint height */
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</head>
<body>
<div class="slide-container">
<h1 class="section-title">Mplus 실행 예시: 핵심 구문</h1>
<div class="content-wrapper">

<div class="summary-column">
<div class="info-card">
<div class="info-header">
<i class="fas fa-cogs text-blue-600"></i>
                    분석 설정 (Analysis)
                </div>
<p class="info-text">
<span class="highlight-text">MIXTURE</span> 모형을 지정하고, 국소해(Local Maxima) 방지를 위해 충분한 <span class="highlight-text">STARTS</span>(랜덤 시작값)를 설정합니다.
                </p>
</div>
<div class="info-card" style="border-left-color: #f59e0b;">
<div class="info-header" style="color: #b45309;">
<i class="fas fa-balance-scale text-yellow-600"></i>
                    모형 비교 검정
                </div>
<p class="info-text">
                    부트스트랩 기반의 <span class="highlight-text">LRTBOOTSTRAP</span> 옵션을 사용하여 BLRT 검정을 수행, 최적의 K를 결정합니다.
                </p>
</div>
<div class="info-card" style="border-left-color: #10b981;">
<div class="info-header" style="color: #047857;">
<i class="fas fa-chart-bar text-green-600"></i>
                    주요 출력 (Output)
                </div>
<p class="info-text">
<span class="highlight-text">TECH11</span>(LMR-LRT), <span class="highlight-text">TECH14</span>(BLRT), <span class="highlight-text">ENTROPY</span> 등 핵심 적합도 지수를 요청합니다.
                </p>
</div>
</div>

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<div class="dot dot-yellow"></div>
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<span class="ml-2 text-slate-400 text-sm font-mono">input.inp</span>
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<div class="code-content">
<span class="kwd">TITLE:</span> <span class="str">LPA with 4 profiles</span><span class="punc">;</span><br/>
<span class="kwd">DATA:</span> <span class="cmd">FILE</span> = data.dat<span class="punc">;</span><br/>
<span class="kwd">VARIABLE:</span> <br/>
<span class="cmd">NAMES</span> = y1-y6<span class="punc">;</span> <br/>
<span class="cmd">CLASSES</span> = <span class="str">c(4)</span><span class="punc">;</span> <span class="cmt">! 4개 프로파일 지정</span><br/>
<br/>
<span class="kwd">ANALYSIS:</span> <br/>
<span class="cmd">TYPE</span> = <span class="str">MIXTURE</span><span class="punc">;</span><br/>
<span class="cmd">STARTS</span> = <span class="num">500 100</span><span class="punc">;</span> <span class="cmt">! 초기값 설정</span><br/>
<span class="cmd">LRTBOOTSTRAP</span> = <span class="num">500</span><span class="punc">;</span> <span class="cmt">! BLRT 반복</span><br/>
<br/>
<span class="kwd">MODEL:</span> <span class="str">%OVERALL%</span> <span class="str">[y1-y6]</span><span class="punc">;</span><br/>
<br/>
<span class="kwd">OUTPUT:</span> <br/>
<span class="str">TECH11 TECH14 ENTROPY</span><span class="punc">;</span><br/>
<br/>
<span class="kwd">PLOT:</span> <br/>
<span class="cmd">TYPE</span> = <span class="str">PLOT3</span><span class="punc">;</span> <span class="cmd">SERIES</span> = y1-y6(*)<span class="punc">;</span>
</div>
</div>
</div>
</div>
<div class="footer-note">
<i class="fas fa-sticky-note text-yellow-500"></i>
<p>전체 코드와 세부 옵션 설정은 <strong>[부록: 전체 구문 노트]</strong>를 참고해주세요.</p>
</div>
</div>

</style>
</head>
<body>
<div class="slide-container">
<h1 class="section-title">R(tidyLPA) 실행 워크플로우</h1>

<div class="workflow-grid">

<div class="workflow-card">
<div class="card-header">
<div class="card-icon"><i class="fas fa-layer-group"></i></div>
<span>1. 프로파일 추정</span>
</div>
<div class="code-snippet">
<p><span class="syntax-purple">estimate_profiles</span>(1:6,<br/>
<span class="syntax-blue">variances</span> = <span class="syntax-green">"varying"</span>,<br/>
<span class="syntax-blue">covariances</span> = <span class="syntax-green">"zero"</span>)</p>
</div>
<div class="code-comment">
<i class="fas fa-info-circle text-blue-500"></i>
<span>1~6개 클래스 자동 비교, 분산 구조 설정</span>
</div>
</div>

<div class="workflow-card">
<div class="card-header">
<div class="card-icon"><i class="fas fa-clipboard-check"></i></div>
<span>2. 적합도 확인</span>
</div>
<div class="code-snippet">
<p><span class="syntax-purple">get_fit</span>(res) %>%<br/>
<span class="syntax-purple">select</span>(AIC, BIC, Entropy)</p>
</div>
<div class="code-comment">
<i class="fas fa-check-circle text-green-500"></i>
<span>주요 적합도 지수 추출 및 비교</span>
</div>
</div>

<div class="workflow-card">
<div class="card-header">
<div class="card-icon"><i class="fas fa-chart-line"></i></div>
<span>3. 결과 시각화</span>
</div>
<div class="code-snippet">
<p><span class="syntax-purple">plot_profiles</span>(res,<br/>
<span class="syntax-blue">ci</span> = <span class="syntax-orange">TRUE</span>,<br/>
<span class="syntax-blue">add_line</span> = <span class="syntax-orange">TRUE</span>)</p>
</div>
<div class="code-comment">
<i class="fas fa-eye text-purple-500"></i>
<span>95% 신뢰구간 포함 프로파일 플롯 생성</span>
</div>
</div>
</div>

<div class="full-code-section">
<div class="pipeline-desc">
<h3><i class="fas fa-code-branch text-blue-600"></i> 통합 파이프라인</h3>
<p>데이터 로드부터 추정까지 한 번에 연결하는 tidyverse 스타일 구문입니다.</p>
<div class="mt-4 flex flex-wrap gap-2">
<span class="badge badge-primary">dplyr</span>
<span class="badge badge-success">magrittr</span>
<span class="badge badge-warning">ggplot2</span>
</div>
</div>
<div class="pipeline-preview">
<p>df %>%</p>
<p>  <span class="syntax-purple">select</span>(y1, y2, y3, y4) %>%</p>
<p>  <span class="syntax-purple">estimate_profiles</span>(1:4) %>%</p>
<p>  <span class="syntax-purple">plot_profiles</span>()</p>
</div>
</div>
</div>

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</head>
<body>
<div class="slide-container">

<div class="header">
<h1 class="main-title">Stata 실행 예시: 단계별 분석 코드</h1>
<p class="subtitle">일반화 구조방정식 모형(GSEM)을 활용한 잠재프로파일분석 절차</p>
</div>

<div class="steps-grid">

<div class="step-card">
<div class="card-header">
<div class="step-number">1</div>
<div class="card-title">모형 추정 (Estimation)</div>
</div>
<div class="code-wrapper">
<div class="code-block">
<span class="code-keyword">gsem</span> (y1-y6 <- _cons),<br/>
                      <span class="code-opt">family</span>(gaussian)<br/>
                      <span class="code-opt">lclass</span>(C 4)
                    <span class="code-comment">// 4개 잠재클래스로 모형 설정</span>
</div>
</div>
<div class="card-footer">
<div class="key-point">
<i class="fas fa-check-circle mt-1"></i>
<span>연속형 변수는 gaussian 분포 가정, lclass로 K 수 지정</span>
</div>
</div>
</div>

<div class="step-card">
<div class="card-header">
<div class="step-number">2</div>
<div class="card-title">사후확률 (Posterior)</div>
</div>
<div class="code-wrapper">
<div class="code-block">
<span class="code-keyword">estat</span> lcprob<br/>
<span class="code-keyword">predict</span> pr*, <span class="code-opt">classpr</span>
<span class="code-comment">// 클래스 비율 확인 및<br/>// 개별 사후확률 변수 생성</span>
</div>
</div>
<div class="card-footer">
<div class="key-point">
<i class="fas fa-chart-pie mt-1"></i>
<span>lcprob로 집단 비율 확인, predict로 분류 확률 저장</span>
</div>
</div>
</div>

<div class="step-card">
<div class="card-header">
<div class="step-number">3</div>
<div class="card-title">평균 비교 (Compare)</div>
</div>
<div class="code-wrapper">
<div class="code-block">
<span class="code-keyword">margins</span>, <span class="code-opt">over</span>(C)<br/>
<span class="code-keyword">marginsplot</span>
<span class="code-comment">// 클래스별 평균 프로파일<br/>// 계산 및 그래프 출력</span>
</div>
</div>
<div class="card-footer">
<div class="key-point">
<i class="fas fa-balance-scale mt-1"></i>
<span>각 잠재계층별 결과변수 평균 차이 검증 및 시각화</span>
</div>
</div>
</div>
</div>

<div class="footer-note">
<i class="fas fa-lightbulb note-icon"></i>
<div class="note-text">
<strong>Note:</strong> 복잡한 공분산 구조 설정, 시작값(startvalues), 수렴 기준 등 상세 옵션은 지면 관계상 생략되었습니다. 실제 분석 시에는 <code>help gsem</code>을 참고하여 옵션을 추가하십시오.
        </div>
</div>
</div>

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<body>
<div class="slide-container">
<h1 class="section-title">기초분석 실습 예제</h1>
<div class="grid-container">

<div class="card">
<div class="card-header">
<div class="icon-box icon-data"><i class="fas fa-database"></i></div>
<div class="card-title">1. 데이터 특성</div>
</div>
<div class="card-content check-list">
<p><strong>표본:</strong> n=1,000명, 6개 연속형 지표</p>
<p><strong>전처리:</strong> 경도 왜도 존재, FIML 결측 처리(<3%)</p>
<p><strong>설정:</strong> 대각 공분산, 500 Random Starts</p>
</div>
</div>

<div class="card">
<div class="card-header">
<div class="icon-box icon-comp"><i class="fas fa-balance-scale"></i></div>
<div class="card-title">2. 모형 비교 (K=1~6)</div>
</div>
<div class="card-content check-list">
<p><strong>정보기준:</strong> K 증가 시 BIC/SABIC 지속 감소</p>
<p><strong>검정:</strong> BLRT(p<.001), LMR(p<.01) 모두 유의</p>
<p><strong>결정:</strong> K=5부터 해석 난해 → <span class="highlight-stat">K=4 채택</span></p>
</div>
</div>

<div class="card">
<div class="card-header">
<div class="icon-box icon-final"><i class="fas fa-check-circle"></i></div>
<div class="card-title">3. 최종 모형 (K=4)</div>
</div>
<div class="card-content">
<div class="result-row">
<div class="result-item">
<span class="result-val text-blue-600">0.82</span>
<span class="result-label">Entropy</span>
</div>
<div class="result-item">
<span class="result-val text-green-600">18.7%</span>
<span class="result-label">최소집단</span>
</div>
<div class="result-item">
<span class="result-val text-purple-600">Good</span>
<span class="result-label">해석력</span>
</div>
</div>
<p style="text-align: center; margin-top: 10px; font-size: 1rem; color: #64748b;">
                *분류 정확도와 집단 크기 모두 양호
            </p>
</div>
</div>

<div class="card">
<div class="card-header">
<div class="icon-box icon-int"><i class="fas fa-chart-line"></i></div>
<div class="card-title">4. 해석 및 시각화</div>
</div>
<div class="card-content">
<p class="mb-2"><strong>유형 명명:</strong> 고/중/저/불균형 4개 패턴</p>
<p class="mb-2"><strong>효과크기:</strong> Cohen's d = 0.85~1.23 (Large)</p>
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            scales: {
                x: { display: false },
                y: { display: false, min: -1.5, max: 1.5 }
            },
            elements: { point: { radius: 0 } }
        }
    });
</script>

/* Step 1 Styles */
    .step-1 .step-header {
        background-color: #3b82f6;
    }
    .step-1 .keyword-item {
        border-color: #3b82f6;
    }

/* Step 2 Styles */
    .step-2 .step-header {
        background-color: #10b981;
    }
    .step-2 .keyword-item {
        border-color: #10b981;
    }

/* Step 3 Styles */
    .step-3 .step-header {
        background-color: #f59e0b;
    }
    .step-3 .keyword-item {
        border-color: #f59e0b;
    }

.arrow-icon {
        font-size: 2rem;
        color: #94a3b8;
        z-index: 5;
    }
</style>
</head>
<body>
<div class="slide-container">
<h1 class="section-title">공변인 포함: 3-Step Approach</h1>
<div class="flow-container">
<div class="flow-line"></div>

<div class="step-card step-1">
<div class="step-header">
<i class="fas fa-layer-group step-icon"></i>
<p class="step-title">Step 1<br/>측정모형</p>
</div>
<div class="step-body">
<p class="keyword-item">순수 측정모형 추정</p>
<p class="keyword-item">공변인(x) 제외</p>
<p class="keyword-item">최적 프로파일 수 결정</p>
</div>
</div>

<i class="fas fa-chevron-right arrow-icon"></i>

<div class="step-card step-2">
<div class="step-header">
<i class="fas fa-filter step-icon"></i>
<p class="step-title">Step 2<br/>오분류 계산</p>
</div>
<div class="step-body">
<p class="keyword-item">최대사후확률(MAP) 분류</p>
<p class="keyword-item">오분류행렬(E) 산출</p>
<p class="keyword-item">Entropy 확인</p>
</div>
</div>

<i class="fas fa-chevron-right arrow-icon"></i>

<div class="step-card step-3">
<div class="step-header">
<i class="fas fa-chart-line step-icon"></i>
<p class="step-title">Step 3<br/>보정 회귀</p>
</div>
<div class="step-body">
<p class="keyword-item">분류오차 보정</p>
<p class="keyword-item">공변인 효과 추정</p>
<p class="keyword-item">R3STEP / Auxiliary</p>
</div>
</div>
</div>
</div>

.card-title {
        font-size: 1.4rem;
        font-weight: 700;
        color: #1e293b;
    }
    .card-content {
        font-size: 1.15rem; /* ~18pt */
        color: #475569;
        line-height: 1.5;
    }
    .highlight-stat {
        font-weight: 700;
        color: #1e40af;
        background-color: #dbeafe;
        padding: 2px 8px;
        border-radius: 6px;
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    .result-row {
        display: flex;
        justify-content: space-between;
        margin-top: 8px;
        background: white;
        padding: 12px 16px;
        border-radius: 8px;
        border: 1px solid #e2e8f0;
    }
    .result-item {
        display: flex;
        flex-direction: column;
        align-items: center;
    }
    .result-label { font-size: 0.9rem; color: #64748b; margin-top: 4px; }
    .result-val { font-size: 1.4rem; font-weight: 800; color: #0f172a; }
</style>
</head>
<body>
<div class="slide-container">
<h1 class="section-title">고급분석 종합 예제 (4-Profile Model)</h1>
<div class="grid-container">

<div class="card">
<div class="card-header">
<div class="icon-box icon-scenario"><i class="fas fa-project-diagram"></i></div>
<div class="card-title">1. 분석 시나리오</div>
</div>
<div class="card-content">
<p class="mb-2"><strong>모형:</strong> 4개 프로파일 + 공변인(3-step) + 원위결과(BCH) + 다집단(성별)</p>
<p><strong>데이터:</strong> 표본 <span class="highlight-stat">N=1,200</span> (남 52.3%, 여 47.7%), 지표 6개, 공변인 3개</p>
</div>
</div>

<div class="card">
<div class="card-header">
<div class="icon-box icon-result"><i class="fas fa-clipboard-check"></i></div>
<div class="card-title">2. 핵심 결과 (Results)</div>
</div>
<div class="card-content">
<div class="result-row">
<div class="result-item">
<span class="result-val text-blue-600">0.87</span>
<span class="result-label">Entropy</span>
</div>
<div class="result-item">
<span class="result-val text-green-600">9,156</span>
<span class="result-label">BIC</span>
</div>
<div class="result-item">
<span class="result-val text-purple-600">p<.001</span>
<span class="result-label">BCH 유의성</span>
</div>
</div>
<p class="mt-3 text-sm text-gray-500 text-center">※ 4개 집단 간 성취도 차이가 남녀 모두에서 유의함</p>
</div>
</div>

<div class="card">
<div class="card-header">
<div class="icon-box icon-compare"><i class="fas fa-users"></i></div>
<div class="card-title">3. 집단 비교 (Gender)</div>
</div>
<div class="card-content">
<p class="mb-2"><strong>비율 차이:</strong> 성별에 따른 프로파일 분포 유의차 (<span class="highlight-stat">χ²=15.67***</span>)</p>
<p><strong>특징:</strong> 고성과군 비율 여(31.2%) > 남(28.5%), 중간군 남(35.2%) > 여(33.8%)</p>
</div>
</div>

<div class="card">
<div class="card-header">
<div class="icon-box icon-valid"><i class="fas fa-check-double"></i></div>
<div class="card-title">4. 해석 타당성</div>
</div>
<div class="card-content">
<p class="mb-2"><strong>분류 정확도:</strong> 3-step 보정으로 분류오차 최소화 확인</p>
<p><strong>시사점:</strong> 성별에 따른 맞춤형 개입 필요성 지지, 고성과군 타겟팅 전략 수립</p>
</div>
</div>
</div>
</div>

.card:nth-child(4) { border-left-color: #f59e0b; } /* Amber */
    .card:nth-child(4) .icon-box { background: #fffbeb; color: #d97706; }
    .card:nth-child(4) .check-icon { color: #d97706; }

</style>
</head>
<body>
<div class="slide-container">
<header class="header">
<h1 class="section-title">전체 요약 및 핵심 포인트</h1>
</header>
<div class="grid-container">

<div class="card">
<div class="card-header">
<div class="icon-box"><i class="fas fa-brain"></i></div>
<h2 class="card-title">이론적 기초</h2>
</div>
<ul class="check-list">
<li class="check-item">
<i class="fas fa-check-circle check-icon"></i>
<span class="check-text">정규 혼합 모형(Gaussian Mixture) 기반의 사람중심 접근</span>
</li>
<li class="check-item">
<i class="fas fa-check-circle check-icon"></i>
<span class="check-text">EM 알고리즘(E-step & M-step)을 통한 반복적 모수 추정</span>
</li>
<li class="check-item">
<i class="fas fa-check-circle check-icon"></i>
<span class="check-text">모형 식별성 확보를 위한 공분산 제약과 초기값 설정 필수</span>
</li>
<li class="check-item">
<i class="fas fa-check-circle check-icon"></i>
<span class="check-text">LCA(범주형 지표)와 달리 연속형 지표의 평균·분산 패턴 분석</span>
</li>
</ul>
</div>

<div class="card">
<div class="card-header">
<div class="icon-box"><i class="fas fa-chart-bar"></i></div>
<h2 class="card-title">기초 분석</h2>
</div>
<ul class="check-list">
<li class="check-item">
<i class="fas fa-check-circle check-icon"></i>
<span class="check-text">K 결정: AIC/BIC, LMR-LRT, Entropy, 해석가능성 종합 고려</span>
</li>
<li class="check-item">
<i class="fas fa-check-circle check-icon"></i>
<span class="check-text">정보기준(BIC 등)은 낮을수록 우수하나, 절대적 기준은 아님</span>
</li>
<li class="check-item">
<i class="fas fa-check-circle check-icon"></i>
<span class="check-text">해석: 표준화 평균(Z-score) 프로파일 플롯으로 패턴 명명</span>
</li>
<li class="check-item">
<i class="fas fa-check-circle check-icon"></i>
<span class="check-text">시각화: 95% 신뢰구간(CI)과 집단 크기를 함께 제시하여 타당성 확보</span>
</li>
</ul>
</div>

<div class="card">
<div class="card-header">
<div class="icon-box"><i class="fas fa-layer-group"></i></div>
<h2 class="card-title">고급 분석</h2>
</div>
<ul class="check-list">
<li class="check-item">
<i class="fas fa-check-circle check-icon"></i>
<span class="check-text">3-Step 접근: 측정 모형을 고정한 채 공변인 및 결과변수 분석</span>
</li>
<li class="check-item">
<i class="fas fa-check-circle check-icon"></i>
<span class="check-text">BCH/DCAT: 분류 오차를 보정한 원위결과(Distal outcome) 검증</span>
</li>
<li class="check-item">
<i class="fas fa-check-circle check-icon"></i>
<span class="check-text">다집단 분석: 성별/국가 등 집단 간 프로파일 구조 불변성 확인</span>
</li>
<li class="check-item">
<i class="fas fa-check-circle check-icon"></i>
<span class="check-text">종단 LTA: 시점 간 잠재 계층의 변화(전이확률) 추적</span>
</li>
</ul>
</div>

<div class="card">
<div class="card-header">
<div class="icon-box"><i class="fas fa-clipboard-check"></i></div>
<h2 class="card-title">실무 권장사항</h2>
</div>
<ul class="check-list">
<li class="check-item">
<i class="fas fa-check-circle check-icon"></i>
<span class="check-text">민감도 분석: 초기값(Starts) 증가, 공분산 구조 변경 테스트</span>
</li>
<li class="check-item">
<i class="fas fa-check-circle check-icon"></i>
<span class="check-text">분류 불확실성 보고: Entropy, 평균 사후확률(AVEPP) 명시</span>
</li>
<li class="check-item">
<i class="fas fa-check-circle check-icon"></i>
<span class="check-text">재현성 확보: 분석 코드, Seed 번호, 소프트웨어 버전 공개</span>
</li>
<li class="check-item">
<i class="fas fa-check-circle check-icon"></i>
<span class="check-text">가정 점검: 데이터의 정규성, 독립성, 표본 크기 사전 검토</span>
</li>
</ul>
</div>
</div>
</div>